An operations research approach to the design of optimal acceptance sampling plans

Abstract

The major achievement of this research was to demonstrate that a general model building approach to optimal cost acceptance sampling is possible. The guiding premise for this study was that under the classical application of acceptance sampling by attributes the industrial manager is forced to make decisions regarding producer's and/or consumer's risk that are not economically based. Through the use of cost models it is possible to determine the economic sampling plan based on the various costs and the distribution of defectives. Acceptance sampling situations were divided into six factors; the objective, sampling method, rectification method, sampling distribution, prior distribution and sampling form. Each factor was subdivided into a number of sub-classes defining the specifics of the sampling operation. The objective expresses the reason for sampling. Cost minimization, profit maximization and cost minimization subject to a certain quality constraint were considered in developing the list of objectives. The sampling method relates to the physical nature of testing and the disposition of sampled items while the rectification method concerns the screening, replacement, repair and general disposition of rejected lots. The sampling distribution classification allows for the common case of sampling without replacement (hypergeometric distribution) or its approximations (binomial and Poisson distributions). The prior distribution, on the other hand, is the assumed distribution of defectives in the lot. The final factor, sampling form, was sub-classified into single sampling, double sampling, sequential sampling and multiple sequential sampling. ...