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Chapter 8 Alternatives to Shewhart Charts

Chapter 8 Alternatives to Shewhart Charts. Introduction. The Shewhart charts are the most commonly used control charts. Charts with superior properties have been developed.

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Chapter 8 Alternatives to Shewhart Charts

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  1. Chapter 8Alternatives to Shewhart Charts

  2. Introduction • The Shewhart charts are the most commonly used control charts. • Charts with superior properties have been developed. • “In many cases the processes to which SPC is now applied differ drastically from those which motivated Shewhart’s methods.”

  3. 8.1 Introduction with Example

  4. 8.2 Cumulative Sum Procedures:Principles and Historical Development

  5. Cusum Example N(0,1) N(0.5,1)

  6. Cusum Example

  7. Runs Criteria and their Impacts • Runs Criteria • 2 out of 3 beyond the warning limits (2-sigma limits) • 4 out of 5 beyond the 1-sigma limits • 8 consecutive on one side • 8 consecutive points on one side of the center line. • 8 consecutive points up or down across zones. • 14 points alternating up or down. • Somewhat impractical • Very short in-control ARL (~91.75 with all run rules)

  8. Cusum Procedures (8.1) (8.3)

  9. Cusum Example(Table 8.2)

  10. Cusum Example

  11. ARL for Cusum Procedure(Table 8.3)

  12. 8.2.2 Fast Initial Response Cusum

  13. FIR Cusum vs Cusum(Table 8.4) N(0.5,1)

  14. FIR Cusum vs Cusum(Table 8.5) N(0,1)

  15. Table 8.6 ARL for Various Cusum Schemes (h=5, k=.5)

  16. 8.2.3 Combined Shewhart-Cusum Scheme

  17. 8.2.4 Cusum with Estimated Parameters • Parameter estimates based on a small amount of data can have a very large effect on the Cusum procedures.

  18. 8.2.5 Computation of Cusum ARLs

  19. 8.2.6 Robustness of Cusum Procedures (8.4)

  20. 8.2.7 Cusum Procedures for Individual Observations

  21. 8.3 Cusum Procedures for Controlling Process Variability

  22. (8.5)

  23. 8.4 Applications of Cusum Procedures • Cusum charts can be used in the same range of applications as Shewhart charts can be used in a wide variety of manufacturing and non-manufacturing applications.

  24. 8.6 Cusum Procedures for Non-conforming Units (8.6) (8.7)

  25. 8.6 Cusum Procedures for Non-conforming Units: Example

  26. 8.6 Cusum Procedures for Non-conforming Units: Example

  27. 8.7 Cusum Procedures for Non-conformity Data

  28. 8.7 Cusum Procedures for Non-conformity Data: Example

  29. 8.7 Cusum Procedures for Non-conformity Data: Example

  30. 8.7 Cusum Procedures for Non-conformity Data • The z-values differ considerably at the two extremes: c15 and c2

  31. 8.8 Exponentially Weighted Moving Average Charts • Exponentially Weighted Moving Average (EWMA) chart is similar to a Cusum procedure in detecting small shifts in the process mean.

  32. 8.8.1 EWMA Chart for Subgroup Averages (8.9) (8.10)

  33. 8.8.1 EWMA Chart for Subgroup Averages (8.11)

  34. 8.8.1 EWMA Chart for Subgroup Averages • Selection of L (L-sigma limits), , and n: • For detecting a 1-sigma shift, L = 3.00,  = 0.25 • Comparison with Cusum charts • Computation requirement: About the same • EWMA are scale dependent, SH and SL are scale independent • If the EWMA has a small (large) value and there is an increase (decrease) in the mean, the EWMA can be slow in detecting the change. • Recommendation of using EWMA charts with Shewhart limits

  35. Table 8.12 EWMA Chart for Subgroup Averages: Example

  36. 8.8.2 EWMA Misconceptions

  37. 8.8.3 EWMA Chart for Individual Observations (8.9)’ (8.10)’

  38. 8.8.4 Shewhart-EWMA Chart • EWMA chart is good for detecting small shifts, but is inferior to a Shewhart chart for detecting large shifts. • It is desirable to combine the two. The general idea is to use Shewhart limits that are larger than 3-sigma limits.

  39. 8.8.6 Designing EWMA Charts with Estimated Parameters • The minimum sample size that will result in desirable chart properties should be identified for each type of EWMA control chart. • As many as 400 in-control subgroups may be needed if  = 0.1.

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