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

Abstract

This paper compares three different types of control charting methods used in the and gamma distributions while the control charts for skewed distributions studied are the weighted variance chart `WV − chart´ , weighted standard deviation chart `WSD − chart´ and skewness correction chart (SC − 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 − and WSD − charts have better ARL0 performances than the WV − chart. The SC − and WSD − charts have about the same ARL0 performances. Keywords: Control chart; skewed distribution; weighted variance (WV); weighted standard deviation (WSD); skewness correction (SC); average run length (ARL); process mean.