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Statistical Process Control: Monitoring and Corrective Action

Statistical Process Control (SPC) is a methodology for monitoring a process, identifying special causes of variation, and taking corrective action when necessary. This chapter explores the use of control charts, the different types of control charts, and how to develop and interpret them.

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Statistical Process Control: Monitoring and Corrective Action

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  1. Chapter 14 The Management & Control of Quality, 7e Statistical Process Control

  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

  3. Histograms vs. Control Charts • Histograms do not take into account changes over time. • Control charts can tell us when a process changes

  4. Control Chart Applications • Establish state of statistical control • Monitor a process and signal when it goes out of control • Determine process capability

  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.

  6. Control In Control Out of Control Capability Capable Not Capable IDEAL Capability Versus Control

  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)

  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

  9. 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

  10. 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.

  11. 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

  12. Shift in Process Average

  13. Identifying Potential Shifts

  14. Cycles

  15. Trend

  16. Final Steps • Use as a problem-solving tool • Continue to collect and plot data • Take corrective action when necessary • Compute process capability

  17. Key Idea Control charts indicate when to take action, and more importantly, when to leave a process alone.

  18. Process Capability Calculations

  19. Spreadsheet Template

  20. Special Variables Control Charts • x-bar and s charts • x-chart for individuals

  21. 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.

  22. 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

  23. 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.

  24. Control Chart Formulas

  25. 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

  26. Control Chart Design Issues • Basis for sampling • Sample size • Frequency of sampling • Location of control limits

  27. 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.

  28. 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.

  29. Economic Tradeoffs

  30. LTL UTL Red Zone Red Zone Green Zone nominal value Yellow Zones Pre-Control

  31. 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.

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