Exact Properties of Demerit Control Charts

Abstract

A demerit rating system is used to simultaneously monitor counts of several different types of defects in a complex product. The demerit statistic is a linear combination of the counts of these different types of defects. The traditional recommendation is to plot the demerit statistic on a control chart with symmetric 3-sigma control limits. This approach to demerit rating systems is reviewed. An alternative method for determining control limits for the demerit control chart, based on the exact distribution of linear combinations of independent Poisson random variables, is proposed. This method is generalized for use with the exact distribution of linear combinations of independent random variables in a broad family of discrete distributions.