On the effect of measurement errors and auto-correlation on the performance of Hotelling’s T2 control chart

Independency of observations is one of the fundamental assumptions in control charts. However, in some processes this assumption is violated and data are auto-correlated. Also, it is assumed that the measurement errors are absent in measurement system while, this assumption is usually violated. The existence of the auto-correlation and measurement errors causes the poor performance of the control charts. In other words, the average run length in the case of out-of-control (OC) situations increases in the presence of auto-correlation and measurement errors. In this paper, the effect of autocorrelation and measurement errors on the performance of Hotelling’s T2 control charts in Phase II in multivariate normal processes is investigated in terms of average run length (ARL) criterion. The first order auto-regressive model as auto-correlation structure between observations within each sample is discussed in this paper. To decrease the effect of auto-correlation and measurement errors on the performance of the Hotelling’s T2 control chart, jump strategy and multiple measurements methods are applied, respectively. The effect of auto-correlation and measurement errors, individually and simultaneously, as well as the performance of the suggested methods to address these effects is appraised through simulation studies and a numerical example. The effect of number of measurements and jumps on the ARL values of the proposed control chart is also evaluated. Results show the acceptable performance of the multiple measurements and jumps methods in diminishing the effect of measurement errors and auto-correlation, respectively. At last, a real case is presented to show the application of the proposed scheme.