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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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Chapter 14

Statistical

Process

Control

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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


Shift in Process Average

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


Identifying Potential Shifts

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


Cycles

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


Trend

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


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


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


Process Capability Calculations

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


Spreadsheet Template

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


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


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


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


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


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


Control Chart Formulas

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


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


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


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


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


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


Economic Tradeoffs

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


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


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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