Hypothesis testing of process capability index Cpk from the perspective of generalized fiducial inference

Abstract

AbstractHypothesis testing of is an essential part for decision making on process capability. The difficulty to test the hypothesis of is the complexity of the natural estimator distribution even under the normal distribution. Thus, traditional methods of the hypothesis testing of based on the natural estimator only give the approximate test method under the normal distribution and seldom discuss the hypothesis testing under some commonly used but complex non‐normal distributions. The emerging generalized fiducial inference (GFI) in recent years is an effective method for statistical inference on complex statistics. Thus, we first propose a novel hypothesis testing method for based on generalized p‐value. For application, the mathematic expression of the proposed method for the commonly used normal distribution, Gamma distribution, Weibull distribution, and two‐parameter exponential distribution is derived in detail. Next, to study the performance of the proposed method in terms of the frequency property, the real probabilities of Type I error and Type II error are calculated through simulation. The calculated results show that the proposed method has satisfactory performance for different distributions. Finally, the implementation of the proposed method is illustrated by two real examples.