Robust Scale Estimator-Based Control Charts for Marshall-Olkin Inverse Log-Logistic Distribution

Abstract

The combination of Shewhart X and S-control charts developed to control the process variability based on
the assumption that the underlying distribution of the quality characteristic is normal. The normality assumption is
often violated when the underlying distribution of the characteristic under consideration is skewed; therefore, the use of the Shewhart X and S control charts on real-life data might lead to inaccurate estimation of control limits. The robust methods of estimation of control chart statistics can be used in such situations. In this paper, the robust scale estimator was used to estimate the mean, variance and median based on Marshall-Olkin Inverse log-logistic distribution. Monte Carlo simulation study was conducted using Marshall-Olkin Inverse log-logistic distribution to determine the performance of the proposed method in comparison with the Shewhart S and MAD methods. The proposed control limits showed an improvement over the Shewhart and stocktickerMAD control charts for non-normal process.