Presentation on theme: "Chapter 9A Process Capability and Statistical Quality Control"— Presentation transcript:
1 Chapter 9A Process Capability and Statistical Quality Control Process VariationProcess CapabilityProcess Control ProceduresVariable dataAttribute dataAcceptance SamplingOperating Characteristic Curve
2 Basic Causes of Variation Assignable causes are factors that can be clearly identified and possibly managed.Common causes are inherent to the production process. In order to reduce variation due to common causes, the process must be changed.Key: Determining which is which!
3 Types of Control Charts Attribute (Go or no-go information)Defectives refers to the acceptability of product across a range of characteristics.p-chart applicationVariable (Continuous)Usually measured by the mean and the standard deviation.X-bar and R chart applications
4 Types of Statistical Quality Control ProcessProcessAcceptanceAcceptanceControlControlSamplingSamplingVariablesVariablesAttributesAttributesVariablesVariablesAttributesAttributesChartsChartsChartsCharts
5 Excellent review in exhibit TN8.5. Statistical Process Control (SPC) ChartsUCLLCLSamples over timeNormal BehaviorLook for trends!UCLLCLSamples over timePossible problem, investigateExcellent review in exhibit TN8.5.UCLLCLSamples over timePossible problem, investigate
6 Control LimitsWe establish the Upper Control Limits (UCL) and the Lower Control Limits (LCL) with plus or minus 3 standard deviations. Based on this we can expect 99.7% of our sample observations to fall within these limits.xLCLUCL99.7%
7 Example of Constructing a p-Chart: Required Data SampleSample sizeNumber of defectives
8 Statistical Process Control Formulas: Attribute Measurements (p-Chart) Given:Compute control limits:
9 Example of Constructing a p-chart: Step 1 1. Calculate the sample proportions, p (these are what can be plotted on the p-chart) for each sample.
10 Example of Constructing a p-chart: Steps 2&3 2. Calculate the average of the sample proportions.3. Calculate the standard deviation of the sample proportion
11 Example of Constructing a p-chart: Step 4 4. Calculate the control limits.UCL =LCL = (0)
12 Example of Constructing a p-Chart: Step 5 5. Plot the individual sample proportions, the averageof the proportions, and the control limits
13 R Chart Type of variables control chart Shows sample ranges over time Interval or ratio scaled numerical dataShows sample ranges over timeDifference between smallest & largest values in inspection sampleMonitors variability in processExample: Weigh samples of coffee & compute ranges of samples; Plot
14 R Chart Control Limits From Table (function of sample size) Sample Range in sample i# Samples
15 R Chart ExampleYou’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control?
16 R Chart Hotel Data Sample Day Delivery Time Mean Range Sample Mean =
17 R Chart Hotel Data Sample Day Delivery Time Mean Range LargestSmallestSample Range =
18 R Chart Hotel Data Sample Day Delivery Time Mean Range
19 R Chart Control Limits Solution From Table (n = 5)
21 X Chart Type of variables control chart Shows sample means over time Interval or ratio scaled numerical dataShows sample means over timeMonitors process averageExample: Weigh samples of coffee & compute means of samples; Plot
22 X Chart Control Limits From TableMean of sample iRange of sample i# Samples
23 X Chart ExampleYou’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control?
24 X Chart Hotel Data Sample Day Delivery Time Mean Range
25 X Chart Control Limits Solution* From Table(n = 5)
27 X AND R CHART EXAMPLE IN-CLASS EXERCISE The following collection of data represents samples of the amount of force applied in a gluing process:Determine if the process is in controlby calculating the appropriate upper and lowercontrol limits of the X-bar and R charts.
29 Example of x-bar and R charts: Step 1 Example of x-bar and R charts: Step 1. Calculate sample means, sample ranges, mean of means, and mean of ranges.
30 Example of x-bar and R charts: Step 2 Example of x-bar and R charts: Step 2. Determine Control Limit Formulas and Necessary Tabled Values
31 Example of x-bar and R charts: Steps 3&4 Example of x-bar and R charts: Steps 3&4. Calculate x-bar Chart and Plot Values
32 Example of x-bar and R charts: Steps 5&6: Calculate R-chart and Plot Values
33 SOLUTION: Example of x-bar and R charts: 1. Is the process in Control?2. If not, what could be the cause for the process being out of control?
34 Process CapabilityProcess limits - actual capabilities of process based on historical dataTolerance limits - what process design calls for - desired performance of process
35 Process Capability How do the limits relate to one another? You want: tolerance range > process range1. Make bigger2. Make smallerTwo methods of accomplishing this:Implies having greater control over processÞ Good!Bad idea
36 Process Capability Measurement Cp index = Tolerance range / Process rangeWhat value(s) would you like for Cp?Þ Larger Cp indicates a more reliable and predictable process (less variability)The Cp index is based on the assumption that the process mean is centered at the midpoint of the tolerance range
39 While the Cp index provides useful information on process variability, it does not give information on the process average relative to the tolerance limits. Note:LTLUTL
40 Cpk Index = process mean (Unknown but can be estimated Refers to the LTLRefers to the UTL= process mean (Unknown but can be estimatedwith the grand mean)s = standard deviation (Unknown but can beestimated with the average range)Together, these process capability Indices show how well parts being produced conform to design specifications.
41 Since Cp and Cpk are different we can conclude that the process is not centered, however the Cp index tells us that the process variability is very lowLTLUTL
42 An example of the use of process capability indices The design specifications for a machined slot is 0.5± .003 inches. Samples have been taken and the process mean is estimated to be The process standard deviation is estimated to be .001.What can you say about the capability of this process to produce this dimension?
44 Sampling Distributions (The Central Limit Theorem) Regardless of the underlying distribution, if the sample is large enough (>30), the distribution of sample means will be normally distributed around the population mean with a standard deviation of :
45 Computing Process Capability Indexes Using Control Chart Data Recall the following info from our in class exercise:Since A2 is calculated on the assumption of three sigma limits:
47 Suppose the Design Specs for the Gluing Process were 10. 7 Suppose the Design Specs for the Gluing Process were 10.7 .2, Calculate the Cp and Cpk Indexes:Answer:
48 Note, multiplying each component of the Cpk calculation by 3 yields a Z value. You can use this to predict the % of items outside the tolerance limits:From Appendix E we would expect:= .044 or 4.4%non-conforming product from this process.792 * 3 = 2.38.597 * 3 = 1.79.008 or .8% of the curve.036 or 3.6% of the curve
49 Capability Index – In Class Exercise You are a manufacturer of equipment. A drive shaft is purchased from a supplier close by. The blueprint for the shaft specs indicate a tolerance of 5.5 inches ± .003 inches. Your supplier is reporting a mean of inches. And a standard deviation of inches.What is the Cpk index for the supplier’s process?
51 Your engineering department is sent to the supplier’s site to help improve the capability on the shaft machining process. The result is that the process is now centered and the CP index is now On a percentage basis, what is the improvement on the percentage of shafts which will be unusable (outside the tolerance limits)?
52 To answer this question we must determine the percentage of defective shafts before and after the intervention from our engineering department
53 Before: From Table From Table .004 .089 Total % outside (3x.88) =2.67s3x.444 = 1.33sTotal % outsideTolerance = = .093 or 9.3%-4
54 AfterSince the process is centered then Cpk = Cp; Cp = UTL-LTL / 6s, so the tolerance limits are .75 x 6s = 4.5s apart each 2.25s from the meanFrom Table.0122.25s2.25sSo % outside ofTolerance =.012(2) = .024Or 2.4%-4
55 So the percentage decrease in defective parts is 1 – (2.4/9.3) = 74%
57 Basic Forms of Statistical Sampling for Quality Control Sampling to accept or reject the immediate lot of product at hand (Acceptance Sampling).Sampling to determine if the process is within acceptable limits (Statistical Process Control)
58 Acceptance Sampling Purposes Advantages Determine quality level Ensure quality is within predetermined levelAdvantagesEconomyLess handling damageFewer inspectorsUpgrading of the inspection jobApplicability to destructive testingEntire lot rejection (motivation for improvement)
59 Acceptance Sampling Disadvantages Risks of accepting “bad” lots and rejecting “good” lotsAdded planning and documentationSample provides less information than 100-percent inspectionNo information is obtained on the process. Just sorting “good” parts from “bad” parts
60 Risk Acceptable Quality Level (AQL) a (Producer’s risk) Max. acceptable percentage of defectives defined by producer.a (Producer’s risk)The probability of rejecting a good lot.Lot Tolerance Percent Defective (LTPD)Percentage of defectives that defines consumer’s rejection point. (Consumer’s risk)The probability of accepting a bad lot.