A Comparison of Performances of Three Types of Control Charts for Skewed Distributions

This paper compares three different types of control charting methods used in the monitoring of a process mean from a skewed distribution. The skewed distributions considered are the Weibull, lognormal and gamma distributions while the control charts for skewed distributions studied are the weighted variance X chart `WV X chart′ , weighted standard deviation X chart `WSD X chart′ and skewness correction X chart (SC X chart). These charts will be evaluated based on their in-control average run length (ARL0) performances. ARL is defined as the average number of sample points that must be plotted on a control chart before the first point plots beyond the control limits. Since these charts are designed based on the three standard deviation width, ARL0 ≈ 370 is considered when the underlying distribution of a process is normal. A good chart has a large ARL0 value when the process follows a skewed distribution. A performance comparison based on a simulation study using the Statistical Analysis System (SAS) version 9 program shows that the SC X and WSD X charts have better ARL0 performances than the WV X chart. The SC X and WSD X charts have about the same ARL0 performances.