Estimating the Time of a Step Change in Gamma Regression Profiles Using MLE Approach

Abstract

Sometimes the quality of a process or product is described by a functional relationship between a response variable and one or more explanatory variables referred to as profile. In most researches in this area the response variable is assumed to be normally distributed; however, occasionally in certain applications, the normality assumption is violated. In these cases the Generalized Linear Models (GLM) such as Gamma regression models are used to characterize the profile. Also, in statistical process control finding the real time of change in process, called as change point, is necessary because it leads to saving time and cost in finding assignable cause(s). Therefore, in this paper we consider Gamma regression profile and use maximum likelihood to estimate the real time of a step change in Phase II. We evaluate accuracy and precision of the proposed change point estimator by simulation. The results show the proposed change point estimator is effective in estimating the real time of step shifts in the process parameters of Gamma regression profiles. Also, a confidence set for the process change point based on the logarithm of the likelihood function is presented. Finally, the performance of the estimator is illustrated through a numerical example.