The Design of and<i>R</i>Control Charts for Skew Normal Distributed Data

Abstract

The Shewhart-type control chart is traditionally developed under the normality assumption. In practice, however, this assumption may not hold. Because the skew normal distribution represents a broad distribution class and is more flexible than is the normal distribution, we propose two new control charts to monitor process mean and spread for skew normal distributed data. Moreover, to facilitate practical implementation, tables of charting constants are provided. We conducted simulation studies to compare the false alarm rates, and the results show that new proposed charts perform better than others as skewness increases. Finally, an illustrative example is provided.