2. 1 Chapter 6 Statistical Process Control (SPC)

3. 2 Descriptive Statistics 1. Measures of Central Tendencies (Location) Mean Median = The middle value Mode - The most frequent number 2. Measures of Dispersion (Spread) Range R=Maximum-Minimum Standard Deviation Variance

4. 12345678 xxx xx µ ( x-µ) The Standard Deviation

5. River Crossing Problem RiverABC 111 211 336 331 336 331 366 321 221 211 Average2.5 Range255 St Dev0.70711.50922.4152

6. 5 Inferential Statistics Population (N) Parameters Samples (n) Statistics 1. Central Tendency: 2. Dispersion:

7. 6 The Normal (Gaussian) Curve -3  -2  -1  +1  +2  +3  68.26% 95.46% 99.73%

8. 7 Red Bead Experiment

9. 8 Types of Control Charts Quality Characteristic n>6 Variable Attribute Type of Attribute Constant sample size? Constant sampling unit? p-chart np-chart u-chart c-chart X and MR chart X-bar and R chart X-bar and s chart DefectiveDefect Yes No n>1

10. 9 Data Information 1.Central Tendency 2.Dispersion 3.Shape Action Stats Decision No Action

11. 10 The Shape of the Data Distribution mean = median = mode mode mean median Skewed to the right (positively skewed) median mode mean Skewed to the left (negatively skewed) “Box-and-Whisker” Plot Pearsonian Coefficient of Skewness

12. 11 Control Charts +3σ Average -3σ Common Cause (Chance or Random) Special Cause (Assignable) Special Cause (Assignable)

13. 12 Central Limit Theorem Standard Error of the Mean Population (individual) Distribution Sample (x-bar) Distribution μ

14. 13 X-Bar and R Example 1.164.162.161.163.166 2.168.164.167.166.164.165 3.164.166.161.165 4.169.164.163.167 5.168.165.162.164.168X-Double Bar X-Bar.1666.1664.1642.1640.1638.1662.16487R-Bar R.005.006.003.006.003.00483 Rational Subgroup Subgroup Interval

15. 14 X-Bar and R Control Chart Limits nA2A2 D4D4 d2d2 21.8803.2681.128 31.0232.5741.693 4.7292.2822.059 5.5772.1142.326 6.4832.0042.534 UCL x-Bar.16487 + (.577 x.00483) =.1676 LCL x-Bar.16487 - (.577 x.00483) =.1621 UCL R 2.114 x.00483 =.0102

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17. 16 Attribute Control Chart Limits DefectivesDefects Changing Sample Size Fixed Sample Size

18. 17 n235250200250260225270269237240*n-bar = 243.6 p.0766.0600.1100.0200.0462.0667.0815.0409.0820.0417p-bar=.06238 p-Chart Example UCL p LCL p *Note: Use n-bar if all n’s are within 20% of n-bar

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20. 19 The α and β on Control Charts +3σ Average -3σ α =.00135 β β β

21. 20 Out of Control Patterns 2 of 3 successive points outside 2  4 of 5 successive points outside 1  8 successive points same side of centerline -3  33 22 11 -1  -2  Average

22. 21 Control Chart Patterns Gradual Trend “Freaks” Sudden Shifts Cycles Instability “Hugging” Centerline“Hugging Control Limits”

23. 22 Six Sigma Process Capability C p k = 1.5 3.4 ppm USLLSL  1.5  C p = 2.0.54 ppm

24. 23 Cause and Effect Diagram a.k.a. Ishikawa Diagram, Fishbone Diagram Process PersonProcedures MaterialEquipment BCA

25. 24 Pareto Chart a.k.a. 80/20 Rule Vital Few Trivial (Useful) Many

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30. 29 Taguchi Loss Function.500.520.480 The Taguchi Loss Function: L (x) = k (x-T) 2 Loss ($).500.520.480 Traditional Loss Function: Loss ($)

31. 30 Response Curves Most “Robust” Setting