IJE TRANSACTIONS B: Applications Vol. 28, No. 2, (February 2015) 224-233 Please cite this article as F. Sogandi, A. Amiri, Estimating the Time of a Step Change in Gamma Regression Profiles Using MLE Approach, International Journal of Engineering (IJE), TRANSACTIONS B: Applications Vol. 28, No. 2, (February 2015) 224-233 International Journal of Engineering Journal Homepage: www.ije.ir Estimating the Time of a Step Change in Gamma Regression Profiles Using MLE Approach F. Sogandi, A. Amiri* Industrial Engineering Department, Shahed University, Tehran, Iran PAPER INFO Paper history: Received 04 May 2014 Received in revised form 08 July 2014 Accepted 13 November 2014 Keywords: Gamma Regression Profile Change Point Estimation Maximum Likelihood Estimator (MLE) Statistical Process Control (SPC) Phase II. 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 that 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 real case. doi: 10.5829/idosi.ije.2015.28.02b.08 1. INTRODUCTION 1 Control chart is an effectual tool to reduce variation of process and to monitor quality characteristics. Occasionally, quality of a product or performance of a process is described by a relationship between a response variable and one or more explanatory variables that known as profile. According to the type of this relationship, profiles are classified into categories such as simple linear profiles, multiple linear profiles, polynomial profiles, multivariate linear profiles, non- linear profiles, logistic profiles, and so on. Control charts have been proven to be effective in detecting out-of-control signals. However, usually the time of the control chart signals is after the real time of a change. Identification of the exact time which in process has changed would simplify exploration and removing of the assignable cause. Consequently, having an estimate of the process change point would be very useful due to reduction of risk of misdiagnosing the 1 *Corresponding Author’s Email: amiri@shahed.ac.ir (A. Amiri) control chart signals, which often leads to unnecessary and costly adjustments of the process. Change point problems are classified according to change types including step, drift and monotonic shifts. Generally, step shift happens when the parameter changes suddenly and remains constant until the assignable cause is detected and removed. To find the real time of a change, many authors have suggested several methods. See a comprehensive review on change point estimation methods for control chart post signal diagnostics by Amiri and Allahyari [1]. Perry and Pignatiello [2] showed that the performance of an MLE is better than the built-in EWMA and CUSUM estimator in identifying the change point of a normal and Poisson process, respectively. Amiri and Khosravi [3] proposed an MLE change point estimator in high quality processes under a drift in nonconforming proportion parameter. Amiri and Khosravi [4] proposed an MLE change point estimator under monotonic change for process fraction nonconforming in a high-quality process monitored by a cumulative count of conforming control chart. Ghazanfari et al. [5] suggested a