McWilliams, Thomas P. (1987, ASQC) Northeastern University, Boston, MA
Statistical quality control applications frequently involve decisions made on the basis of sample information. The appropriate sample size is typically chosen in advance to meet some specified criteria. For example, in a hypothesis testing problem, the sample size must be large enough so that the test has acceptably high probabilities in distinguishing between the null and alternative hypotheses, as determined by the OC curve.
Sequential statistical techniques do not specify an appropriate sample size prior to the sampling process. Instead, the sampling process continues only until enough information has been collected to provide strong evidence in support of either hypothesis. Examples of sequential procedures include curtailed versions of fixed sample size tests, double sampling plans, and item-by-item procedures where a decision criteria is checked after each item is inspected. In each of these cases, the number of observations required to reach a decision is now random and is not known in advance of the sampling process.
When comparing fixed and sequential test procedures having equivalent OC curves, the sequential procedures typically have the advantage of requiring, on the average, fewer observations. If inspection is costly, time-consuming, or destructive, this advantage will be important. Disadvantages include the need for more "bookkeeping" during the inspection process; the existence of uncertainty regarding the number of observations which will be required to reach a decision, and the fact that sequential procedures are mathematically more difficult to design and evaluate than fixed sample size procedures.
This paper presents the general logic of sequential procedures with particular emphasis on item-by-item hypothesis testing applications. An extensive collection of examples is included, involving sampling by attributes (binomial, hypergeometric, and Poisson sampling) and by variables (normally distributed observations). Sequential alternatives to fixed sample size procedures are presented in the cases of acceptance sampling and of hypothesis tests involving the mean of a process. Sequential life tests are also briefly discussed. Computational methods (with emphasis on the direct method) are discussed which allow the reader to determine appropriate sequential plans and to evaluate their average sample number and OC curves. The concept of truncating sequential procedurse at prespecified limits is also presented.