SYE6047 Chap.9 Attribute Control Charts and Revision
Attribute Control Charts and Revision
Monitor a fraction in time order
A p chart follows the fraction of inspected units that are nonconforming in each sample. It is appropriate when each unit can be classified into two states under a consistent definition and sample sizes are known. The centre line is the pooled fraction, total nonconforming divided by total inspected.
The standard error depends on both that pooled fraction and the sample size.
Limits reflect sampling variation
For equal sample sizes, one pair of three-sigma limits applies to all points. For unequal sample sizes, the limits vary because small samples naturally produce more variable fractions. A computed lower limit below zero is set to zero because a negative nonconforming fraction is impossible.
Control limits describe the process and sampling plan; a customer requirement remains a separate comparison.
Signals require investigation
A point beyond the upper limit indicates behaviour not well explained by the initial common-cause model. It does not tell the analyst what happened. The correct next step is to investigate date, material, method, operator, equipment and measurement records.
Deleting the point because it is inconvenient changes the evidence and usually narrows the limits artificially.
Revision represents a changed process
If the investigation verifies an assignable cause and shows that it has been removed from normal operation, recalculating the centre and limits can estimate the corrected process.
The original chart must remain visible, the exclusion must be documented and the revised limits must be tested with future data. The published sample paper explicitly exercises this sequence: initial chart, assignable cause, removal and revised limits.
What this chapter covers
- 01
Binary unit classification
- 02
Sample fraction nonconforming
- 03
Pooled centre line
- 04
Equal-size p-chart limits
- 05
Unequal-size limits
- 06
Signal investigation
- 07
Assignable cause evidence
- 08
Revised baseline interpretation
Worked example · free
Investigate first, revise second
- 4Calculate the pooled fraction and standard error.
- 3Calculate and apply the control limits.
- 5Interpret the signal and state revision conditions.
Key terms
- P Chart
- A control chart for the fraction of inspected units classified as nonconforming.
- Pooled Fraction
- Total nonconforming units divided by total inspected units across baseline samples.
- Assignable Cause
- A verified event or condition that explains a special-cause signal.
- Baseline Revision
- Transparent recalculation after a verified process change or justified exclusion.
- Varying Limit
- A control boundary that changes with sample size because sampling variation changes.
Attribute Control Charts and Revision FAQ
Why do p-chart limits change with sample size?
The standard error of a sample fraction is inversely related to the square root of sample size. Smaller samples vary more naturally, so their limits are wider when the pooled fraction is unchanged. Carry the inspected total beside every point and calculate its own boundary; an average denominator can hide a signal or manufacture one.
Why is a negative lower limit replaced by zero?
A fraction nonconforming cannot be less than zero. The calculation may produce a negative three-sigma boundary when the centre is low, but the feasible lower boundary is zero.
What does a revised p chart prove?
It estimates the behaviour of the corrected process under its revised baseline if the cause removal and definitions are sound. It does not prove that the fraction meets a customer requirement or that no future special cause can occur.
Exam move
Practise the sample paper's full chain, not just the formula: pool counts, calculate limits, plot, identify the signal, require cause evidence, recalculate transparently and interpret. Always keep unit counts separate from defect counts and mark whether sample sizes are equal. Create one table with sample order, nonconforming count, inspected total, fraction and individual limits.
This exposes denominator changes before they distort interpretation. For equal samples, verify the common limits; for unequal samples, compute the changing envelope from the pooled centre. Apply zero and one as feasible bounds only after the three-sigma calculation. When a point crosses a limit, attach an investigation note naming the event, evidence, correction and affected sample. If no event is verified, retain the point.
If a cause is removed, preserve the initial chart, recompute openly and test future samples against the revised baseline. Finish every answer with two distinct sentences: what statistical control says about process behaviour and whether any separate customer requirement is met. That separation mirrors the sample paper's reasoning without copying its questions.
