Application of the generalized folded-normal distribution to the process capability measures

Abstract

A generalized folded distribution arises when deviations are measured and the weighted magnitude is recorded, where the weight depends on the degree and the direction (sign) of the deviation. When the underlying distribution is normal, the resulting distribution is referred to as the generalized folded-normal distribution. In this paper, we derive explicit forms of the cumulative distribution function and the probability density function of the generalized folded-normal distribution, and calculate the expected value and the variance. An application of the generalized folded-normal distribution to the process capability measures is illustrated.