Evaluation of process capability in gamma regression profiles

Abstract

In many industrial and non-industrial processes, the quality of a product or a process are described by a functional relationship between a response variable and one or more independent variables, known as profile. On the other hand, the process capability indices provide numerical measures of the process ability. Few researches have been done to evaluate the process capability of profiles; especially for linear profiles. In the present article, we calculate the $S_{\text{pmk}}$ index to measure the process capability for gamma regression profiles and we also construct an approximate confidence interval using the bootstrap method. The performance of the proposed method is assessed through a simulation study. Moreover, we show that the $S_{\text{pmk}}$ index is very robust when the true distribution of data is a lognormal or a Weibull. Finally, the applicability of the proposed index is illustrated using two real examples.

Keywords:

• Confidence interval
• Gamma regression profile
• Process capability index
• Process yield