Generalized one-tailed hypergeometric test with applications in statistical quality control

Abstract

In this article, we propose the generalized one-tailed hypergeometric test with fuzzy hypotheses for both test methods: significance testing (by controlling the type I error) and hypothesis testing (by controlling both error types). With regard to the fuzzy set theory, this test is the generalization of the conventional hypergeometric test for a proportion and provides an additional gradual consideration of the indifference zone in compliance with expert opinion or user priorities. Further, a practical application for one of the most promising resulting test types (right-tailed hypothesis testing) is carried out in statistical quality control. In particular, single sampling plans for attributes are determined via an algorithm based on the Fibonacci sequence. In addition, a parametric sensitivity analysis of calculated sampling plans is carried out in relation to changes of the lot size, consumer’s and producer’s risks, as well as of specified target values of quality levels. Moreover, the impact of various shapes of membership functions (piecewise linear, convex, concave, and s-shaped) is investigated by comparing respective sampling plans.