Monitoring the asymmetry parameter of a skew-normal distribution

Abstract

In various industries, especially manufacturing and chemical industries, it is often observed that the distribution of a specific process, initially having followed a normal distribution, becomes skewed as a result of unexpected causes. That is, a process deviates from a normal distribution and becomes a skewed distribution. The skew-normal (SN) distribution is one of the most employed models to characterize such processes. The shape of this distribution is determined by the asymmetry parameter. When this parameter is set to zero, the distribution is equal to the normal distribution. Moreover, when there is a shift in the asymmetry parameter, the mean and variance of a SN distribution shift accordingly. In this paper, we propose procedures for monitoring the asymmetry parameter, based on the statistic derived from the noncentral t-distribution. After applying the statistic to Shewhart and the exponentially weighted moving average (EWMA) charts, we evaluate the performance of the proposed procedures and compare it with previously studied procedures based on other skewness statistics.