Statistical Performance of X ̅ and R Control Charts for Skewed Distribution - Case Study

Abstract

The purpose of the article is to determine the Type I error and Average Run Length values for charts and R, for which control limits have been determined based on the Skewness Correction method (SC method), with an unknown probability distribution of the qualitative feature being tested. The study also used the Monte Carlo Simulation, in which two sampling methods were used to obtain random input scenarios - matching theoretical distributions (selected skewed distributions) and bootstrap resampling based on a manufacturing company’s measurement data. The presented article is a continuation of Czabak-Górska's (2016) research. The purpose of the article was to determine Type I error value and ARL type A for chart and R, for which the control limits were determined based on the skewness correction method. For this purpose, measurement data from a company producing car seat frames. Presented case study showed that the chart determined using the skewness correction method works better for the data described by the gamma or log-normal distribution. This, in turn, may suggest that appropriate distribution was selected for the presented data, thanks to which it is possible to determine the course and nature of the process, which is important from the point of view of its further analysis, e.g. in terms of the process capability.