ABSTRACT
Double-and multiple-sampling plans reflect the tendency of many experienced inspectors to give a questionable lot an additional chance. Thus, in double sampling if the results of the first sample are not definitive in leading to acceptance or rejection, a second sample is taken which then leads to a decision on the disposition of the lot. This approach makes sense, not only as a result of experience, but also in the mathematical properties of the procedure. For one thing, the average sample number (ASN) can usually be made to be less for a double-sampling plan than for a single-sampling plan with the same protection. A natural extension of double sampling is to allow further additional samples to be taken to
achieve even more discrimination in the disposition of a lot. Such procedures are called multiplesampling plans when, as with double sampling, the last sample is constructed to force a decision at that point. That is, for a specific last sample (say the kth sample) it is so arranged that rk¼ akþ 1, where rk is the rejection number and ak is the acceptance number. Thus, double sampling is simply a special case of multiple sampling where k¼ 2. Multiple-sampling plans allow even more flexibility and still further reduction in average sample
size over double-sampling plans, but are often found to be difficult to administer because of the complexity of handling and recording all the samples required. As an example of the reduction in sample size that can be obtained, MIL-STD-105E (Code H, 1.5 AQL [acceptable quality level], normal inspection) shows that for plans matched to the single-sampling plan n¼ 50, c¼ 2, the ASN at the 95th percentile is
Single 50 Double 43 Multiple 35
This is typical of the efficiency in sampling which may be generated by the use of double-and multiple-sampling procedures. Efficiency of this sort may be costly, however, in terms of administration, since there is an increasingly variable workload in going from single to double to multiple sampling. These plans offer an additional dimension to the application of sampling plans, however, by providing increased economy and flexibility when properly applied. Double-and multiple-sampling plans are said to be matched to single-sampling plans when their
operating characteristic (OC) curves coincide. The inherent shape of a multiple-sampling OC curve is, however, different from that of a single-sampling OC curve. Hence, plans are often matched at two points, usually at p.95 and p.10. Inspection is often curtailed, that is, inspection is stopped after reaching a decision, or semicurtailed,
that is stopped only on a decision to reject. In either case the first sample is almost always inspected in full so that estimates and records kept on the first sample will have a consistent sample size. Usually the
the operation of the plan if no problems occur.
