POLYTECHNIC OF NAMIBIA

POLYTECHNIC OF NAMIBIA
Master of Industrial Engineering Quality & Reliability (QRE920S) Dr Michael Sony

Session 3 : Quality and Reliability Tools/Techniques

Quality Tools Seven Basic Tools of Quality Flow Chart /Run chart
Control Chart Check Sheet Histogram Pareto Diagram Cause and Effect Diagram Scatter Diagram Discuss the application of these tools at your work place

Histogram

Histograms Histogram A bar graph plot of the data, with the bars placed adjacent to each other. Frequency histogram The vertical axis of a histogram represents the class frequency. Relative frequency histogram The vertical axis of a histogram represents the relative class frequency.

Histograms Characteristics of data detected by histograms

Histogram – Exercise 2 A potato chip manufacturer is studying the problem of broken potato chips. It is an Industry norm that number of broken chips in a packet should be less than 5. As part of the initial investigation, the manufacturer randomly samples 100 packages and counts the number of broken chips per package. Analyze the spread data of data

Quality Tools Seven Basic Tools of Quality Purpose To look at one particular set of results To check for patterns in a process To examine large amounts of data The purpose of a Histogram is to take the data that is collected from a process and graph it to show how the data is distributed. The histogram will show: The centre of the data. The spread of the data. The skew of the data (slant, bias or run at an angle). The occurrence of out of range conditions. The presence of peaks within the data.

Normality

Normal Distribution

Normal Distribution Most of nature and human characteristics are normally distributed, and so are most production outputs for well- calibrated machines. When a population is normally distributed, most of the observations are clustered around the mean

Exercise 3 A manufacturer wants to set a minimum life expectancy on a newly manufactured light bulbs. A test is conducted on time to failure data on two bulbs. Estimate its parameters and also test whether data follows normality. A)What percentage of bulb fails before 240 hrs. B) What percentage of bulbs fail between 240 and 260 hrs.

Exercise 3 C) The manufacturer wants to set the minimum life expectancy of the light bulbs so that less than 5 percent of the bulbs will have to be replaced. What minimum life expectancy should be put on the light bulb labels? d) Set 3σ control limits

Pareto Chart

Exercise 4 Suppose you work for a company that manufactures motorcycles. You hope to reduce quality costs arising from defective speedometers. During inspection, a certain number of speedometers are rejected, and the types of defects recorded. Use a Pareto chart to identify which defects are causing most of your problems.

Quality Tools POLYTECHNIC OF NAMIBIA Seven Basic Tools of Quality Cause & Effect Diagram For identifying areas for improvement. For finding potential causes of problems. For developing possible preventive actions. What are the potential uses of the tool?

Scatter Diagram

Quality Tools POLYTECHNIC OF NAMIBIA Seven Basic Tools of Quality Scatter Diagram Purpose Easier to see direct relationship Identifies the correlations between a quality characteristic and the factor that driving it There is a direct relationship between time spent cooking by employees and defects. As Time cooking increases, so does the amount of defects. Discuss the relationship between time spent cooking by employees and defects?

Quality Tools POLYTECHNIC OF NAMIBIA Seven Basic Tools of Quality Interpreting Scatter Diagram There is a direct relationship between time spent cooking by employees and defects. As Time cooking increases, so does the amount of defects.

Exercise 5 Voice of Customer
You are interested in how well your company's camera are meeting customers' needs. Market research shows that customers become annoyed if they have to wait longer than 5.5 seconds between flashes. Voice of an Engineer You collect a sample of 40 batteries randomly that have been in use for varying amounts of time and measure the voltage remaining in each battery immediately after a flash (VoltsAfter), as well as the length of time required for the battery to be able to flash again (flash recovery time, FlashRecov). The efficiency of flash is best when voltage is above 1 v (i) Create a scatterplot to examine the results. Include a reference line at the critical flash recovery time of 5.5 seconds and also flash efficiency. Fit a regression equation and comment of model fit (ii) Create a scatterplot, grouped by formulation, to examine the results. Include a reference line at the critical flash recovery time of 5.5 seconds. Fit a regression equation and comment of model fit

Check list

Quality Tools POLYTECHNIC OF NAMIBIA Seven Basic Tools of Quality Check Sheets Benefits Collect data in a systematic and organized manner To determine source of problem To facilitate classification of data (stratification) Scatter Diagram There is a direct relationship between time spent cooking by employees and defects. As Time cooking increases, so does the amount of defects.

Flow chart

Quality Tools Seven Basic Tools of Quality Activity Decision Inspection Transportation Delay Storage Flow Chart Symbols

Quality Tools Creating a flow chart
Define the Process Steps by Observing the Process Sort the Steps into the Order of their Occurrence in the Process Place the Steps in Appropriate Flow Chart Symbols Create the Chart Evaluate the chart for completion

Run Chart

Run Chart Run Chart to look for evidence of patterns in your process data. Run Chart plots all of the individual observations versus the subgroup number, and draws a horizontal reference line at the median . The nonrandom behavior includes trends, oscillation, mixtures, and clustering in your data. Such patterns suggest that the variation observed is due to special causes - causes arising from outside the system that can be corrected. Common cause variation is variation that is inherent or a natural part of the process. A process is in control when only common causes affect the process output.

Mixtures A mixture is characterized by frequent crossing of the center line. Mixtures often indicate combined data from two populations, or two processes operating at different levels. p-value for mixtures is less than 0.05, you may have mixtures in your data. An observed number of runs that is greater than the expected number of runs indicates mixtures. When you perform a hypothesis test in statistics, a p-value helps you determine the significance of your results. Hypothesis tests are used to test the validity of a claim that is made about a population. This claim that’s on trial, in essence, is called the null hypothesis. The alternative hypothesis is the one you would believe if the null hypothesis is concluded to be untrue. The evidence in the trial is your data and the statistics that go along with it. All hypothesis tests ultimately use a p-value to weigh the strength of the evidence (what the data are telling you about the population). The p-value is a number between 0 and 1 and interpreted in the following way: A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis. A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis. p-values very close to the cutoff (0.05) are considered to be marginal (could go either way). Always report the p-value so your readers can draw their own conclusions.

Clusters Clusters may indicate special-cause variation, such as measurement problems, lot-to-lot or set-up variability, or sampling from a group of defective parts. Clusters are groups of points in one area of the chart. If the p-value for clustering is less than 0.05, you may have clusters in your data. An observed number of runs that is less than the expected number of runs indicates clusters.

Trends A trend is a sustained drift in the data, either up or down.
Trends may warn that a process will soon go out of control. A trend can be caused by factors such as worn tools, a machine that does not hold a setting, or periodic rotation of operators. If the p-value for trends is less than 0.05, you may have a trend in your data.

Oscillation Oscillation occurs when the data fluctuates up and down, which indicates that the process is not steady. If the p-value for oscillation is less than 0.05, you may have oscillation in your data.

Exercise a Suppose you work for a company that produces several devices that measure radiation. As the quality engineer, you are concerned with a membrane type device's ability to consistently measure the amount of radiation. You want to analyze the data from tests of 20 devices collected in an experimental chamber. After every test, you record the amount of radiation that each device measured. As an exploratory measure, you decide to construct a run chart to evaluate the variation in your measurements.

Logical order of tools

Quality Tools Logical order for the 7 tools Flow Chart Check Sheet
Histograms Scatter Diagrams Control Charts Cause & Effect Pareto Analysis Big Picture Data Collection Data Analysis Problem Identification Prioritization Early stages Medium Final Stages

PDSA and QC Tools ACT ACT PLAN PLAN STUDY STUDY DO DO Brainstorming
Pareto analysis ACT ACT PLAN PLAN Why-Why diagram Run charts Cause &effect diagram STUDY STUDY DO DO Control charts Histograms Scatter diagrams Check sheets Control charts Scatter diagrams Check sheets Pareto charts Run charts

Control Charts

Quality Advocates Dr. Walter Shewhart (1891-1967)
Father of Statistical Process Control Control of Quality of Manufactured Product Van Nostrand Reinhold, 1931 Defined two aspects of quality What the customer wants (subjective) What the physical properties are (objective)

Quality Advocates Dr. Shewhart was the first person to encourage the use of easy-to-use statistics to remove variation ‘common cause variation’ – normal process fluctuations ‘special cause variation’ – uncontrolled influence

Quality Advocates Dr. Shewhart proposed that controlled and uncontrolled variation exists. A phenomenon will be said to be controlled when, through the use of past experience, we can predict, at least within limits, how the phenomenon may be expected to vary in the future. Here it is understood that prediction within limits means that we can state, at least approximately, the probability that the observed phenomenon will fall within the given limits.

Quality Advocates Dr. Walter Shewhart proposed: Common (Chance) Causes
Controlled variation that is present in a process due to the very nature of the process. Special (Assignable) Causes Uncontrolled variation caused by something that is not normally part of the process.

Control Charts The study of a process over time can be enhanced by the use of control charts. Process variation is recorded on control charts, which are powerful aids to understanding the performance of a process over time.

Control Charts Control charts are decision-making tools. They provide an economic basis for making a decision as to whether to investigate for potential problems, to adjust the process, or to leave the process alone: First and most important, control charts provide information for timely decisions concerning recently produced items. If an out-of-control condition is shown by the control chart, then a decision can be made about sorting or reworking the most recent production. Control chart information is used to determine process capability, or the level of quality the process is capable of producing. Samples of completed product can be statistically compared with the process specifications. This comparison provides information concerning the process’s ability to meet the specifications set by the product designer. Continual improvement in the production process can take place only if there is an understanding of what the process is currently capable of producing.

Control Charts 2. Control charts are problem-solving tools. They point out where improvement is needed. They help to provide a statistical basis on which to formulate improvement actions. Control chart information can be used to help locate and investigate the causes of the unacceptable or marginal quality. By observing the patterns on the chart the investigator can determine what adjustments need to be made. This type of coordinated problem solving utilizing statistical data leads to improved process quality. During daily production runs, the operator can monitor machine production and determine when to make the necessary adjustments to the process or when to leave the process alone to ensure quality production.

Control Charts Variation, where no two items or services are exactly the same, exists in all processes. 1. Within-piece variation, or the variation within a single item or surface. For example, a single square yard of fabric may be examined to see if the color varies from one location to another. 2. Piece-to-piece variation, or the variation that occurs among pieces produced at approximately the same time. For example, in a production run filling gallon jugs with milk, when each of the milk jugs is checked after the filling station, the fill level from jug to jug will be slightly different. 3. Time-to-time variation, or the variation in the product produced at different times of the day—for example, the comparison of a part that has been stamped at the beginning of a production run with the part stamped at the end of a production run.

Control Charts Chance, or common causes are small random changes in the process that cannot be avoided. These small differences are due to the inherent variation present in all processes. They consistently affect the process and its performance day after day, every day. Variation of this type is only removable by making a change in the existing process. Removing chance causes from a system usually involves management intervention.

Control Charts Assignable causes are variations in the process that can be identified as having a specific cause. Assignable causes are causes that are not part of the process on a regular basis. This type of variation arises because of specific circumstances.

Control Charts UCL = Process Average + 3 Standard Deviations
LCL = Process Average - 3 Standard Deviations X UCL + 3 Process Average - 3 LCL TIME

Basic Principles General model for a control chart UCL = μ + kσ CL = μ
LCL = μ – kσ where μ is the mean of the variable, and σ is the standard deviation of the variable. UCL=upper control limit; LCL = lower control limit; CL = center line. where k is the distance of the control limits from the center line, expressed in terms of standard deviation units. When k is set to 3, we speak of 3-sigma control charts. Historically, k = 3 has become an accepted standard in industry. (Proposed by Walter A. Shewhart in1920’s)

Control Charts Graph of sample data plotted over time UCL LCL
Assignable Cause Variation Graph of sample data plotted over time UCL Process Average  Mean LCL Random Variation

Basic Principles of Control Charts
Types of the control charts Variables control charts Variable data are measured on a continuous scale. For example: time, weight, distance or temperature can be measured in fractions or decimals. Applied to data with continuous distribution Attributes control charts Attribute data are counted and cannot have fractions or decimals. Attribute data arise when you are determining only the presence or absence of something: success or failure, accept or reject, correct or not correct. For example, a report can have four errors or five errors, but it cannot have four and a half errors. Applied to data following discrete distribution

Control Charts Variables Control Charts

Individual Control Charts
is a control chart of individual observations. Use individuals charts to track the process level and detect the presence of special causes when the sample size is 1 Difficult or impossible to group measurements into subgroups Measurements are expensive, production volume is low, or products have a long cycle time. The moving range is an alternative way to calculate process variation by computing the ranges of two or more consecutive observations

Individual Control Charts

Exercise 6 The data were taken from the machine, measuring overall flow rate of oil . Calculate the control limits and comment on the process.

Exercise 6

Process Out Of Control A point falls outside control limits
assignable cause present process producing subgroup avg. not from stable process must be investigated, corrected

Process Out Of Control Unnatural runs of variation even within 3 limits 7 or more points above or below center line (in a row) 10 out of 11 points on one side 12 out of 14 points on one side 6 points increasing/decreasing 2 out of 3 in Zone A (WL) 4 out of 5 in Zone B

Process Out Of Control 3. For two zones 1.5 each
2 or more points beyond 1.5

ANALYSIS FOR OUT-OF-CONTROL
Patterns 1. Change/Jump in level shift in mean Causes - process parameters change, diff / new operator, change in raw material 2. Trend or steady change in level drifting mean – common, upward or downward direction tool wear, gradual change in temp. viscosity of chemical used

ANALYSIS FOR OUT-OF-CONTROL
3. Recurring cycles wavy, periodic high & low points seasonal effects. Recurring effects of temp., humidity (morning vs evening) 4. Two populations (mixture) many points near or outside limits due to large difference in material quality 2 or more machines different test method mtls from different supplier

Test for special causes k
POLYTECHNIC OF NAMIBIA Test for special causes k 1 point more than K standard deviations from center line K points in a row on same side of center line K points in a row, all increasing or all decreasing K points in a row, alternating up and down K out of K + 1 points > 2 standard deviations from center line (same side) K out of K + 1 points > 1 standard deviation from center line (same side) K points in a row within 1 standard deviation of center line (either side) K points in a row > 1 standard deviation from center line (either side)

x (average)- R chart

x (average)- R chart Subgroup exists Subgroup size less than 10

Variable Control Chart – x (average)- R chart
1. Select quality characteristic Measurable data (basic units, length, mass, time, etc.) Affecting performance, function of product From Pareto analysis – highest % rejects, high production costs Impossible to control all characteristics - selective or use attributes chart

2. Choose rational subgroup Rational subgroup - variation within the group can be detected between groups changes Two ways selecting subgroup samples Select subgroup samples at one instant of time or as close as possible Select period of time products are produced

Rational subgroup from homogeneous lot : same machine, same operator Decisions on size of sample empirical judgment + relates to costs choose n = 4 or 5  use R-chart when n  10  use s-chart frequency of taking subgroups often enough to detect process changes Guideline of sample sizes/frequency using Say, 4000 parts/day 75 samples if n = 4  19 subgroups or n = 5 15 subgroups

3. Collect data Use form or standard check sheet
Collect a minimum of 25 subgroups Data can be vertically / horizontally arranged Subgroup Number Measure 1 2 3 4 5 …… ….. …. 25 x1 x2 x3 x4 x5 35 40 32 37 34 38 x 35.6 37.0 R 8 6

4. Determine trial control limits
Calculate Central line X = R = X = avg. of subgroup avg. xi = avg. of ith subgroup g = no. of subgroups R = avg. of subgroup ranges Ri = range of ith subgroup Where A2, D4, D3 are factors - vary according to different n

5. Revised Control Limits
First plot preliminary data collected using control limits & center lines established in step 4 Use/adopt standard values, if good control i.e. no out-of-control points If there are points out-of-control discard from data, look at records – if show an assignable cause – don’t use

Exercise 8 You work at an automobile engine assembly plant. One of the parts, a camshaft, must be 600 mm +2 mm long to meet engineering specifications. There has been a chronic problem with camshaft length being out of specification, which causes poor-fitting assemblies, resulting in high scrap and rework rates. Your supervisor wants to run X and R charts to monitor this characteristic, so for a month, you collect a total of 100 observations (20 samples of 5 camshafts each) from all the camshafts used at the plant, and 100 observations from each of your suppliers.

x bar- s control chart

Sample Std. Deviation Chart (x - s control chart )
Both R and s measure dispersion of data R chart - simple, only use XH (highest) and XL(lowest) s chart - more calculation - use ALL xi’s  more accurate, need calculate sub-group sample standard deviation When n <= 10 R chart  s chart n  10 - s chart better , R not accurate any more

Exercise 9 You are conducting a study on the CTQ of the diameter of shaft. 20 samples with sub group 10 is drawn. Calculate the process mean and Standard deviation. Find the control limits for the X- and s-charts.

be used for categorical variables.
Control Charts Charts may be used for categorical variables. [i.e.: attributes]

Preliminary decisions on Attribute or variable
For situations in which summary measures are required, attribute charts are preferred. Information about the output at the plant level is often best described by proportion-nonconforming charts or charts on the number of nonconformities. These charts are effective for providing information to upper management. On the other hand, variable charts are more meaningful at the operator or supervisor level because they provide specific clues for remedial actions.

Preliminary decisions on sample size
The choice of sample size for attribute charts is important. process has a nonconformance rate of 2.5%, a sample size of 25 is not sufficient because with this sample size nonconforming items per sample is only A sample size of 100 here is sufficient, as the average number of nonconforming items per sample would thus be 2.5

Cautionary Caveat: Sigma limits
One, two, or three-sigma zones and rules pertaining to these zones will not be used because the underlying distribution theory is non normal.

Control Charts Counts/ defects Sample size constant C- chart
Sample size not constant u chart

Sample size not constant U chart

C chart A nonconformity is defined as a quality characteristic that does not meet some specification. A nonconforming item has one or more nonconformities that make it nonfunctional. A c-chart is used to track the total number of nonconformities in samples of constant size. The area of opportunity may be single or multiple units of a product (e.g., 1 TV set or a collection of 10 TV sets). For items produced on a continuous basis, the area of opportunity could be 100 m2 of fabric or 50 m2 of paper

C chart

C chart The occurrence of nonconformities is assumed to follow a Poisson distribution. This distribution is well suited to modeling the number of events that happen over a specified amount of time, space, or volume. x represents the number of nonconformities in the sample unit and c is the mean p(x) represents the probability of observing x nonconformities. Poisson distribution, the mean and the variance are equal

Control Charts

Exercise 10 Samples of fabric from a textile mill, each 100 m2 , are selected, and the number of occurrences of foreign matter are recorded. Data for 25 samples are given in data file. Construct a c-chart for the number of nonconformities. What proportion of items will fall within the control limits.

Hypothesis Testing Goal: Keep a, b reasonably small

Probability Limits The 3σ limits, shown previously, are not necessarily symmetrical. This means that the probability of an observation falling outside either control limit may not be equal. Suppose that the process mean is c0 and symmetrical control limits are desired for type I error of α.

Sample size not constant µ chart

u chart If the area of opportunity changes from one sample to another, the centerline and control limits of a c-chart change as well. Sample size varies, u-chart is used The output per production run can vary because of fluctuating supplies of labor, machinery, and raw material; consequently, the number inspected per production run changes, thus causing varying sample sizes

u chart

Control Charts

Exercise 12 The number of nonconformities in carpets is determined for 20 samples, but the amount of carpet inspected for each sample varies. Results of the inspection are shown in Table Construct a control chart for the number of nonconformities per 100 m2

Control Charts defectives proportion p chart np chart
Number of defectives

P chart A chart for the proportion of nonconforming items (p-chart) is based on a binomial distribution. where x is the number of nonconforming items in the sample and n represents the sample size.

P chart A p-chart is one of the most versatile control charts.
Used to control the acceptability of a single quality characteristic (say, the width of a part), a group of quality characteristics of the same type or on the same part (the length, width, or height of a component), or an entire product can be used to measure the quality of an operator or machine, a work center, a department, or an entire plant. p-chart provides a fair indication of the general state of the process by depicting the average quality level of the proportion nonconforming.

P chart

Control Charts

Ex 13 Twenty-five samples of size 50 are chosen from a plastic-injection molding machine producing small containers. The number of nonconforming containers for each sample is shown . Plot the p chart and comment. Management has decided to set a standard of 7% for the proportion

Ex 14 Twenty random samples are selected from a process that makes vinyl tiles. The sample size as well as the number of conforming tiles are shown in Table. Comment on the process

Control Charts defectives proportion p chart np chart
Number of defectives

NP Chart In processes for which 100% inspection is conducted to estimate the proportion nonconforming, a change in the rate of production may cause the sample size to change. A change in sample size causes the control limits to change, although the centerline remains fixed. As the sample size increases, the control limits become narrower. As stated previously, the sample size is also influenced by the existing average process quality level.

NP Chart

Ex 14i You work in a toy manufacturing company and your job is to inspect the number of defective bicycle tires. You inspect 200 samples in each lot and then decide to create an NP chart to monitor the number of defectives. To make the NP chart easier to present at the next staff meeting, you decide to split the chart by every 10 inspection lots.

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