Control Charts for Monitoring the Mean of Skew-Normal Samples

Abstract

The presence of asymmetric data in production processes or service operations has prompted the development of new monitoring schemes. In this article, an adapted version of the exponentially weighted moving averages (EWMA) control chart with dynamic limits is proposed to monitor the mean of samples from the skew-normal distribution. The detection ability of the proposed control chart in online monitoring was investigated by simulating the average run length (ARL) performance for different out-of-control scenarios. The results of the simulation study suggest that the proposed scheme overcomes the main drawback of the recently developed Shewhart-type control scheme. As shown in this article, the existing Shewhart-type procedure exhibits the undesirable property of taking longer to detect changes in the mean value of skewed normal observations due to increases in the shape parameter of the basic distribution than in stable conditions. The proposed control chart was shown to work fairly acceptably in all considered out-of-control scenarios.

Keywords

• asymmetric data
• average run length
• ARL-unbiasedness
• control charts
• phase II
• skew-normal distribution