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

Sometimes the quality of a process or product is described by a functional relationship between aresponse variable and one or more explanatory variables referred to as profile. In most researches inthis area the response variable is assumed to be normally distributed. However, occasionally in certainapplications, 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 statisticalprocess control finding the real time of change in process, called as change point, is necessary becauseit leads to saving time and cost in finding assignable cause(s). Therefore, in this paper we considerGamma regression profile and use maximum likelihood to estimate the real time of a step change inPhase II. We evaluate accuracy and precision of the proposed change point estimator by simulation.The results show that the proposed change point estimator is effective in estimating the real time ofstep shifts in the process parameters of Gamma regression profiles. Also, a confidence set for theprocess change point based on the logarithm of the likelihood function is presented. Finally, theperformance of the estimator is illustrated through a real case.