Monitoring and Change Point Estimation of AR(1) Autocorrelated Polynomial Profiles

Abstract

In this paper, a remedial measure is first proposed to eliminate the effect of autocorrelation in phase-ІІ monitoring of autocorrelated polynomial profiles, where there is a first order autoregressive (AR(1)) relation between the error terms in each profile. Then, a control chart based on the generalized linear test (GLT) is proposed to monitor the coefficients of polynomial profiles and an R-chart is used to monitor the error variance, the combination of which is called GLT/R chart. The performance of the proposed GLT/R chart is evaluated by comparing it to ones of prevalent methods including multivariate T2, EWMA/R and T2 residual control charts, in terms of the average run length (ARL) criterion. Furthermore, an estimator based on the likelihood ratio approach is proposed to estimate the change point in the parameters of autocorrelated polynomial profiles. The results of extensive simulation experiments show good performances of the proposed estimator.