# Capability Analysis Using Statgraphics Centurion

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1 Capability Analysis Using Statgraphics Centurion Neil W. Polhemus, CTO, StatPoint Technologies, Inc. Copyright 2011 by StatPoint Technologies, Inc. Web site:

2 Outline Definition of process capability analysis Examples 1. Capability analysis for attributes 2. Estimating capability for variable data 3. Capability indices 4. Statistical tolerance limits 5. Multivariate capability analysis Sample size determination 2

3 Capability Analysis Determination based on data of a process s ability to meet established specifications. Specifications may be stated in terms of variables (such as the tolerance on the diameter of a part) or in terms of attributes (such as the frequency of customer complaints). 3

4 Capability Measurements The essential measure of process capability is DPM (defects per million) or DPMO (defects per million opportunities), defined as the number of times that a process does not meet the specifications out of every million possibilities. DPM may be estimated directly or inferred from statistics such as a capability index or statistical tolerance limit. 4

5 How can we estimate capability using Statgraphics? Direct counting of defects Estimation of DPM from a fitted distribution Indirect inference about DPM from a capability index Demonstration of required capability through a statistical tolerance interval or bound 5

6 Example #1 - defects1.sgd Inspected k=30 batches of n=500 items each. Counted number of defective items. 6

7 Procedure Capability Analysis Percent Defective 7

8 8 Output

9 Conclusions Best estimate for DPM = With 95% confidence, DPM is no greater than 1,377.2 Tolerance limit: 95% of all batches of n=500 items will have no more than 2 defectives Equivalent Z =

10 Example #2 - resistivity.sgd Measured resistivity of n=100 electronic components 10

11 Procedure Capability Analysis Variable Data - Individuals 11

12 12 Selecting Proper Distribution

13 frequency Capability Plot Process Capability for resistivity USL = Largest Extreme Value Mode= Scale= Cpk = 0.85 Ppk = resistivity 13

14 14 Estimate of DPM

15 Capability Indices 15 6ˆ LSL USL C P 3 ˆ ˆ, 3 ˆ ˆ min USL LSL C PK ˆ ˆ, ˆ ˆ min USL LSL Z

16 16 Long-term and Short-term

17 17 Six Sigma Calculator

18 Example #3 - bottles.sgd Measured breaking strength of n=100 glass bottles 18

19 19 Statistical Tolerance Limits

20 20 Tolerance Limit Options

21 frequency Output Fitted Normal Distribution mean=254.64, std. dev.= Limits UTL: LTL: strength 21

22 Conclusions The StatAdvisor Assuming that strength comes from a normal distribution, the tolerance limits state that we can be 95.0% confident that 99.0% of the distribution lies between and This interval is computed by taking the mean of the data +/ times the standard deviation. 22

23 Multivariate Capability Analysis For multiple variables, determines the probability that ALL variables meet their established specification limits. Important when the variables are strongly correlated. 23

24 Example #4 - bivariate.sgd Measurements of height and weight of n=150 items. Specs: height 5 ± 0.3, weight 215 ± 7 24

25 25 Data Input

26 Bivariate Normal Distribution Multivariate Capability Plot DPM = height weight 26

27 weight Capability Ellipse % Capability Ellipse MCP = height 27

28 Multivariate Capability Multivariate capability indices defined to give same relationship with DPM as in univariate case. 28

29 Sample Size Determination - Counting Suppose I wish to estimate DPM to within +/-10% with 95% confidence. 29

30 Sample Size Determination Capability Indices Suppose I wish to estimate Cpk to within +/-10% with 95% confidence. 30 Requires measuring n = 154 items

31 Sample Size Determination Statistical Tolerance Limits 0.04 Normal Distribution Mean=250.0, Std. dev.= n= X 31 A tolerance interval covering 80% of the distance between the spec limits requires a sample of n = 20 items in this case.

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