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Multiple stage sampling plans can save substantial time and resources, when the case is clear-cut. Multiple stage plans provide an alternative to fixed sample plans that can help diminish the producer and consumer risks (α, β) of arriving at a wrong decision. Sequential (SPRTs) tests constitute a natural extension of the double sampling plans.
In this first START sheet, we have overviewed SPRTs for the discrete case, via the development of sequential tests for the Binomial distribution. Such an approach is useful in life testing, when devices are sequentially placed on test for a fixed time "T," and when only the number "Y" of survivals/failures from such tests is recorded. Binomial sequential tests are also useful in SPC/Quality Control acceptance sampling problems, when batch items are tested, one at a time, on a pass/fail basis, to assess the percent of defective items in a lot, instead of by taking a fixed size sample, one at a time. We have also discussed the double sampling plans in detail, and the problem of assessing these plans via the ASN.
In a second, follow-up START sheet, we will discuss the use of SPRT tests with continuous variables, specifically, when testing Exponential lives. Such tests are widely used and are included in the well-known MIL-HDBK-781-D, Reliability Testing for Engineering Development. We will use the same example of this paper and compare, using the corresponding ASN, the efficiency of the two strategies (1) of letting each device extinguish its life, versus that of (2) curtailing the test at a fixed time T, used here, and only observing whether such device passed or failed the test.