Evaluating Parameter Estimation Effect on the Polynomial Profile Monitoring Methods’ Phase II Performance

In several statistical process monitoring applications, it is possible to determine the quality of a product or process using a linear or nonlinear regression relationship called "profile". Basically, standard monitoring methods involve two phases: Phase I and II. Usually, there is a general assumption about knowing the process parameters; yet, this condition is not met in several applications, and parameter estimation takes place using the in-control data set gathered in Phase I. The present study evaluates and compares some Phase II control chart approaches to monitor the second-order polynomial profiles when the parameters of the process are estimated. These methods include Orthogonal, MEWMA and dEWMA-OR control charts. Each control chart performance is measured concerning ARL, SDRL, AARL and SDARL metrics using the Monte Carlo simulation approach. The results showed that parameter estimation strongly affects the in-control and out-of-control performance of control charts, particularly in the case of using only a few Phase-I samples for the parameter estimation. Moreover, the superior overall performance of the Orthogonal method rather than the other competing methods is shown. Furthermore, we concluded that the F estimation method leads to better control chart performance in Phase II.