Process Capability Index for Logistic Regression Profile Based on pmk S Index

A profile is a relationship between a response variable and one or more independent variables that can describe the quality of a process or product. On the other hand, for an in-control process, capability indices are criteria for process quality improvement that allows meeting customer expectations. Although a considerable number of applications and monitoring methods have been already proposed for profiles, a few researches have focused on the process capability index of profiles. In this paper, we propose a new Spmk index to measure process capability when the quality of process is characterized by a logistic regression profile. In addition, we present an approximate 100(1-α)% confidence interval based on percentile bootstrap method. The performance of the proposed index and corresponding confidence interval is evaluated through simulation studies. The result shows that when the number of observations in each level increases the index performs better. Furthermore, increasing number of levels leads to improving precision of the proposed index. Also, the coverage rates of the confidence intervals are greater than 93.6% lower limit of the stated nominal in most cases. Finally, the application of the proposed index is illustrated through a real case.