TRANSFORMING NONNORMAL 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 ty pes of control charts and acceptance sampling plans, as well as in pro cess capability studies. If a characteristic is not normally distribut ed, but normal-based techniques are used, serious errors can result. O ne approach to solving this problem is to transform the non-normal dat a to normality using the Johnson system of distributions. In this pape r, we use the sample quantile ratio, in conjunction with the Shapiro-W ilk test of normality, to find a suitable transformation for non-norma l data. Examples of fitting non-normal SPC data are presented and disc ussed. The effect of the Johnson transformation on an SPC procedure in volving an estimator for the population standard deviation is studied using non-normal data and Johnson-transformed data.