BS ISO 28801:2011 pdf free download – Double sampling plans by atributes with minimal sample sizes, indexed by producer’s risk quality (PRQ) and consumer’s risk quality (CRQ).
3.4 Notation
A notation used to describe such plans is (n, 0, 2; m, 1, 2). This indicates that the acceptance and rejection numbers for the first sample of size n are 0 and 2, and that the acceptance and rejection numbers for the first and second samples combined are 1 and 2, where the second sample is of size m.
4 Operating characteristics
The operating characteristic curves, shown in Figures 1 to 6, indicate the probability that a lot will be accepted under the various sampling plans for a range of quality levels.
The curves are based on the assumption that the sum of the two sample sizes is no more than about 10 % of the lot size. If the sum of the two sample sizes exceeds 10 % of the lot size, then the probabilities of accepting the lot are higher than those shown by the curves at all quality levels, so the producer’s risk is reduced and the consumer’s risk is increased.
NOTE A formula for the operating characteristic curves is provided in A.1.3 for nonconforming items and in A.2.3 for nonconformities.
5 Average sample sizes
5.1 Curtailed inspection
Under curtailed inspection, inspection is stopped as soon as the inspection results are sufficient to establish whether or not the lot is acceptable or, in the case of hypothesis testing, as soon as it is clear which hypothesis will be accepted. In the case of the double sampling plans in this International Standard, inspection would cease as soon as two nonconforming items (nonconformities) were found in the first sample or as soon as one nonconforming item (nonconformity) was found in the second sample. The operating characteristic curves are unaffected by curtailment, but the average sample size is reduced. The reduction is small at good quality levels but substantial at very poor quality levels. The disadvantage of curtailment is that it results in less precise estimates of the lot or process quality level; this matters more in the case of a continuing series of lots.
5.2 Average sample size (ASS I) for uncurtailed inspection
Average sample size curves for uncurtailed inspection for the double sampling plans of this International Standard are shown in Figures 7 to 12. These curves show the average sample sizes that may be expected to occur under the various sampling plans for a range of levels of process quality. For all the plans, the ASSI
— begins at the value n for perfect quality (because only the whole of the first sample is inspected),
— rises to a maximum where the process quality level p is equal to 1/n, i.e. 100/n % nonconforming or 100/n nonconformities per 100 items,
— falls more gradually to the value n as the process quality level p worsens beyond 1/n (again because ultimately only the whole of the first sample is inspected).
NOTE A formula for the average sample size for uncurtailed inspection is provided in A.1.4.1 for nonconforming items and in A.2.4.1 for nonconformities. Formulae for the corresponding maximum ASSI are given in A.1 .5 and A.2.5.
The average sample sizes of the double sampling plans at the PRQ and CRQ for uncurtailed inspection are given in Tables 7 to 12. Also given are the maximum average sample sizes.
EXAMPLE Suppose that it is required to carry out a test of whether the quality level in a large lot is no more than 0,25 % nonconforming. It has been agreed that the probability of acceptance should be at least 95 % if the lot has a quality level of 0,25 % nonconforming, but no more than 5 % if the quality is as bad as 5 % nonconforming.