How this calculation works
An acceptance-sampling plan can accept a poor lot or reject a good one because it inspects only a sample. Its operating-characteristic curve shows how acceptance probability changes with the lot’s defective fraction. This page evaluates a single attributes plan and two risk points. It keeps the sample size, acceptance count and assumed quality fractions visible instead of presenting acceptance as a certainty.
Pa(p) = Σ from d=0 to c choose(n,d) p^d (1−p)^(n−d)A worked example
With n equal to ten, c equal to one and defective fraction 0.1, acceptance includes zero or one defective unit. Its probability is 0.9^10 plus ten times 0.1 times 0.9^9. The result is about 0.736099. At defective fraction zero the acceptance probability is one; with every unit defective and c below n it is zero.
Good to know
No standard inspection-plan selection, switching rules or double sampling is implemented. The tool evaluates the plan you enter and does not declare it compliant with a procurement standard. Accepted lots can still contain defective units. This probability calculation is not lot certification, a safety assurance or an instruction to omit required inspection.
Reference: NIST — operating characteristic curves (opens in a new tab) ↗
What this calculation answers
An acceptance-sampling plan can accept a poor lot or reject a good one because it inspects only a sample. Its operating-characteristic curve shows how acceptance probability changes with the lot’s defective fraction.
This page evaluates a single attributes plan and two risk points. It keeps the sample size, acceptance count and assumed quality fractions visible instead of presenting acceptance as a certainty.
The Binomial probability calculator supplies the underlying fixed-probability count model. An acceptance plan adds an explicit decision threshold and producer/consumer quality points.
Use the right input conventions
Enter defective units, not the total number of defects found on those units. The lot fractions use zero to one, so one percent is 0.01. The plan accepts when the observed defective count is at most c.
The binomial model assumes independent sampling from a sufficiently large lot. A small finite lot sampled without replacement needs a hypergeometric analysis rather than this same curve.
Interpret the result
Producer risk is the probability of rejecting at the entered good-quality fraction. Consumer risk is the probability of accepting at the poor-quality fraction. Their labels describe two specific assumptions, not universal supplier or customer risks.
Changing c generally shifts both risks, so a more permissive plan cannot be described as unconditionally better. The full curve helps show the tradeoff that one point estimate conceals.
Work through the example
With n equal to ten, c equal to one and defective fraction 0.1, acceptance includes zero or one defective unit. Its probability is 0.9^10 plus ten times 0.1 times 0.9^9.
The result is about 0.736099. At defective fraction zero the acceptance probability is one; with every unit defective and c below n it is zero.
Where the model stops
No standard inspection-plan selection, switching rules or double sampling is implemented. The tool evaluates the plan you enter and does not declare it compliant with a procurement standard.
Accepted lots can still contain defective units. This probability calculation is not lot certification, a safety assurance or an instruction to omit required inspection.
A few questions, answered
Does accepting a sample mean the complete lot is defect free?
No. The OC curve explicitly includes acceptance probability at nonzero defective fractions.
What changes in the comparison?
Inspect a larger sample at unchanged acceptance count and compare the risk curve.