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Chapter 14 – Statistical Process Control (SPC)

Control charts for variables and for

attributes, special control charts, control vs. process capability

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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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Variation (from Chapter 11)

Many sources of uncontrollable variation exist (common = chance = random causes)

Special (assignable = special = non-random) causes of variation can be recognized and controlled

Failure to understand these differences can increase variation in a system “Tweaking” a process that is in control (common)

Ignoring a process that is out of control (special)

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Common Causes

Special Causes

Common Causes vs.Special Causes

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Histograms do not take into account changes over time.

Control charts can tell us when a process changes

Histograms

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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

Process capability (Cp or Cpk) Measure of variability against design specifications

Specs set by customer or design engineer Spec width: USL & LSL (or UTL & LTL)

Statistical process control (SPC) Measure of variability against control limits

Control limits calculated from sample data

UCL and LCL

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Capability Versus Control

Control

Capability

Capable

Not Capable

In Control Out of Control

IDEAL

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Commonly Used Control Charts

Variables data x-bar (mean) and R- (range) charts x-bar and s- (standard deviation) charts

Charts for individuals (x-charts) Moving range 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 chart2. Collect Data

Record data Calculate appropriate statistics Plot statistics on chart

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Next Steps3. 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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Mean & Range Control Charts

Take required number of samples Mean (X-bar) charts (see Appendix B)

Calculate mean (X-bar) for each sample Calculate grand mean (X-double-bar) Calculate range (R) for each sample Calculate mean of all sample ranges (R-bar) Calculate UCL and LCL for means Plot grand mean and control limits on X-bar chart

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Mean & Range Control Charts

Range (R) charts (see Appendix B) Calculate UCL and LCL for ranges Plot range mean and control limits on R- chart

Plot additional samples and determine if within range limits

Note: factors based on the size of each sample, not the number of samples!

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Mean (X-bar) Chart Control Limits

UCLX-bar = X-double-bar + A2 (R-bar) LCLX-bar = X-double-bar - A2 (R-bar)

Where X-double-bar = the grand mean,And R-bar = the mean of the sample ranges

And A2 = the value in Appendix B for n

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Range (R) Chart Control Limits

UCLR = D4 (R-bar) LCLR = D3 (R-bar)

Where R-bar = the mean of the sample ranges, and D4 and D3 = the values in Appendix B for n

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Typical Out-of-Control Patterns

Point outside control limits Stop the process!

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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CyclesTHE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson LearningTM

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Trend

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Final Steps5. Use as a problem-solving

tool Continue to collect and plot

data Take corrective action when

necessary6. Compute process capability

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SPC Control Limit Calculations

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Excel Template

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Special Variables Control Charts

x-bar and s-charts Use standard deviation (s) chart in place of R-chart

For each sample: s = ((x – x-bar)2/n-1) For k samples: s-bar = s/k UCLs = B4(s-bar), LCLs = B3(s-bar) Use s-bar rather than r-bar for x-bar calculations

x-chart, moving range charts for individuals x-chart: automated 100% inspection, n = 1 Moving range: better process variability measure

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Charts for Attributes Fraction nonconforming (defective)

p-chart (proportion or percentage chart) Fixed sample size Variable sample size (units produced varies)

np-chart for number nonconforming Fraction x sample size

Charts for defects c-chart (total number of defects/unit) u-chart (average number of defects/unit)

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Control Chart Formulas

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Control Chart Selection

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

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Control Chart Design Issues

Basis for sampling (homogeneous samples)

Sample size (n usually = 3 to 10) Frequency of sampling (cost vs. risk) Location of control limits

Type I vs. Type II risk analysis Cost vs. risk again!

Number of samples (k usually = 25 to 30)

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Sample size and detecting shift

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Pre-Control

nominal value

Green Zone

Yellow Zones

RedZone

RedZone

LTL UTL

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SPC Implementation Requirements

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

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