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

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 1. Prepare  Choose measurement  Determine how to collect data, sample size, and frequency of sampling  Set up an initial control chart 2. Collect Data  Record data  Calculate appropriate statistics  Plot statistics on chart

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10 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

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MANAGING FOR QUALITY AND PERFORMANCE EXCELLENCE, 7e, © 2008 Thomson Higher Education Publishing 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 5. Use as a problem-solving tool  Continue to collect and plot data  Take corrective action when necessary 6. 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

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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 variableattribute n>1? n>=10 or computer? x and MR no yes x and s x and R no yes defectivedefect constant sample size? p-chart with variable sample size no p or np yes constant sampling unit? c u yesno

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.

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

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

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 If the process mean tends to drift, then Cp should be higher.