Description of 21/30409828 DC 2021

This International Standard provides two-stage (double) sampling plans by attributes for inspection for a proportion of nonconforming items in a target population of discrete units, in particular: i) the proportion of nonconforming items in a lot of product items; ii) the proportion of nonconforming function instances of an internal control system (ICS); iii) the proportion of misstatements in a population of accounting entries or booking records; iv) the proportion of nonconforming test characteristics of an entity subject to an acceptance test, e.g. in product and process audits.

The target population is considered as acceptable (tolerable) if the proportion nonconforming does not exceed a specified tolerance p₀, otherwise it is considered as unacceptable (intolerable). Correspondingly, the objective of sampling inspection is to enable a decision between the alternatives of “acceptance” and “rejection”. In different application domains, acceptance and rejection have different practical interpretations, see the explanations in Clause 7.

The sampling inspection procedure starts with a first sample of size n₁ with the following rule: accept if and only if no nonconforming units are found among the n₁ sampled units; reject if and only if at least (stage 1 rejection number) nonconforming units are found among the n₁ sampled units; proceed to the second stage if and only if at least one and at most -1 nonconforming units are found among the n₁ sampled units. In the second stage, sample n₂ units, and decide “accept” if and only if the number of nonconforming units in the second sample is smaller or equal to the stage 2 acceptance number , otherwise reject. The two-stage decision procedure can be expressed equivalently by comparing the limits of a two-sided confidence interval of nominal level () for the proportion nonconforming with the tolerance .

The sampling plans are indexed by three quantities: i) the tolerance ; ii) the nominal confidence level () which is respectively either 0,7, 0,8, 0,9, 0,95 or 0,99; iii) three levels low, mid, high of a scale called Trust. The Trust levels express the user’s degree of confidence into the status of the target population.

The objective of this International Standard is to provide procedures that enable a decision quickly and economically if the proportion nonconforming is particularly low or high. In the latter case, the inspection procedure will in most all cases terminate in stage 1 with small sample sizes n₁. Only under intermediate values of the proportion nonconforming in the target population, the likelihood of proceeding to a second sample is high. The two sample sizes in stage 1 and stage 2 are chosen so as to minimize the expected sample size under the specified confidence level and Trust level.

The plans are preferable to single sampling plans where the cost of inspection is high or where the delay and uncertainty caused by the possible requirement for second samples is inconsequential. The statistical theory underlying the plans, tables and figures is provided in Annex A through K.

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