How this calculation works
A defective-unit fraction has different sampling variability when subgroup size changes. A p chart therefore needs a limit width for each inspected count rather than one horizontal band applied to every subgroup. This page evaluates monitored subgroup counts against a separately established baseline proportion. It also reports the pooled observed fraction as a descriptive summary, without using it to silently replace that baseline.
For subgroup n: limits = p0 ± L√[p0(1−p0)/n], clipped to [0,1]A worked example
At baseline 0.1 and multiplier three, a subgroup of one hundred units has standard error 0.03 and limits 0.01 to 0.19. Four hundred units reduce that standard error to 0.015. Ten defectives among one hundred and forty among four hundred both give observed fraction 0.1. Neither signals, and their pooled fraction remains 0.1 across five hundred inspected units.
Good to know
Independent binomial units and a stable separate baseline are assumed. Overdispersion, autocorrelation and changing defect definitions can invalidate the normal-approximation chart. Sparse expected counts can make these limits inaccurate. This monitoring chart is not an acceptance-sampling plan, a lot-certification procedure or an automatic process-quality approval.
Reference: NIST — proportion control chart (opens in a new tab) ↗
What this calculation answers
A defective-unit fraction has different sampling variability when subgroup size changes. A p chart therefore needs a limit width for each inspected count rather than one horizontal band applied to every subgroup.
This page evaluates monitored subgroup counts against a separately established baseline proportion. It also reports the pooled observed fraction as a descriptive summary, without using it to silently replace that baseline.
The Single acceptance sampling operating characteristic calculator evaluates lot acceptance probability. A p chart monitors observed subgroup fractions against a separate process baseline.
Use the right input conventions
Each row contains inspected units and how many of those units are defective. Counts must be whole numbers and defective units cannot exceed inspected units. Multiple defects on one unit are not separate defective units.
The baseline is a fraction between zero and one, so ten percent is 0.1. The SD multiplier controls normal-approximation limits, which are clipped at the physical zero and one boundaries.
Interpret the result
Larger subgroups give narrower limits because their proportion estimates vary less under the binomial model. A deviation that looks small in percentage points can therefore signal in a large subgroup but not a small one.
The pooled fraction weights by inspected units. Averaging subgroup percentages without their denominators can produce a different answer when subgroup sizes vary.
Work through the example
At baseline 0.1 and multiplier three, a subgroup of one hundred units has standard error 0.03 and limits 0.01 to 0.19. Four hundred units reduce that standard error to 0.015.
Ten defectives among one hundred and forty among four hundred both give observed fraction 0.1. Neither signals, and their pooled fraction remains 0.1 across five hundred inspected units.
Where the model stops
Independent binomial units and a stable separate baseline are assumed. Overdispersion, autocorrelation and changing defect definitions can invalidate the normal-approximation chart.
Sparse expected counts can make these limits inaccurate. This monitoring chart is not an acceptance-sampling plan, a lot-certification procedure or an automatic process-quality approval.
A few questions, answered
Can I count several defects on one unit as several defectives?
No. This p chart counts units classified defective, not total defects per unit.
What changes in the comparison?
Use the same observed fraction in two subgroup sizes and compare their signal decisions.