General control charts for attributes

Abstract

Traditional Shewhart-type control charts ignore the skewness of the plotted statistic. Occasionally, the skewness is too large to be ignored, and in such cases the classical Shewhart chart ceases to deliver satisfactory performance. In this paper, we develop a general framework for constructing Shewhart-like control charts for attributes based on fitting a quantile function that preserves all first three moments of the plotted statistic. Furthermore, these moments enter explicitly into the formulae for calculating the limits. To enhance the accuracy of these limits the value of the skewness measure used in the calculations is inflated by 44%. This inflation rate delivers accurate control limits for diversely-shaped attribute distributions like the binomial, the Poisson, the geometric and the negative binomial. A new control chart for the M/M/Squeueing model is developed and its performance evaluated.