Module 12Module 12

Statistical Process Control

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QuizQuizAccuracy: The degree of closeness of measurements of a quantity to that quantity's actual (true) value. Precision:The degree to which repeated measurements under unchanged conditions show the same results.

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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

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Common Causes

Special Causes

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Histograms do not take into account changes over time.

Control charts can tell us when a process changes

Control Chart Applications

• Establish state of statistical control• Monitor a process and signal when it

goes out of control• Determine process capability

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Capability Versus Control

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Control

Capability

Capable

Not Capable

In Control Out of Control

IDEAL

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)

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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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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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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

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Shift in Process Average

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Identifying Potential Shifts

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Cycles

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Trend

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Final Steps

5. Use as a problem-solving tool– Continue to collect and plot data– Take corrective action when

necessary

6. Compute process capability

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Process Capability Calculations

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Excel Template

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Special Variables Control Charts

• x-bar and s charts• x-chart for individuals

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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

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Control Chart Selection

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Quality Characteristicvariable attribute

n>1?

n>=10 or computer?

x and MRno

yes

x and s

x and Rno

yes

defective defect

constant sample size?

p-chart withvariable samplesize

no

p ornp

yes constantsampling unit?

c u

yes no

Control Chart Design Issues

• Basis for sampling• Sample size• Frequency of sampling• Location of control limits

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Pre-Control

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nominal value

Green Zone

Yellow Zones

RedZone

RedZone

LTL UTL

SPC Implementation Requirements

• Top management commitment• Project champion• Initial workable project• Employee education and training• Accurate measurement system

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