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 prole. Here, we consider a polynomial prole and investigate the eect of the violation of a common independence assumption, implicitly considered in most control charting applications, on the performance of the existing monitoring techniques. We specically consider a case when there is autocorrelation between proles over time. An autoregressive model of order one is used to model the autocorrelation structure between error terms in successive proles. In addition, two remedial methods, based on time series approaches, are presented for monitoring autocorrelated polynomial proles in phase II. Their performances are compared using a numerical simulation runs in terms of an Average Run Length (ARL) criterion. The eects of assignable cause and autocorrelation coecient on the shape of proles are also investigated.

Statistical process control; Polynomial proles; Autocorrelation; Average run length; Assignable cause; Phase II.