The effect of skewness on estimates of some process capability indices

Abstract

The use of process capability indices, which are statistical measures of process capability, is based on several assumptions. For instance, the process monitored is supposed to be stable and the process output should be approximately normally distributed. These assumptions are not always fulfilled in practice. This article focuses on the problem when the process monitored has an output which is non-normally distributed. After presenting a short literature review on research concerning process capability indices and non-normal distributions, the effect of skewness on estimates of process capability indices is studied using a simulation study based on lognormally distributed process outputs. It is found that the effect of skewness is relatively systematic. From the study it is clear that the effect of skewness on estimates of process capability indices is so severe that it has to be considered when studying the capability of a process. Otherwise, erroneous decisions might be made when improving the process studied. It is suggested that further research, for instance, focusing on correction-factors to use when the process output has different skew shapes might be meaningful. However, research focusing on totally new ways of estimating process capability is primarily encouraged.