1. Theoretical Basis for Statistical Process Control (SPC)
Dr. Joan Burtner
Certified Quality Engineer
Associate Professor of
Industrial Engineering and Industrial Management

2. Overview Introduction to SPC Construction of Control Charts
Objectives
Theory of Process Variation
Rational Subgroups
Types of Control Charts
Construction of Control Charts
Control Charts for Attributes
Control Charts for Variables
Interpretation of Control Charts
Manual Application of Tests
Statistical Software Application of Tests
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3. Characterizing Causes of Variation
The intent of process monitoring is to distinguish between random and non-random variation.
Random Cause
Non-random Cause
Common vs.
Special
Chance vs.
Assignable
Chronic vs.
Sporadic
System fault vs.
Local fault
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4. Theory of Process Variation: Statistical Control
The common variations in process variability that are
caused by natural incidences are in general not repetitive,
but various factors due to chance and are called
random variation. All processes are subject to random variation.
If the cause of variation is systematic (not natural) the process variation is called non-random variation. When non-random variation is present, the quality engineer should identify and eliminate the source of the variation.
When a process is subject to non-random variation the process is described as out-of-control.
If only random variation is present, the process is described as in-control.
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5. Control Limits, Random and Nonrandom Sample Observations
Upper
Control
Limit
(UCL)
Non-random
Non-random
+3σ
Process
Mean
99.7%
Lower
Control
Limit
(LCL)
-3σ 1 2 3 4 5 6 7 8 9 10 11 12
Sample number
Source: Ozcan Figure (Modified for Three Sigma Limits)
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6. Statistical Control Chart Types
Attributes
Variables(Subgroups)
c-chart
p-chart
u-chart
Mean Charts
(X-bar Charts)
Variation Charts
σ Method
Range Method
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7. Variables Control Charts (Continuous Data)
When process characteristics can be measured, variables control charts are the appropriate way to display the process monitoring.
The Xbar-chart and the Range chart are displayed and interpreted together.
When the Range chart exhibits out-of-control status, the rules for evaluating the Xbar-chart should not be used.
The Xbar chart is appropriately evaluated after the Range chart indicates that the process is in-control. Use caution when statistical software evaluates both charts simultaneously.
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8. Variables Control Charts
Variables(Subgroups)
Variables (Individuals)
Individual observation
Moving Range
Mean Charts
(X-bar Charts)
Variation Charts
Note that the tests that apply to the subgroup charts do not apply to the Individuals Charts.
σ Method
Range Method
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9. Attribute Control Charts (Discrete Data)
When process characteristics can be counted, attribute-based control charts are the appropriate way to display the process monitoring.
The p-chart is the appropriate control chart for a process with only two outcomes (defective or not defective) when the proportion defective is calculated.
The c-chart is the appropriate tool to display monitoring if the number of occurrences per sampling period is recorded.
The u-chart is the appropriate control chart if the number of occurrences and the number of items per sampling period is recorded. The average number of occurrences per sample is calculated.
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10. Rules for Development of Charts (Devor)
Choose quality characteristic to be measured or counted
Collect at least 25 samples
Develop trial control limits
Evaluate for special causes
Determine special causes and remediate
Eliminate out-of-control points
Recalculate control limits
Continue until chart shows process is in control
Monitor process using established control limits
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11. Look for special cause variation.
Interpretation of Control Charts
Look for special cause variation.
Points that are outside 3 sigma limits
Series of points that are unusually close to 3 sigma limits
Non-random patterns such as linear trends, oscillation, runs above or below centerline, to many successive points near the centerline
Textbook tests for special causes differ slightly from Minitab tests but Minitab allows you to adapt the tests.
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12. References
Devor, R., Chang, T. & Sutherland, J. (2007). Statistical Quality Design and Control, 2nd ed, Upper Saddle River, NJ: Prentice-Hall. ISBN
Ozcan, Y. (2009). Quantitative Methods in Health Care Management 2nd ed, San Francisco, CA: Jossey-Bass. ISBN
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Spring 2017 12