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.

Formulas

Notation

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

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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