An examination of the performance of a natural truncation point and acceptance rule for a curtailed Wald sequential sampling plan with Bernoulli parameters

Abstract

This paper examines the performance of a proposed truncation and acceptance rule for the Wald Sequential Probability Ratio test for Bernoulli parameters, and the rule's influence on errors of the first and second kind as well as the average number of items sampled for inspection. The proposed truncation and acceptance rule suggests that there exists a natural truncation point for every sequential probability ratio test such that the desired error probabilities are not exceeded or that one of the true errors is smaller than desired and the other will exceeded by an insignificant amount. A computer program is used to simulate the sampling process and provide estimates of the true values of a plan's Operating Characteristic curve, its average sample number, as well as the probability of implementing the truncation and acceptance rule. Results suggest that truncation and rejection of a lot at the natural truncation point will maintain a plan's desired Operating Characteristic curve. The cases examined also suggest that any modification to the natural truncation point truncation and acceptance rule may cause an unacceptable deviation from the desired Operating Characteristic curve. Finally, a linear equation was developed which provides an estimate of the upper limit on the probability of implementing a truncartion and acceptance rule, and that is most cases, this upper limit is less than 0.15.