Design of a robust T² control chart, a re‐sampling approach

Abstract

In constructing any control chart, the sample size and the number of samples taken are important issues. When destructive tests are applied to collect data, the sample size and the number of subsamples are usually limited. Lack of sufficient observations affects parameters estimates. Re-sampling techniques are always suggested to increase the accuracy of parameters estimates. Also, the presence of outlying observations severely affect re-sampling and the estimates of the underlying distribution parameters. The limited sample size, limited number of subsamples and presence of outliers are more important in multivariate process analysis. In this study, bootstrap re-sampling technique and robust estimators of mean vector and variance-covariance matrix are simultaneously utilized to design a multivariate robust T 2 control chart to address the three problems in hand. The performance of the proposed robust T 2 control chart is evaluated and compared to the Hotelling T 2 control chart by means of average run length (ARL). Simulation results indicate that the suggested robust T 2 control chart outperforms the Hotelling T 2 in presence of outliers and similarly when there is no outlier. Design of robust control chart for processes generating auto-correlated data applying bootstrap re-sampling technique is an area for further research.