1 Chapter 14 StatisticalProcessControl The Management & Control of Quality, 7e

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 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 SPC relies on control charts

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 Establish state of statistical control Monitor a process and signal when it goes out of control Monitor a process and signal when it goes out of control Determine process capability Determine process capability

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

7 Commonly Used Control Charts Variables data Variables data –x-bar and R-charts –x-bar and s-charts –Charts for individuals (x-charts) Attribute data Attribute data –For “defectives” (p-chart, np-chart) –For “defects” (c-chart, u-chart)

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

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

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.

16 Typical Out-of-Control Patterns Point outside control limits Point outside control limits Sudden shift in process average Sudden shift in process average Cycles Cycles Trends Trends Hugging the center line Hugging the center line Hugging the control limits Hugging the control limits Instability Instability

Shift in Process Average

Identifying Potential Shifts

Cycles

Trend

Final Steps 5. Use as a problem-solving tool –Continue to collect and plot data –Take corrective action when necessary 6. Compute process capability

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

Process Capability Calculations

Spreadsheet Template Spreadsheet Template

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

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.

Charts for Attributes Fraction nonconforming (p-chart) Fraction nonconforming (p-chart) –Fixed sample size –Variable sample size np-chart for number nonconforming np-chart for number nonconforming Charts for defects Charts for defects –c-chart –u-chart

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.

Control Chart Formulas

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

32 Control Chart Design Issues Basis for sampling Basis for sampling Sample size Sample size Frequency of sampling Frequency of sampling Location of control limits Location of control limits

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.

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.

Economic Tradeoffs

37 Pre-Control nominal value Green Zone Yellow Zones Red Zone Red Zone LTLUTL

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.