A robust S² control chart with Tukey's and MAD outlier detectors

Shewhart S² control chart is one of the most commonly used tools to monitor the dispersion of a process. In this article, we evaluate the performance of S² control chart when the unknown parameter is estimated from Phase-I samples. Average ARL and standard deviation of ARL metrics are used to evaluate the performance. In the first stage of the study, new control limit coefficients are derived so that the average ARL is equal to the pre-fixed ARL, ie, 370. Secondly, different proportion of outliers is contaminated into Phase-I samples, and the resulting elevated average ARL and standard deviation of ARL are measured. Finally, the application of Tukey's outlier detector is proposed with Phase-I samples so that the elevation caused by the outliers can be controlled and the average ARL can be pulled back close to the pre-fixed ARL. For illustration, the proposed procedures are applied to a data on compressive strength of parts manufactured by an injection molding process.