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Chapter 14

Chapter 14 Statistical Process Control Statistical Process Control (SPC) A methodology for monitoring a process to identify special causes of variation and signal the need to take corrective action when appropriate SPC relies on control charts Histograms vs. Control Charts

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Chapter 14

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  1. Chapter 14 Statistical Process Control MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  2. Statistical Process Control (SPC) • A methodology for monitoring a process to identify special causes of variation and signal the need to take corrective action when appropriate • SPC relies on control charts MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  3. Histograms vs. Control Charts • Histograms do not take into account changes over time. • Control charts can tell us when a process changes MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  4. Control Chart Applications • Establish state of statistical control • Monitor a process and signal when it goes out of control • Determine process capability MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  5. Key Idea Process capability calculations make little sense if the process is not in statistical control because the data are confounded by special causes that do not represent the inherent capability of the process. MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  6. Control In Control Out of Control Capability Capable Not Capable IDEAL Capability Versus Control MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  7. Commonly Used Control Charts • Variables data • x-bar and R-charts • x-bar and s-charts • Charts for individuals (x-charts) • Attribute data • For “defectives” (p-chart, np-chart) • For “defects” (c-chart, u-chart) MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  8. Developing Control Charts • Prepare • Choose measurement • Determine how to collect data, sample size, and frequency of sampling • Set up an initial control chart • Collect Data • Record data • Calculate appropriate statistics • Plot statistics on chart MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

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  10. Next Steps • Determine trial control limits • Center line (process average) • Compute UCL, LCL • Analyze and interpret results • Determine if in control • Eliminate out-of-control points • Recompute control limits as necessary MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

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  15. Key Idea When a process is in statistical control, the points on a control chart fluctuate randomly between the control limits with no recognizable pattern. MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  16. Typical Out-of-Control Patterns • Point outside control limits • Sudden shift in process average • Cycles • Trends • Hugging the center line • Hugging the control limits • Instability MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  17. Shift in Process Average MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  18. Identifying Potential Shifts MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  19. Cycles MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  20. Trend MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  21. Final Steps • Use as a problem-solving tool • Continue to collect and plot data • Take corrective action when necessary • Compute process capability MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  22. Key Idea Control charts indicate when to take action, and more importantly, when to leave a process alone. MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  23. Process Capability Calculations MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  24. Spreadsheet Template MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  25. MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  26. Special Variables Control Charts • x-bar and s charts • x-chart for individuals MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  27. Key Idea Control charts for individuals offer the advantage of being able to draw specifications on the chart for direct comparison with the control limits. MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  28. Charts for Attributes • Fraction nonconforming (p-chart) • Fixed sample size • Variable sample size • np-chart for number nonconforming • Charts for defects • c-chart • u-chart MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  29. Key Idea Confusion often exists over which chart is appropriate for a specific application, because the c- and u-charts apply to situations in which the quality characteristics inspected do not necessarily come from discrete units. MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  30. Control Chart Formulas MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  31. Control Chart Selection Quality Characteristic variable attribute defective defect no n>1? x and MR constant sampling unit? yes constant sample size? yes p or np no n>=10 or computer? x and R yes no no yes p-chart with variable sample size c u x and s MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  32. Control Chart Design Issues • Basis for sampling • Sample size • Frequency of sampling • Location of control limits MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  33. Key Idea In determining the method of sampling, samples should be chosen to be as homogeneous as possible so that each sample reflects the system of common causes or assignable causes that may be present at that point in time. MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  34. Key Idea In practice, samples of about five have been found to work well in detecting process shifts of two standard deviations or larger. To detect smaller shifts in the process mean, larger sample sizes of 15 to 25 must be used. MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

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  36. Economic Tradeoffs MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  37. LTL UTL Red Zone Red Zone Green Zone nominal value Yellow Zones Pre-Control MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

  38. Key Idea Pre-control is not an adequate substitute for control charts and should only be used when process capability is no greater than 88 percent of the tolerance, or equivalently, when Cp is at least 1.14. If the process mean tends to drift, then Cp should be higher. MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing

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