Process capability analysis of Taguchi index C_pm based on generalized p-value

Product quality is an essential issue to promote product sale, and process capability analysis plays an important role to assess and guarantee the process quality of products. Taguchi index (Figure presented.) is widely adopted to measure the process capability, because it essentially quantifies the quality loss from the actual process quality to the customer need. Large sample approximation and the bootstrap method are often used to test the hypothesis of index (Figure presented.), but they do not have satisfactory performance under small or medium sample size. To address this issue, we propose a novel hypothesis testing method of index (Figure presented.) based on generalized p-value theory. For application, its mathematical expression is derived in detail for the normal, gamma, and Weibull distributions, since these distributions are commonly used in engineering practice. Simulation results show that the supremum of type I error probability of the proposed testing method is closer to the significance level than the existing methods, and its type II error probability is lower as well. Based on the proposed hypothesis testing method, a new procedure of process capability analysis is designed for applications. Finally, two real cases are carried out to show the effectiveness of the newly designed procedure.