Phase II Monitoring of Autocorrelated Polynomial Profiles in AR(1) Processes

In many practical situations, the quality of a process or product can be characterized by a function or profile. Here, we consider a polynomial profile and investigate the effect of the violation of a common independence assumption, implicitly considered in most control charting applications, on the performance of the existing monitoring techniques. We specifically consider a case when there is autocorrelation between profiles over time. An autoregressive model of order one is used to model the autocorrelation structure between error terms in successive profiles. In addition, two remedial methods, based on time series approaches, are presented for monitoring autocorrelated polynomial profiles in phase II. Their performances are compared using a numerical simulation runs in terms of an Average Run Length (ARL) criterion. The effects of assignable cause and autocorrelation coefficient on the shape of profiles are also investigated.