Phase I monitoring of within-profile autocorrelated multivariate linear profiles
Abstract
As one of the most important subareas of statistical process monitoring (SPM), multivariate profile monitoring has attracted attention in recent years. Most researches on multivariate profile analysis have been carried out under the independency assumption of response values. However,
the independency assumption is violated in many real applications, such as when the observations are gathered in short time intervals. In this paper, we focus on Phase I monitoring of multivariate profiles when the consecutive response values within each profile are autocorrelated and follow the autoregressive-moving average (ARMA(1,1)) model. First, a transformation method is applied to eliminate the effect of autocorrelation. Then, two approaches, T2 and Wilks’ lambda, are used
to check the stability of the process under different magnitudes of shifts and different parameters of the ARMA(1,1) model. A numerical example based on simulation studies is applied to evaluate the performance of the applied control charts in the presence of within-profile autocorrelation in
terms of signal probability criterion. The results show that Wilks’ lambda outperforms the T2 chart in almost all out-of-control situations.
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