Weighted variance capability index for general non-normal processes

Process capability indices are considered to be one of the important quality measurement tools for the continuous improvement of quality and productivity. The most commonly used indices assume that process data are normally distributed. However, many studies have pointed out that the normally-based indices are very sensitive to non-normal processes. Therefore we propose a new process capability index applying the weighted variance control charting method for non-normal processes to improve the measurement of process performance when the process data are non-normally distributed. The main idea of the weighted variance method is to divide a skewed or asymmetric distribution into two normal distributions from its mean to create two new distributions which have the same mean but different standard deviations. In this paper we provide an example, a distribution generated from the Johnson family of distributions, to demonstrate how the weighted variance-based process capability indices perform in comparison with another two non-normal methods, namely the Clements and Johnson-Kotz-Pearn methods. This example shows that the weighted variance-based indices are more consistent than the other two methods in estimating process fallout for non-normal processes.