A Robust Design for the Omnibus SPRT Control Chart Under Skewed Data Distributions

Abstract

Control charts are widely used in manufacturing industries to ensure that production levels are stable and satisfactory. Recently, the omnibus sequential probability ratio test (OSPRT) control chart was developed for the purpose of monitoring the mean and variability of a process simultaneously. As the OSPRT chart was proposed for the first time in literature, its development relied entirely on the assumption that data follow the Normal distribution. Nonetheless, researchers are frequently reminded that the quality characteristics of manufacturing processes do not necessarily follow the Normal distribution, e.g., strengths of glass fibres, and lifetimes of products. In this paper, we investigate the extent to which the performances of the OSPRT chart designed for the Normal model deteriorate, in situations where the data distributions are Gamma and Lognormal. Results show that the in-control average run length (ARL) and standard deviation of the run length of the OSPRT chart designed for the Normal distribution deteriorate rapidly as skewness increases. To address this issue, we propose a robust design for the OSPRT chart by adjusting its control limits, known as the skewness correction method. It is shown that the skewness-corrected OSPRT chart enjoys a guaranteed in-control ARL, with a justifiable degradation in its out-of-control performances. Besides, we also show some insights into selecting the charting parameters for the skewness-corrected OSPRT chart in order to achieve an optimum out-of-control ARL performance over various shift sizes. The paper wraps up with an illustrative example of the skewness-corrected OSPRT chart for monitoring the weights of radial tyres.