Change point estimation of gamma regression profiles with a linear trend disturbance

Abstract

Estimating the real time of shifts in process would ease the identification of special causes and leads to saving in time and cost, so it is very important for process improvement. On the other hand, in many applications of statistical process control, quality of a process or product is summarised by a functional relationship referred to as profile. Although there are many real cases with gamma responses in profiles, little studies have been devoted to the estimation of the change point of this type of profiles. The main contribution of the paper is deriving a maximum likelihood estimator for change point estimation in gamma regression profiles with a linear trend disturbance. Also, a T2 control chart is used to detect the out-of-control signal in monitoring gamma regression profiles. The performance of the proposed estimator is evaluated through simulation studies. The results show the accurate and precise estimates of the change point by the proposed estimator. Afterwards, a confidence set estimator 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.