Abstract: Investigating the effects of two real-world-occurring phenomena: 'measurement errors' and 'autocorrelation between observations' on control charts, has caught researchers' attention in recent years. However, their combined effect has rarely been investigated; with only one study for multivariate control charts. In this paper, their combined effects will be investigated for the first time in univariate and multivariate control charts on 'adaptive' and/or 'simultaneous process parameters monitoring' control charts and also for the first time in multivariate control charts by using linearly covariate measurement errors, VARMA (vector mixed autoregressive and moving average) autocorrelation models, and Markov Chain based performance measures. To do so, we add the above-mentioned measurement errors and autocorrelation models to a recently developed adaptive VP (variable parameters) max-type control chart which is capable of monitoring the process parameters simultaneously. Then, we develop a Markov chain model to compute the average and standard deviation of time to chart signal. After developing the control scheme as well as the performance measures in the presence of both measurement errors and autocorrelation, extensive simulation studies will be performed to investigate the combined effects of measurement errors and autocorrelation as well as some methods to alleviate their negative effects. In addition, this paper for the first time uses the skip-sampling strategy in an ARMA/VARMA autocorrelation model for alleviating the autocorrelation effect. At last, an illustrative example involving a real industrial case will be presented.
Contact Mohammad Ghorbani to receive the Zoom link.
