A mathematical programming model for constructing the confidence interval of process capability index<i>C</i>_<i>pm</i>in evaluating process performance: an example of five-way pipe

Abstract

The process capability index Cpm can reflect process loss as well as process yield, thus is the most frequently used index for evaluating product quality in manufacturing industries. When evaluating the process performance, confidence intervals are often used for assurance with regard to the critical value of the process capability index. Unfortunately, sampling distributions of Cpm are obtained in a very complex way, which leads to difficulty in calculating the confidence interval of Cpm. Hence, this paper develops a mathematical programming model to construct the confidence interval of Cpm. Then for verifying the effectiveness of the proposed approach, the Monte Carlo simulation is used to find the coverage percentage. The proposed mathematical programming model can obtain the confidence interval of Cpm without complex statistical computations. Besides, managers can evaluate and monitor the process performance in an easy way. We also provide a case in which a five-way pipe process is presented as an illustration of how the proposed method is implemented.