# Methods and formulas for Attributes Acceptance Sampling

Select the method or formula of your choice.

## Sample size and acceptance number

Minitab uses an algorithm to solve the following equations for n, sample size, and c, acceptance number.

### Notation

TermDescription
αproducer's risk
βconsumer's risk
p1acceptable quality level (AQL)
p2rejectable quality level (RQL) or lot tolerance percent defective (LTPD)

0 < p1< p2< 1

1 > 1-α > β > 0

## Probability of acceptance

The probability of acceptance (Pa) describes the chance of accepting a particular lot based on a specific sampling plan and incoming proportion defective. It is based on the binomial distribution.

### Notation

TermDescription
cacceptance number
nsample size
pfraction defective

## Probability of rejecting

The probability of rejecting (Pr) describes the chance of rejecting a particular lot based on a specific sampling plan and incoming proportion defective. It is simply 1 minus the probability of acceptance.

Pr = 1 – Pa

where:

Pa = probability of acceptance

## Average outgoing quality (AOQ)

The average outgoing quality represents the quality level of the product after inspection. The average outgoing quality varies as the incoming fraction defective varies.

### Notation

TermDescription
Paprobability of acceptance
pincoming fraction defective
Nlot size
nsample size

## Average total inspection (ATI)

The average total inspection represents the average number of units that will be inspected for a particular incoming quality level and probability of acceptance.

### Notation

TermDescription
Paprobability of acceptance
Nlot size
nsample size
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