Chapter 14 Statistical Process Control MANAGING FOR QUALITY

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

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, 7 e, © 2008 Thomson Higher Education Publishing 2

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, 7 e, © 2008 Thomson Higher Education Publishing 3

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, 7 e, © 2008 Thomson Higher Education Publishing 4

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, 7 e, © 2008 Thomson Higher Education Publishing 5

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

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, 7 e, © 2008 Thomson Higher Education Publishing 7

Developing Control Charts 1. Prepare ® ® ® 2. 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, 7 e, © 2008 Thomson Higher Education Publishing 8

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Next Steps 3. Determine trial control limits ® Center line (process average) ® Compute UCL, LCL 4. Analyze and interpret results ® Determine if in control ® Eliminate out-of-control points ® Recompute control limits as necessary MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7 e, © 2008 Thomson Higher Education Publishing 10

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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, 7 e, © 2008 Thomson Higher Education Publishing 15

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, 7 e, © 2008 Thomson Higher Education Publishing 16

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

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

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

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

Final Steps 5. 6. 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, 7 e, © 2008 Thomson Higher Education Publishing 21

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

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

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

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

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, 7 e, © 2008 Thomson Higher Education Publishing 27

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

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, 7 e, © 2008 Thomson Higher Education Publishing 29

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

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

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

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, 7 e, © 2008 Thomson Higher Education Publishing 33

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, 7 e, © 2008 Thomson Higher Education Publishing 34

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

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

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, 7 e, © 2008 Thomson Higher Education Publishing 38