Design of Control Charts for Monitoring Logistic Regression Profiles with Estimated Parameters

The quality of a process can be described using a regression profile relationship between a response variable and some independent variables. Much research has been done on the response variables with continuous and normal distribution. While, in real situations, when a product is conforming or nonconforming on the product line, the assumption of normality is violated and a logistic regression model is used to characterize binary response variables. Also, in many cases the parameters used to design control charts for monitoring profiles are unknown and estimated by using IC reference data, which adversely influences the efficiency of control charts. In recent years, a few authors have been done on the effect of parameter estimation in monitoring profiles, especially profiles whose response variables do not follow the normal distribution. In this paper, Hotelling’s T2 chart and a multivariate exponentially weighted moving average (MEWMA) chart are used to monitor the logistic regression profile in Phase II with estimated parameters. In addition, two criteria including average of average run length (AARL) and standard deviation of average run length (SDARL) are utilized to appraise the effect of parameters estimation in Phase I on the Phase II performance of designed control charts through simulation runs. The results illustrate that the performance of these charts is significantly affected by the estimated parameters in both IC and OC conditions. Also, two methods are utilized to decrease the effect of parameters estimation which include increasing the number of reference profiles in Phase I and modifying the control limits.