Acceptance Sampling Calculator

The Acceptance Sampling Calculator builds a single-sampling attribute plan and tells you how it will behave. You give it a sample size and an acceptance number, together with the quality levels you consider good and bad, and it reports the chance the plan accepts a lot at each of those levels, the resulting producer's and consumer's risks, the worst average outgoing quality the plan can let through, and the smallest sample size that would meet the consumer's risk you asked for.

Quality levels are entered as percent defective, sample and lot sizes in units, and risks come back as percentages or probabilities.

Use it to design or check an attribute inspection plan. It builds the plan from the binomial distribution directly rather than looking one up from a published sampling scheme, and it treats the lot as effectively unlimited.

Purpose and model boundary

This calculator evaluates a single-sample attributes plan: inspect n items from a lot of N, accept the lot when no more than c defectives are found, and otherwise reject it. It reports the plan's operating-characteristic probabilities at an acceptable quality level (AQL) and rejectable quality level (RQL), the associated producer's and consumer's risks, a rectifying-inspection average outgoing quality limit (AOQL), and the first qualifying sample size from the workbook's candidate ladder.

The result describes the mathematical plan entered. It does not select an inspection level, claim conformance to an ANSI/ASQ/ISO sampling standard, determine whether a supplier process is stable, or replace an agreement between producer and consumer.

Inputs and units

• Lot size, N and sample size, n are integer item counts. Both must be positive and the sample cannot exceed the lot.
• Acceptance number, c is an integer defective count from 0 through 10 and cannot exceed n.
• AQL, p_A, RQL, p_R, and target consumer's risk, beta_target are entered as percentages and converted to fractions for calculation. The RQL must exceed the AQL.

The probability model treats an inspected item as defective or non-defective. It does not model defect counts per item or severity classes.

Governing relationships

For incoming defective fraction p, the workbook computes the cumulative binomial acceptance probability

Pa(p; n, c) = sum from k=0 to c of C(n,k) * p^k * (1-p)^(n-k).

The terms are built recursively through c = 10, avoiding factorial overflow. The principal risks are

• producer risk = 1 - Pa(p_A; n, c);
• consumer risk = Pa(p_R; n, c).

For rectifying inspection, the average outgoing quality at incoming rate p is

AOQ(p) = p * Pa(p; n, c) * (N - n) / N.

The workbook evaluates this relationship on its authored incoming-quality grid over the full 0-to-1 domain and reports the greatest grid value as AOQL together with the corresponding incoming rate. This is a discrete grid search, not a continuous optimizer.

Calculation sequence

1. Convert the three percentage inputs to fractions and constrain c to the implemented 0-to-10 binomial term chain.
2. Evaluate Pa at AQL and RQL, then derive producer's risk, consumer's risk, and whether the entered plan meets beta_target.
3. Evaluate the operating-characteristic and AOQ grids used by the chart and AOQL search.
4. Test the candidate sample sizes 5, 8, 13, 20, 32, 50, 80, 125, 200, 315, 500, 800, 1250, 2000 in ascending order. The recommendation is the first candidate that is no larger than N and has Pa(p_R) <= beta_target; otherwise it reports that none in the ladder is large enough.

Outputs and interpretation

Pa at AQL is the chance of accepting a lot at the good-quality point; Pa at RQL is the chance of accepting a lot at the poor-quality point. These are probability-model results, not observed frequencies. Producer's risk measures rejection of a lot at AQL, while consumer's risk measures acceptance of a lot at RQL. The recommended sample size is a ladder result for the current c, RQL, target risk, and lot size; it is not a published sampling-table plan.

Validation and status logic

The workbook evaluates status in this order:

The published limits also reject percentages outside 0% to 100%, an acceptance number outside 0 to 10, and nonpositive integer counts before a workbook calculation is submitted.

Assumptions and limitations

The OC probabilities use independent binomial trials. Sampling without replacement is better represented by a hypergeometric model when the sample is a material share of the lot; the workbook flags a sampling fraction above 10% but does not switch distributions. AOQ assumes rejected lots are screened and defectives corrected or replaced. The result depends on representative random sampling, a consistent definition of defective, and quality levels that are meaningful for the product. AOQL is limited to the workbook's authored search grid, and the sample-size recommendation is limited to the fixed ladder.

Restrictions and non-computing states

The workbook does not switch to a hypergeometric model, search outside its authored AOQL grid, or recommend sample sizes outside its fixed ladder. Rows with invalid lot, sample, acceptance-number, or quality-level inputs do not produce a decision-ready result; consult the status message before using the reported quantities.

Errors and warnings

A rejected entry means a submitted type or value did not satisfy the published input rules and no workbook decision was made. A workbook NOT VALID status means the plan relationships prevent a meaningful result. A CHECK status preserves a computable result but identifies a risk or approximation requiring review. A network, sign-in, or calculation-service error is a delivery failure, not a sampling conclusion.

The workbook derives its relations rather than reproducing any table, chart or figure from a specification, standard or agency publication. Acceptance probabilities are cumulative binomial sums computed directly, and the average outgoing quality limit is found by scanning a grid of incoming rates rather than read from a published curve.

• Wikipedia. Acceptance sampling, for the operating characteristic curve and the two risks. https://en.wikipedia.org/wiki/Acceptance_sampling
• Wikipedia. Binomial distribution, for the acceptance probability. https://en.wikipedia.org/wiki/Binomial_distribution
• Wikipedia. Hypergeometric distribution, which is the correct model when the sample is a large fraction of a finite lot. https://en.wikipedia.org/wiki/Hypergeometric_distribution

Published sampling schemes such as ANSI/ASQ Z1.4 and ISO 2859 define plans by lot size, inspection level and acceptable quality level, along with switching rules between normal, tightened and reduced inspection. This tool implements none of them. It computes the behaviour of a plan you specify. If you are required to follow a published scheme, take the plan from that scheme and use this tool only to understand how it behaves.

Additional source notes migrated from Methodology

The workbook uses the cumulative binomial distribution and the rectifying-inspection AOQ relationship shown above. It computes plans rather than reproducing a published ANSI, ASQ, AIAG, or ISO sampling table; the page's References section carries the licensing and non-endorsement statement.