101 APPROACH TO MEASURE. 112 FAILURE MODE AND EFFECT ANALYSIS FMEA: A General Overview Any FMEA conducted properly and appropriately.

101 APPROACH TO MEASURE

112 FAILURE MODE AND EFFECT ANALYSIS FMEA: A General Overview Any FMEA conducted properly and appropriately will provide the practitioner with useful information that can reduce the risk (work) load in the system, design, process, and service. A good FMEA  Identifies known and potential failure modes  Identifies the causes and effects of each failure mode  Prioritizes the identified failure modes according to the risk priority number (RPN)-the product of frequency of occurrence, severity, and detection  Provides for problem follow-up and corrective action

113 Specifically, an FMEA program should start  When new systems, designs, products, processes, or services are designed  When existing systems, designs, products, processes, or services are about to change regardless of reason  When new applications are found for the existing conditions of the systems, designs, products, processes, or service  When improvements are considered for the existing systems, designs, products, processes, or services WHEN IS THE FMEA STARTED?

114 When is the FMEA Complete? Is there a time when the FMEA may be considered finished or complete? Yes. Only when the system, design, product, process, or service is considered complete and/or discontinued. Who conducts the FMEA? The FMEA is a team function and cannot be done on an individual basis. FAILURE MODE AND EFFECT ANALYSIS

115 FMEA There are two primary flavors of FMEA: Design FMEAs are used during process or product design and development. The primary objective is to uncover problems that will result in potential failures within the new product or process. Process FMEAs are used to uncover problems related to an existing process. These tend to concentrate on factors related to manpower, systems, methods, measurements and the environment. Although the objectives of design and process FMEAs may appear different, both follow the same basic steps and the approaches are often combined.

117 FMEA drives systematic thinking about a product or process by asking and attempting to answer three basic questions:  What could go wrong (failure) with a process or system?  How bad can it get (risks), if something goes wrong (fails)?  What can be done (corrective actions) to prevent things from going wrong (failures)? FMEA attempts to identify and prioritize potential process or system failures. The failures are rated on three criteria:  The impact of a failure - severity of the effects.  The frequency of the causes of the failure - occurrence.  How easy is it to detect the causes of a failure - delectability. FMEA

118 Notice that only the causes and effects are rated - failure modes themselves are not directly rated in the FMEA analysis. FMEA is cause-and-effect analysis by another name – avoid being hung up on the failure mode. The failure mode simply provides a convenient model, which allows us to link together multiple causes with multiple effects. It is easy to confuse failures, causes, and effects, especially since causes and effects at one level can be failures at a lower level. Effects are generally observable, and are the result of some cause. Effects can be thought of as outputs. FMEA

119 Effects are usually events that occur downstream that affect internal or external customers. Root causes are the most basic causes within the process owner’s control. Causes, and root causes, are in the background; they are an input resulting in an effect. Failures are what transform a cause to an effect; they are often unobservable. One can think of failures, effects, and causes in terms of the following schematic: FMEA

120 The failures identified by the team in an FMEA project are prioritized by what are called Risk Priority Numbers, or RPN values. The RPN values are calculated by multiplying together the Severity, Occurrence, and Detection (SOD) values associated with each cause-and-effect item identified for each failure mode. Note: The failure mode itself is not rated and only plays a conceptual role in linking causes with their effects on the product, process, or system. For a given cause-and-effect pair the team assigns SOD values to the effects and causes. Then an RPN is calculated for that pair: RPN = Severity x Occurrence x Detection. Risk Priority Numbers

121 Once the RPN values are assigned to each of the cause-and- effect pairs identified by the team, the pairings are prioritized. The higher the RPN value, the higher the priority to work on that specific cause-and-effect pair. The measurement scale for the SOD values is typically a 5 or 10 point Likert scale (an ordinal rating scale). The exact criteria associated with each level of each rating scale is dependent upon either a company designed rating criteria or a specified rating criteria from an industry specific guideline. We recommend the use of a 10 point Likert scale for each of the three rating criteria: Severity, Occurrence, and Detection. FMEA

122 Once the RPN values are assigned to each of the cause-and- effect pairs identified by the team, the pairings are prioritized. The higher the RPN value, the higher the priority to work on that specific cause-and-effect pair. The measurement scale for the SOD values is typically a 5 or 10 point Likert scale (an ordinal rating scale). The exact criteria associated with each level of each rating scale is dependent upon either a company designed rating criteria or a specified rating criteria from an industry specific guideline. We recommend the use of a 10 point Likert scale for each of the three rating criteria: Severity, Occurrence, and Detection. FMEA

123 Occurrence, or frequency of occurrence, is a rating that describes the chances that a given cause of failure will occur over the life of product, design, or system. Actual data from the process or design is the best method for determining the rate of occurrence. If actual data is not available, the team must estimate rates for the failure mode. Examples:  The number of data entry errors per 1000 entries, or  The number of errors per 1000 calculations. An occurrence value must be determined for every potential cause of the failure listed in the FMEA form. FMEA

124 The higher the likelihood of occurrence, the higher the occurrence value. Once again, occurrence guidelines can be developed and should reflect the situation of interest. FMEA

125 Occurrence guidelines for the system availability FMEA: FMEA

126 The detection rating describes the likelihood that we will detect a cause for a specific failure mode. An assessment of process controls gives an indication of the likelihood of detection. Process controls are methods for ensuring that potential causes are detected before failures take place. For example, process controls can include: Required fields or limited fields in electronic forms, Process and/or system audits, and “Are you sure” dialog boxes in computer programs. If there are no current controls, the detection rating will be high. If there are controls, the detection rating will be low. FMEA

127 The higher a detection rating, the lower the likelihood we will detect a specific cause if it were to occur. Detection guidelines developed for the system availability FMEA: FMEA

129 Conducting an FMEA: Basic Steps 1.Define the scope of the FMEA. 2.Develop a detailed understanding of the current process. 3.Brainstorm potential failure modes. 4.List potential effects of failures and causes of failures. 5.Assign severity, occurrence and detection ratings. 6.Calculate the risk priority number (RPN) for each cause. 7.Rank or prioritize causes. Use the information for data collection effort. 8.In analysis/implementation phases take action on high risk failure modes. 9.Recalculate RPN numbers. FMEA

130 WORKSHEET # 5 : FMEA Draw your process Map and do the FMEA for the whole process or one of the sub-process. Share it with the class Time: 60 Minutes

131 What is Data ? Data is a numerical expression of an activity. Conclusions based on facts and data are necessary for any improvement. -K. Ishikawa If you are not able to express a phenomenon in numbers, you do not know about it adequately. -Lord Kelvin DATA GATHERING

132 TYPES OF DATA CONTINUOUSDISCRETE Measurable e.g. :Length, Temperature Nominal e.g. : Number of defects Ordinal e.g. :Ranking in Customer feedback Data if properly collected Least influenced by individual biases Could be subject to critical analysis Generally beyond language barriers and therefore universal in expression.

133 WHAT IS THE DIFFERENCE BETWEEN A SHAFT DIAMETER THE NUMBER OF SHAFTS REJECTED FOR OVERSIZE DIAMETER The diameter of a shaft can take any value ever after the decimal point e.g.. 19.055, 19.0516 etc.. Data related to this type of parameters are called Continuous data. The number of shaft rejected has necessarily to be a whole number. e.g.. 0, 2, 7, 10 numbers rejected etc.. Data related to this type of parameters are called Discrete data.

134 HOW DO YOU DISTINGUISH BETWEEN CONTINUOUS AND DISCRETE CONTINUOUSDISCRETE They are real numbers Normally, they are measured values They can not take a single value. There is an area associated with it They are continuous Requires less sample size They are whole numbers Normally, they are counted values They can take only ‘Zero’ or non-fractional positive values They are in steps of ‘1’ Requires more sample size to have the more precision

135 WHICH OF THE BELOW ARE CONTINUOUS AND DISCRETE DATA? Width of sheet No. of liners thinned Tubes rejected by Go- No go Gauge Diameter of Piston Height of a Man Sheet thickness Out of 100 sheets the numbers that meet the thickness 4  0.9 Time taken to process a purchase order No. of bugs in a program

136 OBJECTIVES OF DATA COLLECTION To know and quantify the status To monitor the process To decide acceptance or rejection To analyse and decide the course of action HOW TO COLLECT DATA ? Define the purpose Decide the type of analysis Define the period of data collection Is the the required data already available ?

137 SOURCES OF FALSE DATA Fear : Because of unfavorable results Frustration : Because of non-use or misuse of data “Data must be collected, not cooked”. CAUSES FOR MISTAKEN DATA Wrong choice of instrument Lack of calibration Improper sampling Lack of standards Inadequate test facilities Lack of training

138 STRATIFICATION The method of grouping data by common points or characteristics to better understand similarities and characteristics of data is called stratification. Such classification helps in obtaining vital information by distinguishing and comparing data in different class or strata. It also identifies the key strata to concentrate on. The stratification may be based on machines, operators, shifts or any other source of variation.

139 STRATIFICATION The purpose of stratification is to ascertain the difference between different categories and to analyze the reasons behind abnormal distribution. Stratification of data is an effective method for isolating the cause of a problem. You can also stratify the data you collect by different statistical tools which we will learn later.

140 STRATIFICATION-AREA OF APPLICATION Raw Material Quantity supplied, Delivery time, Rejection % - supplier wise and batch wise. Production Rejection percentage with respect to machine, line, shift, season, sources of raw material, tool, jig and so on. Engineering and design Draftsman wise drawing errors, Type of drawing wise.

141 DATA SHEET A check sheet is a convenient and compact format for collection of data. PURPOSE OF CHECK SHEET  Simplification of data gathering  Provide preliminary summarization  Provide a basis for statistical analysis

142 DATA SHEET-AREA OF APPLICATION Raw Material No. of defects, Location of defect, Measurements on quality characteristics Production Measurements on process parameters, No. of defects in products, Location of defect

143 X = Dirt D = Dent S = Scratch B = Bubble Hood Paint Defects Name: ____ Date: ____ Model: ____ DD D S XXX B X No. inspected: _____ LOCATION WISE DATA SHEET

Data Collection Plan Features

Data Collection Plan Features, cont.

147 MEASURES OF CENTRAL TENDENCY ANDDISPERSION

148 The rope is tied at the center of gravity. This Suspended Pipe Is Horizontal The Same Pipe Has Now Tilted WHY ? 12 Center of gravity is the point where the entire mass of the body is supposed to be concentrated. central tendency Thus center of gravity is a measure of central tendency of a body. The rope is tied away from the center of gravity.

149 WHAT IS THE MEASURE OF CENTRAL TENDENCY OF A SET OF NUMBERS? There are three ways in which Central Tendency of Numbers can be measured. These are the 3 M’s  MEAN  MEDIAN  MODE

150 MEANMEAN Mean or Average is normally signified by Mathematically it can be represented as :

151 MEAN CAN ALSO BE FOUND AS FOLLOWS

152 MEDIANMEDIAN This is the value which has equal number of values above it and below it, when arranged in ascending order. Mathematically :

153 We have thus calculated, The Mean, Median and Mode for a given data set The Mean, Median and Mode are equal for a symmetric unimodal distribution. They are not equal if distribution is not symmetric. We have thus calculated, The Mean, Median and Mode for a given data set The Mean, Median and Mode are equal for a symmetric unimodal distribution. They are not equal if distribution is not symmetric. This is the value which occurs with the highest frequency. MODE

154 MEASURES OF DISPERSION  The extent of the spread of the values from the mean value is called Dispersion.  The measures of Dispersions are –Range (R) –Standard Deviation (s) –Variance (s 2 ) –Co-efficient of Variation (CV)  Standard deviation is the most commonly used measure of dispersion.

155 STANDARD DEVIATION OF SAMPLE : OF POPULATION: Degrees of freedom

156  If you are told to decide 5 nos such that the average of these nos is 10 you will realize that you are free to select only 4 of the 5 nos and the 5 th will necessarily be fixed.  e.g. 10, 14, 3 & 17 are the four nos that you have selected. The 5 th no. necessarily will have to be 6.  The no. of values you are free to select is known as the degrees of freedom (d.f.).  In this case the degree of freedom is 4.  In general d.f. = n-r ; where n is the no. of readings & r is the no.of statistical parameters to be found. DEGREES OF FREEDOM

157 Range, R = Largest Observation - Smallest Observation = X max -X min Range, R = Largest Observation - Smallest Observation = X max -X min Variance (s 2 ) is the Square of Standard Deviation.

158 DESCRIPTIVE STATISTICS FROM MINITAB  Make Sure the data window is active.  Choose STAT>BASIC STATISTICS>DISPLAY DESCRIPTIVE STATISTICS  In Variables, enter the column containing the data, click OK.  If you require some particular statistic(s) to be stored, choose STAT > BASIC STATISTICS > STORE DESCRIPTIVE STATISTICS > STATISTICS

159 The entire set of items is called the Population. The small number of items taken from the population to make a judgment of the population is called a Sample. The numbers of samples taken to make this judgment is called Sample size. SAMPLE OF SIZE THREE POPULATION POPULATION AND SAMPLE

160 POPULATION, SAMPLE AND DATA

161 WHAT IS SAMPLING AND WHY DO IT? –Sampling is Collecting a portion of all the data. Using that portion to draw conclusions (make inferences). –Why sample? Because looking at all the data may be Too expensive. Too time-consuming. Destructive (e.g., taste tests). Sound conclusions can often be drawn from a relatively small amount of data.

162 INTRODUCTION TO SAMPLE SIZE The first question people often ask is “How many samples do I need?” The answer is determined by four factors: 1.Type of data Discrete vs. continuous 2.What you want to do Describe a characteristic for a whole group (mean or proportion) –Within a certain precision (± ___ units) Compare group characteristics (find differences between group means or group proportions) –At what power: the probability you want of detecting a certain difference 3.What you guess the standard deviation (or proportion) will be 4.How confident you want to be (usually 95%)

163 SAMPLE SIZE FORMULAS DEPEND ON PURPOSE Purpose of SampleFormula*/ Minitab Commands Estimate average (e.g., determine baseline cycle time) (Where d = precision: ± __ units) Estimate proportion (e.g., determine baseline % defective) (Where d = precision: ± __ units)

164 PRECISION (d) –Precision is how narrow you want the range to be for an estimate of a characteristic. Estimate cycle time within 2 days. Estimate percent defective within 3%. –Use the symbol ‘ d’ to represent precision. Traditional statistics refers to it as “delta,” hence the ‘ d’. –Precision is equal to half the width of a confidence interval. A 95% CI = (48, 52) for cycle time (in days) means we are 95% confident the interval from 48 days to 52 days contains the average cycle time. Width of the CI = 4 days. Precision = d = 2 days (= estimate is within ± 2 days).

165 PRECISION (d) –You decide what precision you want. –Precision is inversely proportional to the square root of sample size.

166 PRECISION AND SAMPLE SIZE –To improve precision, you need to increase sample size (which incurs more cost). –There is no clear-cut answer about how much precision you need; the answer depends on the business impact of using the estimate. –Each situation is unique; don’t pattern your decisions after someone else’s decision.

167 SAMPLE SIZE FOR ESTIMATING AN AVERAGE 95% confidence* means a factor of 2 Estimate of the standard deviation Precision you desire

168 Objective: Practice using the sample size formula for averages. Time: 3 mins. Instructions: Use the sample size formula for averages to answer the following questions. 1.Suppose you want to estimate the average length of incoming phone calls within 1 minute. What sample size do you need? (Historical data show a typical standard deviation = 3 minutes.) 2. How many calls do you need to sample to get an estimate within 1/8 minute? PRACTICE: SAMPLE SIZE FOR ESTIMATING AVERAGES

169 PRACTICE: ANSWERS Question 1. Question 2.

170 HOW TO ESTIMATE THE STANDARD DEVIATION The Catch-22: –To estimate sample size, you need to know the standard deviation. You need to have some idea of the amount of variation in the data because as the variability increases, the necessary sample size increases. –But if you haven’t sampled anything yet, how can you know the standard deviation???

171 Options for estimating standard deviation –Find existing data and calculate s. Use a control chart (for individuals) from a similar process. –Collect a small sample and calculate s. –Take an educated guess based on your process knowledge and memory of similar data (most people are not too good at this). HOW TO ESTIMATE THE STANDARD DEVIATION

172 SAMPLE SIZE FOR ESTIMATING A PROPORTION 95% confidence means a factor of 2 Guess * for p (sample size changes dramatically from p =.01 to p =.50) Precision you desire p 1 p d 2 n = 2

173 Objective: Practice using the sample size formula for proportions. Time: 3 mins. Instructions: Use the sample size formula for proportions to answer the following questions. 1. Suppose you want to estimate (within 2%) the proportion of customers who will buy a new service. You’re guessing that 50% of them will buy. What sample size do you need? 2. How many customers do you need to sample for your estimate to be within 4%? PRACTICE: SAMPLE SIZE FOR ESTIMATING PROPORTIONS

174 PRACTICE: ANSWERS Question 1. Question 2.

175 USING PRECISION TO JUSTIFY SAMPLE SIZES The equations for determining sample sizes can also be used to help you evaluate the trade-offs for spending more money on larger sample sizes in order to gain more precision. Doing this before you collect data can help justify what sample size is appropriate for your project and budget. 1.Determine how many samples you can afford ( n ). 2.Then ask, what will that sample provide in terms of precision? That is, an average within ± d units Or a proportion within ± d %

176 3.Is that precise enough? 4.If not precise enough: Make a table of precision and cost for various sample sizes to determine the gain in precision per rupee spent on samples. Then choose a sample size that you can justify based on the gain in precision or the needed precision for your situation. USING PRECISION TO JUSTIFY SAMPLE SIZES

177 SAMPLING FROM A LIMITED (FINITE) POPULATION The sample size formulas assume the sample size ( n ) is small relative to the population ( N ). –If is > 0.05 You are sampling more than 5% of the population You can adjust the sample size with the Finite Population formula:

178 EXERCISE 1: JUSTIFYING NEEDED SAMPLE SIZE 1.Suppose you want to estimate the average time for payment of a vendor payment process with a precision of 2 days. What sample size do you need? (Historical data shows standard deviation = 4 days.) 2. Suppose you want to estimate (within 5%) the proportion of invoices having mistakes. You’re guessing that 20% of them will have mistakes. What sample size do you need?

179 SAMPLE SIZE RULES OF THUMB Statistic or Chart Recommended Minimum Sample Size (n) Average Proportion Frequency plot (Histogram) 50 Pareto chart50 Scatter plot24 Control chart24

180 POPULATION VS. PROCESS A Population –Situation: You can operationally define the boundaries of an existing (whole) group so that each unit in the group can be identified and, theoretically, numbered. –Sampling Purpose: To describe characteristics of that group. –Example: University alumni (as of Aug 31st) are sampled to determine what percentage will send at least one child to college within the next two years. Sample Use the sample to draw inferences about the whole group: e.g., Average = , Proportion = p

181 A Process –Situation: A process is dynamic and ever-changing; not all units in the process can be identified because some don’t exist yet (such as those made tomorrow). –Purpose: To understand the process for the purpose of taking action to make improvements or to predict future behavior of the process. –Example: We expect 5% to 20% of next month’s invoices to have errors (unless we change the process). POPULATION VS. PROCESS

182 SAMPLING AND IMPROVEMENT PROJECTS To determine the baseline performance of process cycle times and defect rates (e.g., plot sample data on a control chart) To estimate Process Capability (e.g., count defects in a sample) To identify factors (Xs) that cause poor performance or variation in the data (using plots, hypothesis tests, or regression with sample data) To verify that proposed improvements work (compare new data sampled from a process with prior data sampled from that process) To monitor process performance, kick off remedial action if needed, and predict future performance (control chart the sample data from new process) Improvement projects generally apply sampling to process situations:

183 WHY DISTINGUISH POPULATION VS. PROCESS SAMPLING? –Sample size formulas were developed for well-defined, static (and often theoretical) population situations. But most sampling applications are for dynamic, future-unknown process situations. Applying the sample size formulas to process sampling situations can lead to false conclusions, unless certain circumstances are met. –For an inference to be valid, a sample must fairly represent the population or process. Different sampling strategies are needed for populations than for processes to ensure the samples are representative.

184 SAMPLING FROM A STABLE PROCESS –Sample size formulas can be applied to process situations if the process is stable. Reliable estimates can be obtained with certain precision. When making comparisons, differences can be detected if they exist, with certain power.

185 SAMPLING FROM AN UNSTABLE PROCESS –Many processes are unstable. –Collect data anyway and make control charts or time plots. Work to identify and remove special causes. –Use the sample size formula as the lowest figure you should consider; collect more data, if possible. Larger sample sizes are required when special causes are present because long-term variation is greater than short-term variation. To use the formulas, you need to estimate s (or p ); you’ll need to judge how the special causes affect this estimate and square it up to what you believe about the future behavior of the process.

186 –When comparing groups: Try to get samples for each group spread over the same time period. When drawing or reporting conclusions, remember that there is a risk that the conclusions may not hold up well in the future. –If the process is unstable, use a control chart for a very long time span of data, if possible, and circle or highlight the data points or time period represented in your sample. Will give you and others visual perspective of the behavior of the process. Helps you judge the reliability of the conclusions for the future. SAMPLING FROM AN UNSTABLE PROCESS

187 SAMPLING FROM A PROCESS For process situations, we want to ensure we can see the behavior of the process. So we: –Sample systematically or with subgroups (not randomly) across time. Even though random sampling could be applied to stable processes, we use systematic or subgroup sampling and preserve the time order to represent the process behavior better. –Try to sample from enough time periods to fairly represent the sources of variation in the process. Apply your own judgment and process knowledge regarding sources of variation to determine how often to sample (every 10th unit, every 7th unit; every day, every month, etc.). –Generally, collect small samples more frequently to ensure that the process behavior is represented fairly over time. –Make a control chart or time plot to determine if the process is stable or unstable (look for outliers, shifts, trends, or other patterns).

188 REPRESENTATIVE SAMPLES For conclusions to be valid, samples must be representative. –Data should fairly represent the population or process –No systematic differences should exist between the data you collect and the data you don’t collect

189 SUMMARY OF SAMPLING This module has covered: –Sampling is an efficient and effective alternative to looking at all the data. –Population sampling and process sampling have different objectives and approaches. –Representativeness is the most important aspect of sampling. –Proper sampling gives you confidence in your conclusions. –Sample size formulas for population sampling can be applied to stable processes.

190 COMMON PROBLEMS WITH MEASUREMENTS Problems with the measurements themselves 1.Bias or inaccuracy: The measurements have a different average value than a “standard” method. 2.Imprecision: Repeated readings on the same material vary too much in relation to current process variation. 3. Not reproducible: The measurement process is different for different operators, or measuring devices or labs. This may be either a difference in bias or precision. 4. Unstable measurement system over time: Either the bias or the precision changes over time. 5. Lack of resolution: The measurement process cannot measure to precise enough units to capture current product variation.

191 DESIRED MEASUREMENT CHARACTERISTICS FOR CONTINUOUS VARIABLES Data from repeated measurement of same item Good repeatabilit y if variation is small * 1. Accuracy The measured value has little deviation from the actual value. Accuracy is usually tested by comparing an average of repeated measurements to a known standard value for that unit. 2. Repeatability The same person taking a measurement on the same unit gets the same result.

192 3. Reproducibility Other people (or other instruments or labs) get the same result you get when measuring the same item or characteristic. * Small relative to a) product variation and b) product tolerance (the width of the product specifications) DESIRED MEASUREMENT CHARACTERISTICS FOR CONTINUOUS VARIABLES

193 4. Stability Measurements taken by a single person in the same way vary little over time. Time 1 Time 2 Good stability if difference is Small* Observed value Observed value * Small relative to a) product variation and b) product tolerance (the width of the product specifications) DESIRED MEASUREMENT CHARACTERISTICS FOR CONTINUOUS VARIABLES

194 5. Adequate Resolution There is enough resolution in the measurement device so that the product can have many different values. Good if 5 or more distinct values are observed DESIRED MEASUREMENT CHARACTERISTICS FOR CONTINUOUS VARIABLES

195 IMPROVING A MEASUREMENT SYSTEM A measurement system consists of Measuring devices Procedures Definitions People To improve a measurement system, you need to Evaluate how well it works now (by asking “how much of the variation we see in our data is due to the measurement system?”). Evaluate the results and develop improvement strategies.

196 NOTE ON CALIBRATING MEASUREMENT EQUIPMENT Measurement instruments should only be recalibrated when they show special cause evidence of drift. Otherwise, variation could be increased by as much as 40%. This is because adjusting for true common cause variation adds more variation (Deming’s rule 2 of the funnel). Measurements taken from stable instrument Measurements taken with stable instrument recalibrated before each reading

197 GAGE R&R Assessing the accuracy, repeatability, and reproducibility of a continuous measurement system. –A Gage R&R study is used to assess the measurement system for collecting continuous data. It is typically used in manufacturing or other applications where “gages” or devices are used to measure important physical characteristics that are continuous. Examples: thickness, viscosity, strength, stickiness

198 –The Gage R&R study is a set of trials conducted to assess the repeatability and reproducibility of the measurement system. Multiple operators measure multiple units a multiple number of times. Example: 3 operators each measure 7 units twice. “Blindness” is extremely desirable. It is better that the operator not know that the part being measured is part of a special test. At a minimum, they should not know which of the test parts they are currently measuring. –You analyze the variation in the study results to determine how much of it comes from differences in the operators, techniques, or the units themselves. GAGE R&R

199 HOW A GAGE R&R STUDY WORKS –Select units or items for measuring that represent the full range of variation typically seen in the process. Measurement systems are often more accurate in some parts of the range than in others, so you need to test them over the full range. –Have each operator measure those items repeatedly. In order to use Minitab to analyze the results, each operator must measure each unit the same number of times. It is extremely desirable to randomize the order of the units and not let the operator know which unit is being measured. –Minitab looks at the total variation in the items or units measured.

200 –Minitab then estimates the proportion of the total variation that is due to 1.Part-to-part variation: physical or actual differences in the units being measured. 2.Repeatability: Inconsistency in how a given person takes the measurement (lots of inconsistency = high variation = low repeatability). 3. Reproducibility: Inconsistency in how different people take the measurement (lots of inconsistency = high variation = low reproducibility). 4. Operator–part interaction: An interaction that causes people to measure different items in different ways (e.g., people of a particular height may have trouble measuring certain parts because of lighting, perspective, etc.). –If there is excessive variation in repeatability or reproducibility (relative to part-to-part variation), you must take action to fix or improve the measurement process. The goal is to develop a measurement system that is adequate for your needs. HOW A GAGE R&R STUDY WORKS

201 DATA FOR A GAGE R&R STUDY –Each operator measures each unit repeatedly. –Data must be balanced for Minitab—each operator must measure each unit the same number of times. –The units should represent the range of variation in the process. –Operators should randomly and “blindly” test the units; they should not know which unit they are measuring when they record their results.

202 MINITAB OUTPUT

203 Gage R&R Source %Contribution %Study Var Total Gage R&R 37.39 61.15 Repeatability 28.64 53.51 Reproducibility 8.75 29.59 reader 8.75 29.59 Part-To-Part 62.61 79.13 Total Variation 100.00 100.00 Number of Distinct Categories = 2 MINITAB OUTPUT Acceptance criteria for MSA 1.Gage R & R < 10%Excellent 2.Gage R & R 10% to 30% Acceptable 3.Gage R & R > 30%Not acceptable In addition: No. of Distinct categories  4

204 USING THE GAGE R&R ANOVA METHOD Focus on the following: A) p value for the operator term p < 0.05 implies that the operators get significantly different average results. B) p value for the operator × unit number term p < 0.05 implies that the operator to operator differences are not consistent across parts. C) Number of distinct categories If the number is < 4 it implies that the measurement variation is too large to adequately distinguish the part to part variation. D) The R chart by operator If it is stable, this tells is that there are no special causes in the measurement process that could be throwing off our calculations

205 ADEQUATE VS. INADEQUATE MEASUREMENT SYSTEMS Adequate Inadequate Most of the variation is accounted for by physical or actual differences between the units. – What Minitab calls part-to-part variation will be relatively large – All other sources of variation will be small – You can have higher confidence that actions you take in response to data are based on reality The measurement system has sufficient precision to distinguish at least four groups or “categories” of measurements. Variation in how the measurements are taken is high. You can’t tell if differences between units are due to the way they were measured, or are true differences - You can’t trust your data and therefore shouldn’t react to perceived patterns, special causes, etc.—they may be false signals The measurements fall into less than four categories. –

206 GAUGE R & R FROM MINITAB  Open MINITAB Worksheet.  Enter part numbers, operators, data in separate columns  Choose STAT > QUALITY TOOLS > GAGE R&R STUDY (Crossed).  In Part numbers, enter the column of part numbers.  In Operators, enter the column of Operator names  In Measurement data, enter the column of measurements.  Choose ANOVA method (by default).  Click OK.

207 USING THE GAGE R&R ANOVA METHOD Focus on the following: A) p value for the operator term p < 0.05 implies that the operators get significantly different average results. B) p value for the operator × unit number term p < 0.05 implies that the operator to operator differences are not consistent across parts. C) Number of distinct categories If the number is < 4 it implies that the measurement variation is too large to adequately distinguish the part to part variation. D) The R chart by operator If it is stable, this tells is that there are no special causes in the measurement process that could be throwing off our calculations

208 Interpretation of MSA Results Repeatability error shall be low. If it is high, then, a.Instrument is improper b.Method of measurement is not OK c.System improvement is required Reproducibility error shall be low. If it is high, then, a.Train the operator b.Method of measurement is not OK c.Inspector skill not OK

209 Interpretation of MSA Results Part to Part variation shall be High. If it is low, then, a.Instrument is improper b.Method of measurement is not OK

210 WORKSHEET # 6 : GAGE R&R Time: 30 minutes 1) Five rubber bands representing the range of part variation are available to each team. Each team must design, implement and analyze the data from a Gage R&R study using their assigned measurement method. Each team must decide: I)Number of operators II)Number of times they measure each part III)How to randomize the measurement order IV)How to keep the operators “blind” to the part they are measuring yet still track the data necessary for analysis V)How to record the data VI)How to enter the data into Minitab VII)How to run the Gage R&R analysis VIII)How to interpret the results

211 Nominal/Ordinal Measures MSA Introduction Assessing Bias Kappa Example: Nominal MSA Kappa for Multiple Categories Ordinal Responses Recommended Approaches

212 Objectives After completing MSA, participants should be able to:  Describe the characteristics of a good measurement system;  Undertake a formal MSA study, using variance components analysis if the measure is continuous, and both confidence intervals and kappa if the measure is nominal;  Document the MSA for their project;  Explain the value of an MSA.

213 Introduction This section focuses on MSA for data that are nominal or ordinal. Nominal data classifies occurrences into unordered categories, for example:  Color of Product is acceptable or not  A customer survey response on a satisfaction questionnaire is either “yes” or “no”  A customer contact is considered acceptable or not  Categories of idle time

214 Introduction Ordinal data classifies occurrences into ordered categories, for example:  A customer survey response on a questionnaire is “strongly disagree”, “moderately disagree”, “neutral”, “moderately agree”, or “strongly agree”  A sales lead is considered “unlikely”, “likely”, or “very promising”  An IT failure is classified as being of “low”, “medium”, or “high” severity  A package to be delivered is categorized as acceptable, Downgraded or Reject

215 Introduction As with continuous data, nominal and ordinal measurement systems are evaluated in terms of stability, bias, repeatability and reproducibility. Note that the operational definition of the measurement is critical.  Nominal and ordinal data often result from subjective decisions by observers or raters.  This subjectivity frequently results in bias, repeatability, and reproducibility problems.  The more one can remove subjectivity from the rating process, the better.

216 Introduction In this section, we will focus on assessing bias, repeatability and reproducibility for nominal measurement systems. Note: We will only briefly introduce methods for studying ordinal measurement systems. Although we would like a method for studying both repeatability and reproducibility in a single experiment, this is not currently possible for nominal data. For this reason, we will address the components of repeatability and reproducibility in terms of intrarater and interrater agreement. We will rely on a tool called “kappa” to measure intra-rater and inter-rater agreement.

217 Assessing Bias Studies of bias require knowledge of the true measure of an item or occurrence. Studies where rater responses are compared with those of an expert are called expert re-evaluation studies. An expert evaluates the items or occurrences that have been rated by less experienced raters. The expert may be a person or a reference measurement method. The expert’s rating is considered to be the “gold standard”, and is used to determine the percent of correct decisions by all raters. Since this assumption is key, the performance of the expert should be evaluated prior to performing the expert re- evaluation.

218 Assessing Bias Example: Consider an example dealing with security violations (file SecurityAudit.jmp). Two Auditors and one Expert Auditor inspected 25 areas chosen from many areas that could have been inspected, and classified each as P or F (pass or fail). An attempt was made to include areas with security violations as well as without (there should be at least 25% representation of each group).

219 Assessing Bias Auditor 1 agrees with the Expert for 24 of the 25 areas. Auditor 2 agrees with the Expert for 18 of the 25 areas. The percent agreement is dependent upon the areas chosen; had different areas been chosen, the sample percent agreement would differ. In other words, the percent agreement is a sample statistic and is subject to sampling variation. The sample percent agreement is an estimate of a population parameter, the true percent agreement. Thus it is useful to calculate a range of values that is likely to contain the true percent agreement with some high probability.

220 Assessing Bias Recall that such a range of values is called a confidence interval. For each auditor, it is reasonable to assume that the number of instances of agreement for the 25 areas follows a binomial distribution where n = 25 and p = unknown probability of agreement. For each auditor, we are interested in estimating the parameter p, the probability of agreement. As seen earlier, JMP calculates confidence intervals for the parameter p of a binomial distribution under Distribution. It is important to define the agreement response as nominal.

221 Assessing Bias In the Distribution platform, select the agreement for Auditor 1, Exp&Aud1 Agreement, as Y. From the red arrow, select Confidence Interval, and choose 0.95 as the confidence level.

222 Assessing Bias The resulting output gives an interval which, with 95% confidence, contains the true proportion of agreement. Notice that, according to this interval, the true probability of agreement could range from 0.805 to 0.993.

223 Assessing Bias The output for Auditor 2’s agreement with the Expert is given below. What do you conclude? Which actions might be appropriate at this point? Note: 25 is an extremely small sample size for attribute measurement system studies - 50 is considered a minimum.

224 Kappa Nominal measurement studies that address repeatability and reproducibility are often called concordance studies. In such studies, intrarater agreement measures repeatability (within rater), and interrater agreement measures the combination of repeatability and reproducibility (between rater). The probability of overall agreement among raters, or within a rater, can be estimated using a confidence interval. However, analysis using confidence intervals can be misleading, as we shall see. In this section, we will introduce a measure called “kappa”, which is useful in measuring both intrarater and interrater rater agreement for nominal data.

225 Kappa Suppose that a team is studying customer complaint resolution. Twenty-five occurrences of customer complaints and their resolution are presented, in random order, to each of two raters, Lynn and Ted. For each occurrence, each rater is asked to determine whether the outcome was acceptable or not, and to indicate this with a “Yes” or “No” response. The data are summarized in the data table to the right (Lynn&Ted.jmp).

226 Kappa This data can be summarized in tabular form as in the table below. Such a table is called a contingency table. This table can be obtained under Analyze/Fit Y by X, using Lynn as Y and Ted as X.

227 Kappa Note that, in 20 of the 25 occurrences, Lynn and Ted agreed on their assessment of the complaint resolutions. A confidence interval for their probability of agreement can be obtained. An “Agreed” column is defined as shown in the data table to the right. A 95% level confidence interval is obtained as shown earlier. The probability of agreement is likely somewhere between 0.61 and 0.91.

228 Kappa Suppose that, instead of the responses in Table A, the responses in Table B had been obtained. Does one table show more agreement than the other? If so, which? Table A Table B

229 Kappa As another example, consider the two tables below. Which shows the greater degree of agreement? Table A Table B

230 Kappa Consider Table A. How often would you expect Rater1 and Rater 2 to agree based on chance alone? Rater 1 classifies 50% of the occurrences as Yes and 50% as No. Rater 2 does the same. If the two rater’s decisions had nothing to do with each other (i.e., if they were independent), one would expect to see precisely the counts that are given in the table. For example, the probability that both would classify an occurrence as a Yes is 0.5 x 0.5 = 0.25, and the expected count is 100 x 0.25 = 25.

231 Kappa Thus, all we are observing is what would be expected by chance alone, given the raters’ marginal classifications. Since we are interested in non-chance agreement, the question is: “How much of the observed agreement between two raters (or ratings) would not happen by chance alone?” So, we need to develop a measure of non-chance agreement. We do this by estimating the chance agreement, and subtracting it from the overall agreement. This gives us a measure of what the raters would agree upon beyond what they would agree upon by chance alone.

232 Kappa Consider Table B. The second entry in each cell of the table represents chance, or expected, agreement. The expected counts are: In the Yes/Yes cell: 0.90 x 0.40 x 100 = 36.0. In the No/Yes cell: 0.10 x 0.40 x 100 = 4.0. In the Yes/No cell: 0.90 x 0.60 x 100 = 54.0. In the No/No cell: 0.10 x 0.60 x 100 = 6.0.

233 Kappa Kappa is a measure of chance- corrected agreement. The number of occurrences where the raters agree is 40 + 10 = 50. The expected agreement by chance alone is 36 + 6 = 42 The observed agreed count minus the expected agreed count is (40 + 10) – (36 + 6) = 8. We compare this to the number of observations minus expected agreement: 100 – (36 + 6) = 58. The ratio of these values is kappa: 8/58 = 0.138. Kappa can be thought of as the rate of chance-corrected agreement.

234 Kappa Kappa is defined by: JMP computes this value in the Fit Y by X platform, when both variables are nominal and can take on the same values (for example, “Yes” or “No”).

235 Kappa For a given level of chance agreement, values of kappa range from a negative value to 1.  Negative values reflect disagreement  A zero value reflects no agreement  Positive values reflect agreement KappaStrength of Agreement < 0.00Poor or None 0.00 – 0.20Slight 0.21 – 0.40Fair 0.41 – 0.60Moderate 0.61 – 0.80Substantial 0.81 – 1.00Almost perfect Guidelines on strength of agreement are given in the table. A kappa of 0.60 or higher is generally considered acceptable.

236 Kappa One should realize that kappa values depend on the sample selected, and are subject to sampling variation. JMP provides the standard error for the kappa statistic. We can be fairly sure that the true value of kappa lies roughly within two standard errors of the computed kappa. Although we will not emphasize the use of kappa’s standard error, one can use the standard error, with standard normal percentiles, to compute confidence intervals for kappa. For example, for the ratings by Raters 1 and 2 on a previous slide, an approximate 95% level confidence interval is given by the two standard error interval: 0.138 +/- 2(0.044) = 0.050 to 0.226

237 Kappa Kappa can be used to measure both intrarater agreement and interrater agreement. Thus we can use kappa to assess both repeatability and interrater agreement, which includes both repeatability and reproducibility variation. Repeatability Intrarater agreement (Within rater) Reproducibility and repeatability Interrater agreement (Between raters) Kappa

238 Kappa Example. Consider the process of determining whether a sales opportunity can be met or not. Scenarios describing fifty opportunities are randomly presented to three different planners on two different occasions. The data are given in SalesOpportunities.jmp.  A “Y” indicates that the opportunity can be met  An “N” indicates that the opportunity can not be met Part of the data is shown on the next slide.  Mary 1 is the first rating obtained by Mary  Mary 2 is the second rating obtained by Mary

239 Kappa Note that all ratings are nominal.

240 Kappa Assess repeatability for Mary, Frank, and Phil. Why is Phil’s kappa small, compared to Mary’s?

241 Kappa Reproducibility between Mary and Phil can also be studied using kappa. Kappa values for the four combinations of ratings by Mary and Phil are given below. These values were obtained from four Fit Y by X analyses in JMP, and placed in a table manually.

242 Kappa for Multiple Categories Kappa can be generalized to situations where there are more than two ratings by one rater, or where there are several raters. Kappa is also easily generalized to a situation where the response has more than two categories. As an example, consider classifying software problems into causes of failure (Failures.jmp). Four failure modes are possible: A, B, C, and D Since the failure modes are unordered categories, the columns are coded as nominal. Two raters examine the same 50 software failures and classify each as to cause of failure.Note the missing value in row 48.

243 Kappa for Multiple Categories Is the measurement system reproducible? Once again, we use Fit Y by X to generate a contingency table and kappa (on the next slide).

244 Kappa for Multiple Categories Remember that the second entry in each cell is an estimate of the agreement expected by chance. Almost perfect0.81 – 1.00 Substantial0.61 – 0.80 Moderate0.41 – 0.60 Fair0.21 – 0.40 Slight0.00 – 0.20 Poor or None< 0.00 Strength of Agreement Kappa Recall our guidelines for strength of agreement: What can we conclude? The grading is acceptable.

245 Recommended Approach: Nominal MSA 1. Choose 2 to 4 raters. 2. Choose at least 50 occurrences or items to be inspected.  For binomial data, attempt to include at least 25% from each grouping unit.  For nominal data with more than two categories, attempt to obtain an equal distribution of categories. 3. If possible, have each rater inspect each occurrence twice, using randomized presentations. Otherwise, skip to (5). 4. Compute kappa values for each rater to assess repeatability. Any kappa values below 0.60 are a cause for concern. These should lead to actions to improve repeatability.

246 Recommended Approach: Nominal MSA 5. If the repeatability values for each pair of raters are considered acceptable (0.60 or higher), continue:  Compute kappa values for each pair of ratings between raters. Note that, if the intrarater kappas are high, these interrater kappas should be similar for any given pair of raters.  If any of these interrater kappa values are less than 0.60, address differences among the raters.

247 MSA in Transactional Projects Guidelines for MSA in transactional projects: 1. Brainstorm an extensive list of possible sources of variation in the measurement process. 2. Obtain measurement data, and check it for integrity using the methods suggested in the section Preprocessing 1. Pay particular attention to the idea of conducting a Data Audit. 3. Evaluate what you have learned from the brainstorming session and the data integrity check to determine if there are obvious ways to reduce measurement system variation. If there are obvious improvements to be made, make them.

248 MSA in Transactional Projects Guidelines for MSA in transactional projects (continued): 5. Consider the need for a formal MSA study. Situations that require interpretation or knowledge on the part of observers, or that involve subjectivity, often benefit from a formal MSA. 6. If appropriate, conduct a formal MSA study. 7. Document the results of steps 1 – 6 above. This documentation is the MSA for your project. Note that there are at least three possible components to the MSA:  A list of potential sources of variation  A check for data integrity

249 Looking into Data

250 Tool Why Data Continuous data in sequence Continuous data Discrete (multiple categories) Identify special causes, shifts and other patterns Data based Process Analysis to detect special causes, shifts and other patterns and Monitor the process Determine the shape, center, and range of numeric data and type of distribution Determine relative importance or impact of different problems Time Plots Control Charts Frequency plots (histograms) Pareto Charts

251 Objective –Understand the relationship between quality and variation –Be able to differentiate between common and special cause variation –Be able to create and interpret time plots, control charts, histograms and Pareto Charts –Understand the difference between control limits (process capability) and specification limits (customer requirements) –Be able to use Minitab to display data

252 Understanding Variation

253 Data on Shipments per Day The Operations manager at a company was told that the month before, his plant had shipped 79 orders/day early in the month and 135 orders/day near the end of the month. His questions: Was the 79 more typical? Or 135? Was there a clear trend upwards? How does looking at the data this way help? Time Plot of Shipped Orders per Day 3020100 70 80 90 100 110 120 130 140 April 1-30 Number of orders 135 79 His staff charted the orders/day for April.

254 What Is Time-Ordered Data? –Data that is collected regularly –Hourly– Daily –Weekly– Monthly – Quarterly –Data collected over time from a process. Measurements on the first 30 lots completed one week Measurements on every 5th lot Weekly yields from the past two years –The first step in understanding variation should always be to plot such data in time order –Data used for analysis in a DMAIC project can be either existing (historical) data or new data you collect.

255 Why Is Time Order Important? –Process conditions can change over time; data from one point in time is not always comparable to that from another point in time –Biases can enter the data –If you ignore time- related patterns, your conclusions may be false

256 Focus on the Variation –When analyzing time-ordered data, you need to look at the variation, how the data values change from point to point –Certain patterns in the variation can provide clues about the source of process problems

257 What Is Variation? –No two anythings are exactly alike. How a process is done will vary from day to day. Measurements or counts collected on process output will vary over time. –Quantifying the amount of variation in a process is a critical step towards improvement. –Understanding what causes that variation helps us decide what kinds of actions are most likely to lead to lasting improvement.

258 Variation vs. Specifications/Targets –The amount of variation in a process tells us what that process is actually capable of achieving –Specifications tell us what we want a process to be able to achieve

259 Types of Variation –Special Cause: something different happening at a certain time or place –Temporary or local; specific –May come and go sporadically –Evidence of the lack of statistical control is a signal that a special cause is likely to have occurred –Reminder: a process with special cause variation is called unstable –Common Cause: always present to some degree in the process –Common to all occasions and places –Degree of presence varies –Each cause contributes a small effect to the variation in results –Variation due to common causes will almost always give results that are in statistical control –Reminder: a process with only common cause variation is called stable

260 A Time Plot 50 55 60 65 70 11121314151617181 GOAL= reduce variation Target

261 Reacting to Variation The appropriate managerial actions are quite different for common causes than for special causes. Unstable Stable Common cause strategy Stable? Special cause strategy

262 Special Cause Strategy The goal is to eliminate the specific special causes; to make an unstable process stable. –Get timely data so that special cause signal can identified easily. causes are signaled quickly. –Take immediate action to remedy any damage. –Immediately search for a cause. Find out what was different on that occasion. Isolate the deepest cause you can affect. –Develop a longer-term remedy that will prevent that special cause from recurring. Or, if results are good, retain that lesson. – Use early warning indicators throughout your operation. Take data at the early process stages so you can tell as soon as possible when something has changed.

263 Special Cause Strategy You may not need to complete the DMAIC process to address a special cause. –See what changed at the point in time when the special cause appeared. What was different then? –If the cause it not clear, it is no more a special cause for you. –If the cause is clear, confirm it with additional data, if possible. Then develop longer-term action to prevent the special cause (if the impact was bad) or preserve it (if the impact was good).

264 Common Cause Strategy The process shown here is stable. But does it need to be improved? } Customer Needs Time A process with only common causes is said to be “statistically stable” and “in statistical control.” Merely being in statistical control does not mean the results of a system are acceptable. Leaving the process alone is not improvement. Different approach is needed to improve stable system.

265 Improving a Stable Process –When improving a stable system you don’t single out one or two data points. You need to look at all the data—not just high points or low points—not just the points you don’t like—not just the latest point. All the data are relevant –Improving a stable process is more complex than identifying a special cause. More time and resources are generally needed in the discovery process. Common causes of variation can hardly ever be reduced by attempts to explain the difference between individual points if the process is in statistical control –When dealing with special causes, you focus on a few data points. For common cause variation, you need to look at all the data points to fully understand the pattern. You should look at the entire System Processes in statistical control usually require fundamental changes for improvement –Using the DMAIC Method can help you make fundamental changes in a process –This is a TRUE SIX-SIGMA PROJECT

266 Stratification –Sort data into groups or categories based on different factors. –Look for patterns in the way the data points cluster or do not cluster. Example of “Down grading” data stratified by “day of week” MondayTuesdayWednesday Thursday Friday Downgraded Quantity –Mondays are consistently worse than other days — find out why.

267 Disaggregation –Many figures we see are aggregated. For example, if we look at total monthly production figures, each data value is really a combined figure representing all products, lines, shifts, weeks, etc. –If we take apart—disaggregate—these figures, we can often see patterns that are masked in the roll up.

268 How to Disaggregate –Disaggregate by process phase or step –Disaggregate by process output Sum results across all product or service Separate results by product or service type Total Results Results for Product 1 Results for Product 2 Results for Product 3 Results for Product 4 Results for Product 5 Measure time separately for each phase or step Whole process (“Do the job”) Phase 1Phase 2Phase 3 Time to complete entire process

269 9/91 10/91 11/9112/91 1/922/923/924/925/926/927/928/929/92 10/9211/9212/92 1/932/933/934/935/936/937/93 9/91 10/91 11/9112/91 1/922/923/924/925/926/927/928/929/92 10/9211/9212/92 1/932/933/934/935/936/937/93

270 Experimentation –Common cause variation stems from the interaction of a large number of factors in a process –Identifying which of those many factors are contributing the most to the variation can be tricky and time-consuming –Often, people have theories about which factors are most important –Experimentation can help us confirm those theories

271 Experimental Approach –You can be formal or informal in your experimental design –Even if informal, use PDCA: Plan the experiment –Identify factors (potential causes) you want to study –Develop operational definitions of the factors and the responses you will measure –Select/develop your experimental design Do the experiment –Collect data Check the results –Analyze and interpret data Act on what you learn

272 Matching Action to the Type of Variation Discussion –What would it mean in practice to treat a special cause like common cause variation? –What would it mean to treat common variation like special causes?

273 Decide whether each of the following examples describes a special cause or a common cause. Then decide what the appropriate response should be. Remember to treat special causes differently than common causes. Be prepared to discuss your answers with the class. Discuss also what happens if you treat a common cause like a special cause, and vice versa. Time: 10 min. –Example 1: One quality inspector is found to be making errors in filling out the inspection report. Is this a special cause or a common cause? What is an appropriate response to this situation? What might happen if you took the wrong course of action? –Example 2: All inspectors are found to make occasional errors in filling out inspection reports. Is this a special cause or a common cause? What is an appropriate response to this situation? What might happen if you took the wrong course of action?

274 Tools for Understanding Variation –Time plots (“run charts”) –Control charts –Frequency plots –Pareto Charts

275 Time Plots (Run Charts)

276 Time Plots (Run Charts) 3020100 70 80 90 100 110 120 130 140 June 1–30 Production Production in tons

277 Why Use a Run Chart? Use a run chart: –To study observed data for trends or patterns over a specified period of time. –To focus attention on truly vital changes in the process. –To track useful information for predicting trends.

278 When to Use a Run Chart Use a run chart: –To understand variation in the process. –To compare a performance measure before and after implementation of a solution to assess the solution’s impact. –To detect trends, shifts, and cycles in the process.

279 Time Plot / Run Chart Features 3020100 70 80 90 100 110 120 130 140 Production in tons June 1-30 Production in tons Horizontal axis reflects passage of time Vertical axis shows the numerical value or count Data points plotted in time order Points are connected by a line to aid in visual interpretation

280 How to Construct a Run Chart 1. Decide on the measure you want to analyze. 2. Gather data (minimum 20 data points). 3. Create a graph with a vertical line and a horizontal line. 4. On the vertical line (y-axis), draw the scale related to the variable you are measuring. 5. On the horizontal line (x-axis), draw the time or sequence scale. 6. Calculate the median and draw a horizontal line at the median value. 7. Plot the data in time order or sequence. 8. USE MINTAB “QUALITY TOOLS” 9. Identify runs (ignore points on the median). 10. Check the table for run charts.

281 Looking at Both Time and Distribution 3020100 70 80 90 100 110 120 130 140 Production in tons June 1–30 Production in tons

282 Counting Runs on a Run Chart Here is a chart that has the runs circled. A “run” is a series of points on the same side of the median. A run can be any length from 1 point to many points. Too few or too many runs are important signals of special causes—they indicate something in the process has changed. Because you often count runs on a time plot, they are also called run charts. In this example, there are 5 data points on the median, which are ignored because they neither add to nor interrupt any runs. That leaves 20 data points that are counted for the run test, and 11 runs in the example shown here. 10 15 20 25 30 35 40 0510152025 Median 45 20 data points not on median 11 runs Note: Points on the median are ignored. They do not add to or interrupt a run. Time Plot from Exercise 2(F)

283 Runs Above and Below the Median 17 49 19 31 26 9 18 50 19 32 27 9 19 60 24 37 28 10 19 70 28 43 29 10 20 80 33 48 30 11 20 90 37 54 31 11 21 100 42 59 32 11 22 110 46 65 33 11 22 120 51 70 Number of Data Points Not On Median Lower Limit for Number of Runs Upper Limit for Number of Runs Lower Limit for Number of Runs Upper Limit for Number of Runs Number of Data Points Not On Median

284 Signals of Special Causes on Time Plots Special causes may be present if there are: –Too many or too few runs. –6 or more points in a row continuously increasing or decreasing (“trend”). –9 or more points in a row on the same side of the median (“shift”). –14 or more points in a row alternating up and down.

285 Examples of Signals –Too Few Runs –Too Many Runs –Trends: 6 or more points in a row increasing or decreasing MEASUREMENT Median MEASUREMENT Median MEASUREMENT Upward TrendDownward Trend

286 More Examples of Signals –Process Shift: 9 or more points in a row above or below the centerline –Bias or Sampling Problems: 14 or more points in a row alternating up and down (“sawtooth”) MEASUREMENT Median MEASUREMENT

287 Control Charts for Individual Values

288 Control Charts Control Charts: –Are time-ordered plots of results (just like time plots). –Use statistically determined control limits that are drawn on the plot. –Their centerline calculation uses the mean, not the median.

289 Why Use a Control Chart –Statistical control limits establish process capability. –Statistical control limits are another way to separate common-cause and special-cause variation. Points outside statistical limits signal a special cause. –Can be used for almost any type of data collected over time. –Provides a common language for discussing process performance.

290 When to Use a Control Chart Use a Control Chart: –To track performance over time. –To evaluate progress after process changes/improvements. –To focus attention on detecting and monitoring process variation over time.

291 Control Chart Features 0 10 20 30 40 50 60 70 80 90 100 JASONDJFMAMJJASONDJFM Basic features same as a time plot Control limits (calculated from data) added to plot Centerline usually average instead of median UCL LCL Statistical control limits are not based on what we would like the Process to do. They are based on what the process is capable of doing. They are computed from the data using statistical formulas.

292 How to Construct Control Charts 1. Select the process to be charted. 2. Determine sampling method and plan. 3. Initiate the data collection. 4. Calculate the appropriate statistics. 5. Plot the data values on the first chart (mean, median or individuals). 6. Interpret the control chart and determine if the process is “in control.”

293 Individuals Control Chart and Individuals Data The kind of control chart shown on the previous pages is called an individuals chart because the data points are individuals data—actual measurements on a single output. Sales Costs Shipments Cycle Times Efficiencies Losses in money Maintenance time Chemical analyses Pollution levels Production time lost Production amounts Temperatures Pressures Speeds Conductivity Waste

294 What Are Control Limits? Process Distribution Stable Process Returns 40 35 25 20 30 A control limit defines the bounds of common-cause variation in the process. A control limit is a tool we use to help us take the right actions. If all points are between the limits, we assume only common-cause variation is present (unless one of the other Signals of a Special Cause is present). If a point falls outside the limit, you treat it as a special cause / Otherwise, you do not investigate individual data points, but instead study the common- cause variation in all data points.

295 How to Calculate Control Limits There are two formulas commonly used for calculating control limits: XCenterline = X X XR XR R R UCL = + 3.14 ˜ UCL= + 2.66 LCL = – 3.14 ˜ LCL = – 2.66 Control Limits: Method 1 Control Limits: Method 2 Using Median Moving Range Using Average Moving Range UCL = Upper Control Limit. LCL = Lower Control Limit.

296 Control Charts and Tests for Special Causes –On a control chart, any data point outside the control limits is a signal of a Special Cause. –But can you use the previous Tests for special causes on a control chart, too? The answer is: It depends. –Two of the previous tests—counting “runs” and “9 points”—are determined relative to the median of the data. But on a control chart, the centerline is the average, not the median. Solution? You can use the average with caution if you think the data have a roughly “Normal” distribution (this will be covered later in this course). “With caution” means to check your interpretation in other ways before taking action.

297 Plotting the Data in Individual Chart Many people like to plot the Moving Range chart at the same time they plot an individuals chart. The moving ranges are the differences between adjacent points. As Wheeler & Chambers point out in their book Advanced Topics in Statistical Control, “It’s not that [the mR chart] improves the ability of the X-chart to detect signals, but that it serves as a reminder of the correct way of computing the limits for the X-Chart.”

298 CONSTRUCTION OF INDIVIDUAL CHART USING MINITAB Enter data in two columns, one for date/time & the other for the variable. Ensure at least 20 data sets otherwise consult your MBB. Go to Stat, Select Control Chart, Select Individuals, Select the Variable. Go to Test, tick First Four Tests, click ok. Set the Lower Specification Limit by clicking S-limits where non negative values are not feasible. Set the x axis points by selecting Stamp.Go to Frame> select Tick > set the X axis by 1:n/k( where n is the total number of observations and k is selected by you). Click ok, ok.

299 Determining Limits for individual Charts

300 Specification Limits vs. Control Limits –Specification limits Are set by the customer, management, or engineering requirements. Describe what you want a process to achieve. –Control limits Are calculated from the data. Describe what the process is capable of achieving. 70 80 90 100 110 120 1357911131517192123252729313335 UCL LCL Upper spec Lower spec

301 Special Causes, Common Causes, and Process Capability –It is extremely unlikely that an unstable process (with special causes) will ever be “capable.” –In a highly capable process, the control limits are much narrower than the specification limits.

302 Frequency Plots

303 Case Study: Speeding Up Improvements –A company had instituted a “Corrective Action” system used to ensure that improvement suggestions were followed up on. Their goal was to process and close all Corrective Action requests within 50 days. –Several years after the system was started, data on all the Corrective Actions was collected. Someone crunched the numbers and was able to tell management it took an average of 94 days to resolve the issues identified through this system. –Management’s reaction was clear: “We need to reduce our cycle time in half!”

304 One employee decided to create a frequency plot of the actual data, which he then showed to management. How do your reactions differ from just knowing the average was 94 days to seeing the actual distribution? Case Study: Speeding Up Improvements, Cont.

305 Frequency Plots (Histograms) A frequency plot shows the shape or distribution of the data by showing how often different values occur.

306 Why Use Frequency Plots A Frequency Plot: –Summarizes data from a process and graphically present the frequency distribution in bar form. –Helps to answer the question: Is the process capable of meeting customer requirements?

307 When to Use Frequency Plots Use a Frequency Plot: –To display large amounts of data that are difficult to interpret in tabular form. –To show the relative frequency of occurrence of the various data values. –To reveal the centering, spread, and variation of the data. –To illustrate quickly the underlying distribution of the data.

308 Frequency Plot Uses –A Frequency Plot creates a picture of the variation in a process. –It can reveal patterns that provide clues to certain types of problems. –It can verify whether data are distributed normally.

309 Types of Frequency Plots 95 85 75 65 55 45 35 25 DotPlot 9 8 7 6 5 4 3 2 149 25396 974532826 68274435082 42083443 90812156 349 1 Stem-and-Leaf Plot 05 10 95 85 75 65 55 45 35 25 Histogram

310 How to Construct a Frequency Plot 1. Decide on the process measure. 2. Gather data (at least 50 data points). 3. Prepare a frequency table of the data. Count the number of data points. Calculate the range. Determine the number of class intervals. Determine the class width. Construct the frequency table. 4. Draw a frequency plot (histogram) of the table. 5. Interpret the graph.

311 What to Look for on a Frequency Plot 1. Center of the data 2. Range of the data (distances between largest value and smallest value) Center Range

312 What to Look for on a Frequency Plot, Cont. 3. Shape of the distribution (provides information about process capabilities) 4. Comparison with Target and Specification TargetLSLUSL Shape

313 Common Shapes of Frequency Plots Bell shaped. Symmetric. Two humps. Bimodal. Long tail. Not symmetric.

314 Interpreting Distribution If a frequency plot shows a bell-shaped, symmetric distribution… –Conclude: No special causes indicated by the distribution; data may come from a stable process (Caution: special causes may appear on a time plot or control chart). –Action: Make fundamental changes to improve a stable process (common-cause strategy). –Note: We’ll learn more about bell-shaped or “Normal” curves in the next Chapter.

315 Interpreting Distribution If a frequency plot shows a bell- shaped, symmetric distribution… –Conclude: No special causes indicated by the distribution; data may come from a stable process (Caution: special causes may appear on a time plot or control chart). –Action: Make fundamental changes to improve a stable process (common-cause strategy). –Note: We’ll learn more about bell-shaped or “Normal” curves in the next Chapter.

316 Interpreting Distribution If a frequency plot shows a two-humped, bimodal distribution… –Conclude: What we thought was one process operates like two processes (two sets of operating conditions with two sets of output). –Action: Use stratification or other analysis techniques to seek out causes for two humps; be wary of reacting to a time plot or control chart for data with this distribution.

317 Interpreting Distribution If a frequency plot shows a long-tailed distribution (is not symmetric)… –Conclude: Data may come from a process that is not easily explained with simple mathematical assumptions (like normality). A long-tailed pattern is very common when measuring time or counting problems. –Action: You’ll need to use most data analysis techniques with caution when data has a long-tailed distribution. Some will lead to false conclusions. –For example, the control limit calculations are based on the assumption that the data have a bell-shaped curved. Calculating control limits for data with a long-tailed distribution will likely make you overreact to common cause variation and miss some special causes. Other tests that rely on normality include hypothesis tests, ANOVA, and regression. –To deal with data with this kind of distribution, you may need to transform it.

318 Additional Frequency Plot Patterns Basically flat One or more outliers If a frequency plot shows a basically flat distribution… Conclude: Process may be “drifting” over time or process may be a mix of many operating conditions. Action: Use time plots to track over time; look for possible stratifying factors; standardize the process. If a frequency plot shows one or more outliers… Action: Confirm outliers are not clerical error; treat like a special cause. Conclude: Outlier data points are likely the result of clerical error or something unusual happening in the process.

319 Frequency Plot Irregularities Five or fewer distinct values 4.05.06.07.08 4.55.56.57.5 Large pile-up around a minimum or maximum value One value is extremely common Saw-tooth pattern

320 Interpreting Distribution If a frequency plot shows five or fewer distinct values… –Conclude: Measuring device not sensitive enough or the measurement scale is not fine enough. –Action: Fine tune measurements by recording additional decimal points.

321 Interpreting Distribution If a frequency plot shows a large pile up of data points… –Conclude: A sharp cut-off point occurs if the measurement instrument is incapable of reading across the complete range of data, or when people ignore data that goes beyond a certain limit. –Action: Improve measurement devices. Eliminate fear of reprisals for recording “unacceptable” data.

322 Interpreting Distribution If a frequency plot has one value that is extremely common… –Conclude: When one value appears far more commonly than any other value, the measuring instrument may be damaged or hard to read, or the person recording the data may have a subconscious bias. –Action: Check measurement instruments. Check data collection procedures.

323 Interpreting Distribution If a frequency plot shows a saw-tooth pattern… –Conclude: When data appear in alternating heights, the recorder may have a subconscious bias for even (or odd) numbers, the measuring instrument may be easier to read at odd or even numbers, or the data values may be rounded incorrectly. –Action: Check measuring instrument and procedures.

324 Distributions, Capability, and Targets Target USL LSL On target and capable* Target USLLSL Not capable even if on target Target USL LSL Not capable (probably because off target)

325 Interpreting Distribution “Capable” doesn’t just mean what it produces today or tomorrow, but into the future. A process that is barely within the specifications isn’t “capable” because it’s likely something will happen to produce data points outside the specifications. A process needs to be well within the specifications to be considered capable. The distribution of the top chart, for instance, shows that the process is centered around the target and all the current data are well within specifications. It is both capable and on-target. The lower left chart shows a process that is off target—but the output looks like it could be within the specs if the center of the distribution could be moved closer to the target. The third chart shows a process that is not capable—the spread of variation is too wide to reliably produce input within the specification limits. These concepts will be explored in much more depth in the next chapters, when we examine the concept of Process Sigma.

326 Checking Both Time Order and Distribution

327 Checking Both Time Order and Distribution In practice, if your data has a natural time order, you should always do a time plot (or control chart) as well as a frequency plot. Both give you different information. In this case, there are no special causes that appear in the time plot (according to the Tests for Special Causes already taught), but the frequency plot clearly has a bimodal pattern and you’d want to investigate why.

328 WORK SHEET # 7: Interpreting Distribution and Time Order Objective: Gain an understanding of the different types of information provided by frequency plots and time plots, and how looking at the data from different perspectives can lead to different conclusions. Instructions: Divide into pairs or small groups. Read the case study below and discuss your interpretation of the data shown in the back-to-back frequency plots. Then look at the time plot on the next page and discuss the questions shown there. Be prepared to discuss your answers with the class. Time: 10 min.

329 Interpreting Distribution and Time Order This company was having trouble Scheduling the services delivered to its customers because of delays in receiving materials from their suppliers. They went into their computer records and recovered data from the past 40 weeks comparing promised delivery dates to actual delivery dates from their two main suppliers. Based on the frequency plots, which supplier would you recommend this company choose? Note: A negative number indicates the delivery was early.

330 Now look at the time plot of the same data shown previously on the frequency plots. What is your interpretation now that you’ve seen both the time plot and frequency plot? Which supplier would you recommend using? Interpreting Distribution and Time Order, cont. Time Plot of Suppliers A and B Late Deliveries (40 weekly deliveries each) -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 135791113151719212325272931333537 39 =supplier A =supplier B

331 Answer In the frequency plot, Supplier B looks far superior to Supplier A, having a much narrower distribution generally much nearer the target. In the time plot, however, it looks like Supplier A is making rapid strides in improving its ability to deliver on time. You would probably want to collect more data to make sure that Supplier A can sustain its current level of performance.

332 HISTOGRAM FROM MINITAB  Make Sure the data window is active.  Choose GRAPH>HISTOGRAM (or) STAT > BASIC STATISTICS > DISPLAY DESCRIPTIVE STATISTICS  In X (or) Variables, enter the column containing the data, click OK (or) choose GRAPHS > HISTOGRAM OF DATA > OK.  You can choose Type of Histogram, No. of classes by clicking OPTIONS in GRAPH>HISTOGRAM menu.  You can use GRAPH>Dot plot to display the data  You can classify the source wise data to display the data in two different dot plots.

333 DOT PLOT FROM MINITAB  Make Sure the data window is active.  Choose GRAPH> DOTPLOT  Enter the column containing the data, click OK  If you have source wise data, put the source variable (either Text or Numeric) in the next column. Click By Variable in the Dot Plot Menu, select the source column, click ok.  You get the Stratified Dot Plot on the same Graph.

334 STRATIFIED DOT PLOT SHIFT WISE

335 Pareto Diagrams

336 Dividing Data into Categories –So far, we’ve looked at data that has either a time order and/or a numeric order. The tools we used were time plots, control charts, and frequency plots. –But many times you end up with data that can best be analyzed by dividing it into categories. –A Pareto chart is one of the best tools for looking at categorical data.

337 Why Use a Pareto Chart Use a Pareto Chart when you want to: –Understand the pattern of occurrence for a problem. –Judge the relative impact of various parts of a problem (quantifying the problem). –Track down the biggest contributor(s) to a problem. –Decide where to focus efforts. –Often, it is very useful to add cost information to the chart. –A Pareto chart helps you decide where your improvement efforts will have the biggest payoff. Ultimately, you are trying to uncover clues that will help you pinpoint causes. –You can use a Pareto chart only when the problem under study can be broken down into categories and the number of occurrences can be counted for each category.

338 When to Use a Pareto Chart You can use a Pareto Chart when: The problem under study can be broken down into categories.  You want to identify the “vital few” categories—focus your improvement effort. Profit margins are critical in the grocery business.  Anything you can do to eliminate waste has a direct influence on the bottom line. One large grocery store wanted to reduce the amount of money wasted through spoiled food, which obviously could not be sold to the public.  The supervisors of various departments were all clamoring that their problem was worst and should be addressed first. Where should the store focus its attention? They combed through records for the past three months and created the Pareto chart above.

339 Pareto Charts Definition A Pareto chart is a graphical tool that helps you break a big problem down into its parts and identify which parts are the most important. 0 5000 10000 15000 20000 25000 Amount of Spoilage (Rs) Produce Meat Dairy Bakery Other Category Departmental Store Spoilage by Department October – December 2004

340 How to Construct a Pareto Chart 1. Decide which problem you want to know more about. 2. Gather the necessary data. 3. Compare the relative frequency (or cost) of each problem category. 4. List the problem categories (sorted by frequency, in descending order) on the horizontal line and frequencies on the vertical line. 5. Draw the cumulative percentage line showing the portion of the total that each problem category represents (optional). 6. Interpret the results.

341 Examples of Pareto Charts

342 What to Look For: Relative Heights of the Bars Pareto Principle applies: one or a few categories account for most of the problem. Focus improvement effort on top one or two bars. If you see this… Pareto Principle does not hold: bars are all about equal height. Not worth it to investigate tallest bar. Look for other ways to categorize data, or look for different kind of data on this problem. Interpretation & Action

343 What to Look For: Height of the Y-Axis If you see this… Interpretation & Action 0 20 40 60 80 ABCDEFG Y-axis is only as tall as the tallest bar. Height of bars is seen relative to the tallest bar, not in relation to the total number of problems. 0 50 100 150 200 250 ABCDEFG When drawn correctly, it doesn’t appear as if Bar A is really that much taller than other bars. Treat as if the Pareto Principle does not hold (that is, don’t focus solely on Bar A).

344 What to Look for: Size of the Other Category If you see this… Interpretation & Action “Other” bar is small “Other” bar is very tall Perhaps items clustered under Other should be redistributed to existing categories or a new category created. Re-examine “Other” items. Most data accounted for by actual categories. Relative heights of Other bars should accurately reflect the current state. Continue with analysis on tallest bars.

345 What to Look for: The Data Used Ask whether the data used to create the chart are valid. For example, it’s usually risky to take action based on surveys or votes. If you suspect the data may be biased or irrelevant, come up with alternative data you can collect. If you see this… Interpretation & Action Ask if the time period indicated is large enough to fairly represent the process output. Is that one week typical of the process, or would it be better to use data from an entire month? Defects in Packaging June 4 –10 Most important problems Tally of opinions 10/19

346 Summary: What to Look for on a Pareto Chart –Relative heights of the bars (including height of the Y-axis) —make sure the Pareto Principle applies. –Size of the “Other” category—make sure you can’t make another category from some of the “Other” data. –Type of data used to create the chart—is the chart based on valid data?

347 Reacting to a Pareto Chart: When the Pareto Principle Holds If the Pareto principle holds… and a few categories are responsible for most of the problems … Reaction… 1. Begin work on the largest bar(s) 2. When you’ve narrowed down the problem, continue to Step 3: Analyzing Causes 0 5000 10000 15000 20000 25000 Amount of Spoilage Produce Meat Dairy Bakery Other Spoilage by Department 0 2500 5000 7500 10000 12500 Amount Tomatoes Bananas Lettuce Apples Broccoli Oranges Other fruit Other vegetables Category Spoilage by Type of Produce

348 When the Pareto Principle Does NOT Hold When all the bars are roughly the same height and/or many categories are needed to account for most of the problem, you need to find another way to look at the data. 0 10 20 30 40 50 60 70 # of Injuries A: Maintenance B: Forming C: Pressing D: Baking E: Finishing G: Transportation Department Number of Injuries by Department Break down another way Finger 5 15 25 35 45 55 65 # of injuries Back Arm Ankle Shoulder Hand Eye Head Other # of Injuries by Body Part Normalize the data 0 10 20 30 40 50 60 70 80 Inj/100k Hrs EDCBAG Department # of Injuries per 100,000 hours worked Adjust for Impact GA 0 50 100 150 200 250 300 350 Lost Time (days) DB C E Dept Lost time from injuries by Department

349 PARETO DIAGRAM FROM MINITAB  Open MINITAB Worksheet.  Put your data (no. of defects) in one column and the nomenclature in the other column.  Choose STAT > QUALITY TOOLS > PARETO CHART  Choose Chart Defects Table. In labels in: enter the nomenclature column and in frequencies in: enter the no. of defects column.  Enter the required Title.

350 Case Example A company was very much interested in reducing the number of injuries. Their first attempt at data analysis is shown on the left: this Pareto shows the number of injuries categorized by department. The bars are all very similar in height, which means the Pareto Principle does not hold. They used three strategies to look at the data differently in hopes of finding clues that would help them eliminate injuries. Breaking down or categorizing the problem another way. To create the top right chart, the company categorized the data by injured body part instead of department. The Pareto Principle does hold for this chart, so the company would be justified in investigating the causes of Finger injuries first.

351 Case Example Adjusting the counts for impact (time, dollar cost, etc.) The company realized that not all injuries are created equal. Six finger injuries may not have as much impact as one back injury. So the middle chart shows how much each department is affected by injuries, as reflected in hours lost. The Baking department suffers most from injuries—and much more than any other department. Based on this chart, the company could justify focusing its efforts on reducing injuries in the Baking department.

352 Case Example Normalize the data. The departments in this company are not all the same size; the finishing department, for instance is very small compared to maintenance. To truly compare the rate of injuries across departments, the company converted the counts of injuries to the number of injuries that occur per 100,000 hours worked. As you can see, though the finishing department is small, it has a relative high rate of injuries. Based on these four Pareto charts, what would you recommend to this company?

353 WORK SHEET # 8: Review Exercise Open “ProcEx” Hypo Mod- file on milliohms. Do appropriate data graphing and infer about the Process. Specification for Milliohms is 150-280.

354 A Look Ahead –The previous modules provided you with a basic understanding of data collection and analysis. –The next module discusses how to calculate the capability of your process. –To understand process capability, you will be using the concepts of variation, specifications, yield, and distributions.

355 NORMAL DISTRIBUTION

356 GENERIC CAUSES OF VARIATION Machines Materials Methods Measurements Mother Nature People PR PPRROCOCEESSSSPPRROCOCEESSSSEPR PPRROCOCEESSSSPPRROCOCEESSSSE

357 TWO TYPES OF VARIATION NOISE SIGNAL

358 SECOND PRINCIPLE FOR UNDERSTANDING DATA While every data set contains noise, some data sets may contain signals. Before you can detect a signal within any given set, you must first filter out the noise. What would be some criteria to use to decide we had unusual variation?

359  Center of the bar Smooth curve interconnecting the center of each bar Units of Measure THE NORMAL CURVE

360 If the frequency distribution of a set of values is such that : – 68.26% of the values line within ±1  from the mean AND – 95.46% of the values line within ±2  from the mean AND – 99.73% of the values line within ±3  from the mean Then the distribution is normal. NORMAL DISTRIBUTION IS CHARACTERISED BY A BELL SHAPED CURVE. NORMAL DISTRIBUTION

361 THE NORMAL DISTRIBUTION

362 EXPLANATION  In our example the average value (X-bar) is 2.849  Standard Deviation (s) is 0.018  X-bar ± 1s implies the range ( X-bar -1s) to ( X-bar + 1s ) i.e.. (2.849 - 0.018) to (2.849 + 0.018) = 2.831 to 2.867 The number of values between 2.83 and 2.87 are 41 i.e.. 82%.  X-bar ± 2s implies the range (2.849 - 2 x 0.018) to (2.849 + 2 x 0.018) = 2.813 to 2.885 = 2.81 to 2.89 The number of values between 2.81 to 2.89 = 49 i.e.. 98%.  Similarly X-bar ± 3s implies the range 2.80 to 2.90. 100% of items fall under this range.

363 OUR MAN ALWAYS WANTS TO REACH OFFICE ON TIME. HE COLLECTS DATA ON TRAVEL TIME FROM HIS HOUSE TO OFFICE FOR LAST FEW MONTHS. HE FINDS THAT : – THE AVERAGE TIME ( X-bar ) IS 25 MINUTES. – THE STANDARD DEVIATION (s) IS 5 MINUTES. EXAMPLE-NORMAL DISTRIBUTION

364 THE NORMAL CURVE WOULD BE AS FOLLOWS Values (time) 10 15 20 25 30 35 40 68% 95% 99.7% Normal Distribution : Average = 25 Standard Deviation, s = 5

365 15% 50% 84% 98% 99.9% 99.99966% 50% certain, leave 25 minutes before work 84% certain, leave 30 minutes before work 99.99% certain, leave 40 minutes before work 99.99966% certain leave 47.5 minutes before work starts….. HOW MUCH TIME BEFORE SHOULD HE LEAVE HIS HOUSE ?

366 If you know your average value ( ) and your standard deviation (s) then for a given specification limit, it is possible to predict rejections (if any), that will occur even if you keep your process in control. Example: = 2.85, s = 0.02 (The dimensions relate to a punched part). Let us find the percentage rejection if the specified value is 2.85 ±0.04 i.e. 2.81-2.89 HERE IS HOW YOU DO IT HOW TO PREDICT REJECTIONS X X

367 A =Rejections for under size B=OK Items C=Rejections for over size Let the area under the curve = 1 units = Area (A+B+C) The total Rejections = Area A + Area C The total Ok components = Area B 2.81 2.85 2.89 0101 0202 B A C

368 WE NOW INTRODUCE THE CONCEPT OF Z Knowing Z you can use table for one sided normal distribution to find the corresponding areas and hence the rejections. 0101 0202 B A C LSLUSL X

369  The area from Normal table corresponding to 2 is 0.02275  Hence Rejection for Over size (Area C) = 2.275 % NOW LETS DO IT =2.85 s= 0.02 USL=2.89X

370  The area from Normal table corresponding to 2 is 0.02275  Hence Rejection for Under size of holes (Area A) = 2.275 % =2.85 s= 0.02 LSL = 2.81X

371 The total rejections = 2.275+ 2.275 = 4.55%. The items with undersize values may be reworked while those with oversize values are scrapped. It is hence possible to reduce rejection cost by centering your machine at 2.84, so that all your rejections are on the lower side. Rejection will still be 4.55 %, but reworkable.

372 CHECKING FOR NORMALITY USING MINITAB  Make Sure the data window is active.  Choose STAT>BASIC STATISTICS > NORMALITY TEST (or) STAT > BASIC STATISTICS > DISPLAY DESCRIPTIVE STATISTICS  In Variable(s), enter the column(s) containing the data, click OK (or) choose GRAPHS > GRAPHICAL SUMMARY > OK>OK  Read from Anderson-Darling Normality Test, P-value  If P-value is <0.05, treat the data as coming from a Non-normal distribution, otherwise treat the data is coming from normal distribution.

373 NORMAL DISTRIBUTION USING MINITAB  Choose “CALC>PROBABILITY DISTRIBUTIONS > NORMAL” In Mean enter “Mean”, and in Standard Deviation enter “SD”  You can choose either “Probability density / Cumulative probability”  Enter the input in “Input Column” if it is in a column or in “Input constant”, click “OK”.  You can calculate Z from given Probability from “Inverse Cumulative Probability”

374 BINOMIAL DISTRIBUTION AND POISSON DISTRIBUTION

375 BINOMIAL DISTRIBUTION When to Use: When the variable is in terms of attribute data and in binary alternatives such as good or bad, defective or nondefective, success or failure etc. Conditions:  The experiment consists of ‘n’ identical trials  There are only two possible outcomes on each trial. We denote as Success (S) and Failure(F).  The probability of ‘S’ remains the same from trial to trial and is denoted by ‘p’ and the probability of ‘F’ is ‘q’.  p+q = 1  The trials are independent

376 BINOMIAL DISTRIBUTION The binomial random variable ‘X’ is the number of successes (failures) in ‘n’ trials.

377 EXAMPLE-BINOMIAL DISTRIBUTION A machine that produces stampings for gas cylinders is malfunctioning and producing 10% defectives. The defective and non-defective stampings proceed from the machine in a random manner. If 5 stampings are collected randomly, what is the probability that 3 of them are defective. Let ‘X’ is the number of defectives in n= 5 trials p =0.1; q = 1-0.1 = 0.9

378 POISSON DISTRIBUTION When to Use: No. of accidents in a specified period of time No. of errors per 100 invoices No. of telephone calls in a specified period of time No. of surface defects in a casting No. of faults of insulation in a specified length of cable No. of visual defects in a bolt of cloth No. of spare parts required over a specified period of time The no. of absenteeism in a specified period of time The number of death claims in a hospital per day The number of breakdowns of a computer per month The PPM of Toxicant found in water or air emission from a manufacturing plant

379 POISSON DISTRIBUTION Conditions:  When ‘n’ is very large and ‘p’ is very small in binomial distribution.  The experiment consists of counting the number of times a particular event occurs during a given unit of time or in a given area or volume or weight or distance etc.  The probability that an event occurs in a given unit of time is same for all the units.  The no. of events that occur in one unit of time is independent of the number that occur in other units.  The mean no. of events in each unit will be denoted by.

380 POISSON DISTRIBUTION The Poisson random variable ‘X’ is the number of events that occur in specified period of time.

381 EXAMPLE-POISSON DISTRIBUTION Suppose the number of breakdowns of machines in a day follows Poisson distribution with an average no. of breakdowns is 3. Find the probability that there will be no breakdowns tomorrow.

382 WORK SHEET # 9: LET’S TRY TOGETHER... Your firm’s accountant believes that 10% of the company’s invoices contains arithmetic errors. To check this theory, the accountant randomly samples 25 invoices and finds that seven contain errors. What is the probability that the 25 invoices written, seven would contain errors if the accountant’s theory was correct? The average no. of Monday absentees in an organization is 2.5. What is the probability that exactly 5 employees are absent on a given Monday?

383 CAPABILITY RATIOS Cp, Cpk, Pp, Ppk

384 IMPORTANT SPC RATIOS USED This compares the requirement of the process output vis-a-vis the inherent variability of the process. Higher value than 1 implies that the process has got the capability to give the product within the set limits. LSL x USL - 3+ 3

385 PROCESS POTENTIAL INDEX (Cp) Maximum Allowable Range of Characteristic Normal Variation of Process Cp = The numerator is controlled by Design Engineering The denominator is controlled by Process Engineering

386 This gives us the positioning of the mean vis-a-vis the USL and the relationship between the two. This gives us the positioning of the mean vis-a-vis the LSL and the relationship between the two. Cpk - Process Performance Index. This is important Cpk = Minimum of (Cpu and Cpl) ; for bilateral tolerances = C pu ;for unilateral tolerance on upper side i.e.. = Cpl ;for unilateral tolerance on lower side i.e.. X +Y -O X +O -Y

387 These ratios help you in:  Predicting whether rejections will take place on the higher side or on the lower side.  Taking centering decisions.  Deciding whether to consider broadening of tolerances  Taking Decisions on whether to go in for new m/cs.  Deciding on the level of inspection required.

388 LSLUSL Failure likely on lower side LSLUSL LSLUSL CENTERING RELATED PROBLEMS LSLUSL LSLUSL TOLERANCE OR NEW MACHINE DECISION Failure likely on higher side LSLUSL LSLUSL SOME TYPES

389 IMPORTANT SPC RATIOS USED Pp is based on same equation as Cp with one exception; Pp employs the long term standard deviation (whereas Cp employs the short term standard deviation). Ppk is based on same equation as Cpk with one exception; Ppk employs the long term standard deviation (whereas Cpk employs the short term standard deviation).

390 DPU, TOP, DPO, DPMO

391 Every possibility of making an error is called an opportunity The total opportunities available for an error to take place are Number Checked. x Number of Opportunities per unit If there are more than 1 Opportunities. The sigma can be calculated by finding DPMO. Knowing DPMO we refer to the DPMO Table to get the Sigma value One could inflate the opportunities, and hence get an enhanced Sigma But the opportunities.are limited to what exactly is checked for. E.g. a sheet is checked for thickness, length & width and can be rejected for either.Hence the number of opportunities. is 3 THE CONCEPT OF OPPORTUNITY DPMO = Defects x 10 6 Units chkd. x Opp. DPMO = Defects x 10 6 Units chkd. x Opp.

392 Defect : Any non-conformity in a product or service –e.g. Late delivery or no. of Packages rejected Units : The nos. checked or inspected – 100 deliveries were monitored for being late, no. of units are 100 – 1000 tubes were checked for oversize dia., no. of units are 1000 Opportunity : Anything that you measure or check for. –Each Finished Package is checked for 4 defects at final inspection, the no. of opportunities is 4 per package. A FEW TERMINOLOGIES

393 WHAT IS A DEFECT?  A defect is any variation of a required characteristic of the product (or its parts) or services or process output which is far enough from its target value to prevent the product from fulfilling the physical and functional requirements of the customer/business, as viewed through the eyes of your customer/business manager.

394 An 'unit' may be as diverse as a: Piece of equipment Line of software Order Technical manual Medical claim Wire transfer Hours of Work A transacted unit Customer contact DEFINING AN UNIT

395  No. of opportunities = No. of points checked  If you don’t check some points then it becomes a passive opportunity. We should take only active opportunities into our calculation of defects per opportunity (d.p.o), and Sigma level.

396 TOP = NO. OF UNITS CHECKED x NO. OF OPPORTUNITIES OF FALIURE PER UNIT TOP = NO. OF UNITS CHECKED x NO. OF OPPORTUNITIES OF FALIURE PER UNIT e.g. If in final inspection 100 packages were checked, each having 4 opportunities. TOP = 4 x 100 =400 TOTAL OPPORTUNITY (TOP)

397 DPO = DEFECTS TOP e.g. If in the above example, Four defects were found DPO = 4= 0.01 400 DPMO = NO. OF DEFECTS x 10**6 NO. OF UNITS x OPP. e.g. In the above example DPMO = 4 x 10**6 = 10,000 PPM 100 x 4 DEFECTS PER OPPORTUNITY (DPO) & DEFECTS PER MILLION OPPORTUNITY (DPMO)

398 DPU = NO. OF DEFECTS NO. OF UNITS CHECKED e.g. In the above example DPU = 4/100 = 0.04 DEFECTS PER UNIT (DPU)

399 CATEGORY DEFECTS UNITS OPP TOP DPU DPMO TYPE1 TYPE2 TYPE3 TYPE4 TYPE5 COMPOSITE 10 02 22 25 16 ?? 2 1 5 3 2 ?? 1000 1500 1300 2500 3000 ?? DPMO =  DEFECTS x 10 6  TOP DPMO =  DEFECTS x 10 6  TOP  Units x  Opp.) Should not be taken in the denominator as in the normal case WORKSHEET # 10: EVALUATE THE SIGMA RATING

400 CALCULATION OF SIGMA RATING

401 This Z value is known as the SIGMA RATING Knowing the sigma rating we can establish the rejections that can be expected from the process The average, the standard deviation & the specification limits are required to get the sigma rating There are 2 kinds of sigma ratings.The short term Sigma & the long term Sigma (to be seen in detail later) One should not confuse between the sigma rating & the standard deviation THE SIGMA RATING

402 Is a measure of variation of the process It is independent of the specification limits. It is represented by s. Is a measure which compares process variability vis a vis the requirements It is dependent on the specification limits, mean &std.deviation. It is represented by Z and pronounced as zee. SIGMA RATINGSTD.DEV STANDARD DEVIATION VS. SIGMA RATING

403 For every Z there is a definite rejection level and the same can be expressed in PPM SHORT TERM SIGMA RATING PPM 2345623456 308537 66807 6210 233 3.4 KNOWING Z, WE CAN FIND THE REJECTION IN PPM

404 Six sigma is when the inherent variability of the process is half that of the requirements LSLUSL 66 33 33 66 A WORD OF CAUTION: It is possible to achieve six sigma by widening specifications but the issue is that would the customer accept it. WHAT IS SIX SIGMA

405  It states that the averages of a sample tend to be normally distributed though the individual values may belong to a population which is not normal.  The normality generally begins with a sample size of 4 or 5  This is one of the reasons why we do not use single pieces but sub groups CENTRAL LIMIT THEOREM

406 PROCESS RESPONSE TIME WHITE NOISE BLACK NOISE RATIONAL SUBGROUPS

407 RATIONAL SUBGROUP CONCEPT Subgroups or samples should be selected so that if assignable causes are present, the chance for differences between subgroups will be maximized, while the chance for differences due to these assignable causes within a subgroup will be minimized. Time order is frequently a good basis for forming subgroups because it allows to detect assignable causes that occur over time. Two general approaches for constructing rational subgroups: Consecutive units of production Random sample of all process output over the sampling interval

408 A VERY SMALL SUB GROUP (OF SAY 1) IS TAKEN ? The white noise will be reflected as black noise i.e.. inherent variability will be interpreted as process shift. A VERY LARGE SUBGROUP(OF SAY 100) IS TAKEN ? The black noise will be reflected as white noise i.e..process shift will be reflected as variability inherent in the process. THE TIME BETWEEN THE SUB GROUPS SHOULD IDEALLY BE SUCH THAT IT COINCIDES WITH THE TIME THAT THE PROCESS NORMALLY SHIFTS. WHAT HAPPENS IF....

409 Process mean is centered but variability is higher Ideal situation : Variability less than reqd. Mean centered LSLUSL LSLUSL 1 st Type of problem: Variability greater than reqd. Mean centered THE 2 COMMON TYPES OF PROBLEMS

410 Variability is ok but process mean is shifted Ideal situation : Variability less than reqd. Mean centered LSLUSL 2 nd Type of Problem Mean shifted Variability is ok LSLUSL THE 2 nd TYPE OF PROBLEM

411 LSL X USL LSL X USL Cumulative short-term capability Cumulative long-term capability LONG TERM AND SHORT TERM VARIABILITY

412 LONG TERM VS. SHORT TERM SIGMA When inherent variability of the process only is used to determine the sigma value assuming mean is centered at the target it is called SHORT TERM sigma.This is the best that the process is capable of and is also called Process Entitlement When over a period of time assignable causes creep in, the capability of the process to meet the requirements diminishes.This sigma which represents the capability of the process to meet the requirements over a period of time considering that extraneous conditions cause process shifts from that at which it was set is called the LONG TERM sigma

413 LONG TERM VS. SHORT TERM SIGMA Hence normally short term sigma is higher than long term. If not specified than short term(Z ST )=long term(Z LT ) + SHIFT(Z SHIFT, 1.5  if unspecified  Z ST = Z LT + 1.5

414 SHORT TERM SIGMA Z ST = |SL - T| s ST Where T = Target Value s ST  Std.Dev of data collected on short term basis LONG TERM SIGMA Z LT = |SL - X-bar| s LT Where X-bar = Average Value s LT = Std.Dev of data collected on long term basis It is a measure of inherent variation of the process It is a measure of inherent variation + control of the process MATHEMATICALLY...

415 Z ST Z SHIFT 1 6 2.5 1.5 0.5 4 HIGH VARIATIONLOW VARIATION HIGH SHIFT LOW SHIFT VARIATION & CONTROL THE PROBLEM CONTROL THE PROBLEM VARIATION THE PROBLEM LEAVE THE PROCESS THE FOUR BLOCK ANALYSIS

416 EXAMPLE  We checked 500 Purchase Orders (PO) and PO had 10 defects then, d.p.u. = d/u = 10/500 = 0.02  In a P.O. we check for the following: a) Supplier address/approval b) Quantity as per the indent c) Specifications as per the indent d) Delivery requirements e) Commercial requirements  Then there are 5 opportunities for the defects to occur. Then, The total no. of opportunities = m u = 5x500 = 2500

417 EXAMPLE  Defects per opportunity, d.p.o. = d/(m u) = 10/2500 = 0.004  If expressed in terms of d.p.m.o. (defects per million opportunities) it becomes d.p.m.o. = d.p.o. x 10 6 = 4000 PPM From d.p.o., we go to the normal distribution tables and calculate Z LT and corrected to Z ST by adjusting for shift (1.5  ) then,  Z LT = 2.65; and  Z ST = 2.65 + 1.5 = 4.15

418 For a 100% inspection process, 10000 units are produced. Each can be rejected for 8 different reasons. 100 were rejected. What is the DPU, TOP, DPMO & DPO. For the above the next day 20 units were rejected such that 2 units had 3 defects & 1 unit had 2 defects rest all had 1 defect. Find the DPU,TOP, DPMO & hence DPO. 20000 Items are supplied by a vendor. 5% of these are to be checked as per the sampling plan for 5 characteristics. 100 items are rejected. At what sigma can one estimate the Sigma of the process of the vendor to be. WORK SHEET # 11: EXERCISES

419 To calculate Z we need to know the average, std.dev and specification limits How then would we find Z for attribute data ? Attribute data is measured in terms of rejections Knowing your rejection levels in PPM we can use the table of Sigma - PPM correlation to get the sigma value of the process Ex : Rejection of 6 sheets of 1000 produced would mean 6000 PPM i.e. a sigma of approx 4 The normal distribution table can be used to find the sigma value given the rejection in PPM. Z AND PPM ARE INTERCONVERTIBLE

420 The diameter of a rod produced is 100mm, the standard deviation is 1mm and it has a unilateral tolerance of 104mm. Hence, Z=( 104-100)/(1)=4 This implies that out of every 1 million pieces produced 6210 are likely to be defective. 10000 tubes were checked for internal diameter with go- no-go gauge out of which 62 were defective.This implies a PPM of 62 x10 6 /10000 =6200 which implies that the process of the tube i.d. formation is approximately a Four Sigma process. EXAMPLE

421 FIRST TIME YIELD AND ROLLED THROUGHPUT YIELD

422 Input 100 stage 1stage 4stage 3stage 2stage 5 Output 98 Input 100 stage 1stage 4stage 3stage 2stage 5 Output 98 YES! ARE BOTH THE PROCESSES EQUALLY EFFICIENT?

423 PROCESS 1 Input 100 stage 1stage 4stage 3stage 2stage 5 1 Reject 1 Output 98 Input 100 stage 1stage 4stage 3stage 2stage 5 PROCESS 2 Rework 2 3 15 Rework 6 Reject 1 1 Output 98 NO! ARE BOTH THE PROCESSES EQUALLY EFFICIENT?

424 IN BOTH THE CASES THE OUTPUT/INPUT RATIO IS THE SAME. WHAT THEN IS THE DIFFERENCE ? In the first case the output/input ratio is the only measure of the process efficiency & is called the CLASSICAL YIELD (Y FT ) or FIRST TIME YIELD. In the second case the extent of rework that the process generates can also be a measure of the efficiency of the process & is known as ROLLED THROUGHPUT YIELD(Y RT ). Rework would mean additional cost of manpower,material, handling, creating excess capacity etc. and many a times it is preferred to use rolled yield rather than the classical yield.

425 113,617 parts per million wasted opportunities 45,000 ppm wasted 21,965 ppm wasted 46,652 ppm wasted ROLLED THROUGHPUT YIELD

426 1009697 stage 1stage 2stage 3 91 Y 1 = 0.97Y 2 = 0.99Y 3 = 0.95 Y RT = Y FT1 x Y FT2 xY FT3 = 0.91 or 91% METHOD 1: This means that 91 % of the items will pass through without any rejection or rework HOW DO WE DETERMINE THE ROLLED YIELD ?

427 Y FT = e -DPU METHOD 2 : 1.Calculate defects per unit (DPU) 2.The first time yield is approximately equal to e -DPU Example: There are 6 boxes each having 10 cups. 3 cups are found to have a scratch mark. What is the probability that a box does not have any scratch mark. HOW DO WE DETERMINE THE ROLLED YIELD ?

428 METHOD 1: 60 cups have 3 defects Hence scratches per cup = 3/60 = 0.05. Hence probability of no scratch for a given cup is 1-0.05 =0.95 The probability of none of the cups having a scratch in a box of 10 cups are 0.95*0.95*0.95...........10times = 0.95 10 = 0.5987 Y RT = 59.87 %

429 METHOD 2: Probability of 1 cup having a scratch = 0.05 Hence the no. of defects in a given box (DPU) = 0.05 *10 =0.5 Y FT = e -DPU = e -0.5 = 0.606 Y FT = 60.6 % This difference between the two methods is because the 2 nd method tends to the value obtained by the 1 st method (which is the actual value) as the distribution tends towards Poisson distribution.

430 In an organization the repair rate for winding, machining, laminating and processing depts. are 80%, 98%, 68% & 99%. What is the Y RT, PPM & sigma rating of the process For a production of 10000 and a Y RT of 96% and having 4 opportunities. Find the no. of defects, DPU, TOP & DPO, DPMO. In the process of producing 7500 units 50 defects were observed. The total type of defects that could have occurred were 10. Find DPU, TOP, DPO &Y FT. WORK SHEET # 12: EXERCISES

431 The yield is of 96.5%. What is the PPM level ? What is the PPM level for DPU of 2.5? For a Z LT of 3.65, what is the PPM level ? WORK SHEET # 13: EXERCISES

432 WORK SHEET # 14: EXERCISES

433 WORK SHEET # 15: EXERCISES

434 CONTINUOUS DATA Step 1: Ensure Gauge R&R (if the CTQ is measured using an instrument) is < 30%. Otherwise improve measurement system Step 2: Collect the data (Minimum of 50 readings) on the CTQs as per the data collection plan. Step 3: Plot Histogram (Follow MINITAB steps. GO TO: Stat > Basic Statistics > Display Descriptive Statistics >Enter Variables > ‘Click’ Graphs > ‘Tick’ Graphical Summary>OK> OK Step 4: Read mean & standard deviation and interpret the data as coming from Normal distribution if p > 0.05, otherwise treat the data as coming from a non-normal distribution.

435 CONTINUOUS DATA Step 5: In case, your data is chronological, Check for trend or special cause using individual control chart(For normal Data)/Time plot(Run Chart) for Non-normal data. Step 6: Do the process capability analysis as follows. i.Stat > Quality Tools > Capability Analysis (Normal) > Enter Variable > Sample Size = 1 > Enter Specification Limits ( L/ U/ or both) > Go to Options>Remove the tick from Within subgroup analysis>OK>OK ii.Read Expected performance in PPM if the data is normal iii.Read Observed performance if the data is non-normal. iv.In either case go to PPM – Sigma conversion table and find the Sigma rating.

436 EXAMPLE (Normal) PPM = 848771.67 Sigma Level = 0.47

437 EXAMPLE (Non-Normal) PPM = 760000 Sigma Level = 0.80

438 QUESTIONS FOR THE MEASURE STAGE DATA COLLECTION PLAN  What input and process measures are critically important to understanding the performance of this process?  Does the sampling plan accurately reflect the population and/or the process? Has the team properly planned for randomness in their sample?  What did the team do to assure reliability and validity of the measurement process (e.g., using Gage R&R)?

439 VARIATION ãWhat variation did the team measure in the process (as displayed in charts such as histograms, run charts, box plots, etc.)?  SIGMA LEVEL ãWhat is the current process sigma level and goal for this project? ãHow do findings in the Measure Phase impact this estimated benefit of the project? QUESTIONS FOR THE MEASURE STAGE

440 NEXT STEPS ãIs additional data collection required before the Analyze Phase can begin? ãWhat hypotheses about the root causes of defects will the team investigate? ãWhen will root cause analysis be completed? ãWhat “quick hit” improvements has the team found? QUESTIONS FOR THE MEASURE STAGE Management often decides to go after obvious Quick Hits before completing the Analyze Phase. Brainstorm Quick Hits for your project!

443 Sigma and DPMO conversion table

446 SUMMARY OF QUALITY TOOLS/TECHNIQUES

101 APPROACH TO MEASURE. 112 FAILURE MODE AND EFFECT ANALYSIS FMEA: A General Overview Any FMEA conducted properly and appropriately.

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101 APPROACH TO MEASURE. 112 FAILURE MODE AND EFFECT ANALYSIS FMEA: A General Overview Any FMEA conducted properly and appropriately.

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Presentation on theme: "101 APPROACH TO MEASURE. 112 FAILURE MODE AND EFFECT ANALYSIS FMEA: A General Overview Any FMEA conducted properly and appropriately."— Presentation transcript:

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