A Standard Deviation Control Chart for the Marshall Olkin Inverse Log-logistic Distribution

Abstract

Most process data in real life applications are positively skewed distribution, thereby the traditional Shewhart-S control chart with the assumption of normality may not be appropriate. A control chart for tracking the dispersion of data from Marshall Olkin Inverse Log-logistic distribution (MOILLD) is presented in this study. The performance of the proposed control chart is compared with control charts based on the Shewhart, Skewness Correction (SC), Weighted Standard Deviation (WSD), and Median Absolute Deviation (MAD) using simulation study. The simulation results demonstrate that when skewed data are from MOILLD, the proposed control chart detects out-of-control points faster than existing methods and therefore, outperforms the existing control standard deviation control charts. The proposed control chart was further applied to a real-life skewed data and the obtained results aligned with the simulated results. Therefore, it is recommended that users in the manufacturing and industry sectors implement the proposed approach, particularly in cases where the process data exhibit positive skewness.