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


1 Department of Industrial Engineering,Iran University of Science and Technology

2 Department of Industrial Engineering,Tarbiat Modares University


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 e ect 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 e ects of assignable cause and autocorrelation coecient on the shape of
pro les are also investigated.