Transforming non-normal data to normality in statistical process control

Quality characteristics analyzed in statistical process control (SPC) often are required to be normally distributed. This is true in many types of control charts and acceptance sampling plans, as well as in process capability studies. If a characteristic is not normally distributed, but normal-based techniques are used, serious errors can result. One approach to solving this problem is to transform the non-normal data to normality using the Johnson system of distributions. In this paper, we use the sample quantile ratio, in conjunction with the Shapiro-Wilk test of normality, to find a suitable transformation for non-normal data. Examples of fitting non-normal SPC data are presented and discussed. The effect of the Johnson transformation on an SPC procedure involving an estimator for the population standard deviation is studied using non-normal data and Johnson-transformed data.