Selection of a tightened-normal-tightened system for given values of the acceptable quality level and limiting quality level using weighted Poisson distribution

Since the first acceptance sampling plans have been developed 80 years ago, a number of selection principles have emerged. The majority of these principles are characterised by the fact that they look upon producer and consumer as two opposing parties. However, in many occasions, e.g., in final inspection, producer and consumer represent the same party and, therefore, the used sampling plan should not make an attempt to discriminate between their interests. In this case, the interest is to avoid wrong decisions, i.e., reject product of sufficient quality and accept product of insufficient quality. Thus, the natural objective in these cases is to use overall risk for a wrong decision as optimisation criteria. Optimum result can be arrived further by the weighted Poisson distribution. In this paper, a table and procedure are given for finding the tightened-normal-tightened system involving minimum sum of producer's and consumer's risks for specified acceptable quality level and limiting quality level using the weighted Poisson distribution. This is the case with the tightened-normal-tightened system for given acceptable quality level and limiting quality level involving minimum risks using the weighted Poisson distribution.