Effect of Nonnormality on the Economic Design of Warning Limit Charts

Abstract

Control charts are widely applied to monitor manufacturing processes. In 1962, Page presented a modified chart with warning limit, which includes an upper and lower warning band. In 1975, Gordon and Weindling presented a cost model for determining the five parameters of a warning limit chart: the sample size, the sampling interval between successive subgroups, the control limit coefficient, the warning limit coefficient, and the significant run length. When conducting the design of control charts, one usually assumes the measurements are normally distributed. However, this assumption may not be tenable in some specific production processes. Burr developed a general probability distribution to represent a wide range of density functions, including normal and nonnormal ones. In this article, we study the effect of nonnormality on the design of warning limit charts by combining Gordon and Weindling's cost model with the Burr distribution. In this study, it is observed that negative skewness leads to wider control and warning limits. In addition, larger kurtosis results in a longer significant run length and wider control and warning limits.