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

In some statistical process monitoring applications, the quality of a product or process can be determined by a linear or nonlinear regression relationship called "profile". Basically, standard monitoring methods involve two phases: Phase I and Phase II. Usually, it is assumed that the process parameters are known, however this condition in many applications is not met and parameters are estimated using the in-control data set collected in Phase I. The present study evaluates and compares some Phase II control chart approaches for monitoring the second order polynomial profiles when the process parameters are estimated. These methods includes Orthogonal, MEWMA and dEWMA-OR control charts. The performance of each control chart is measured in terms of ARL, SDRL, AARL and SDARL metrics using Monte Carlo simulation approach. The results showed that the in-control and out-of-control performance of control charts is strongly affected by parameter estimation, especially when only a few Phase I samples are used to estimate the parameters. Moreover, the superior overall performance of the Orthogonal method rather than the other competing methods is shown. Furthermore, we concluded that F estimation method leads to better performance of control charts in Phase II.