Double sampling plans by attributes with minimal sample sizes, indexed by producer's risk quality (PRQ) and consumer's risk quality (CRQ)
ISO 28801:2011 provides double sampling plans by attributes for the acceptance inspection of lots of discrete items. The plans are indexed by the producer's risk quality (PRQ) and the consumer's risk quality (CRQ) where the nominal producer's and consumer's risks are respectively either (5 %, 5 %), (5 %, 10 %) or (10 %, 10 %). Plans are provided for inspection for percent nonconforming and for inspection for nonconformities per 100 items. The lot is accepted if there are no nonconforming items (nonconformities) in the first random sample, and rejected if it contains two or more nonconforming items (nonconformities). If precisely one nonconforming item is found in the first sample, a second random sample is drawn; the lot is then accepted if the second sample contains no nonconforming items (nonconformities) and rejected otherwise.
The objective of ISO 28801:2011 is to provide procedures that enable lot disposition to be determined quickly and economically if quality is particularly good or bad. For intermediate quality, a second sample is drawn in order to be able to discriminate more reliably between acceptable and unacceptable lots. The two sample sizes are chosen to minimize the maximum expected sample size with respect to incoming quality subject to the nominal risks not being exceeded.
Similarly, the plans may be used to test the hypothesis that a lot or process quality level is equal to the PRQ (i.e. acceptable) against the alternative hypothesis that the quality level is equal to the CRQ (i.e. unacceptable).
The plans are preferable to single sampling plans where the cost of inspection is high, where the delay and uncertainty caused by the possible requirement for second samples is inconsequential and where a relatively large ratio of the consumer's risk quality to the producer's risk quality can be tolerated.
The plans are suitable for isolated lots or for short series of lots, where the sum of the two sample sizes is no larger than about 10 % of the size of the lot. The plans are also suitable for continuing series of lots when lots that fail to satisfy the acceptance criteria are 100 % inspected and all nonconforming items replaced by conforming items; however, for continuing series of lots, consideration should also be given to using double sampling plans from ISO 2859-1.
The statistical theory underlying the plans, tables and figures is provided in Annex A.