On monitoring the attributes of a process

Abstract

Two prominent monitoring procedures in statistical quality control are the p-chart for the proportion of items defective, and the c-chart, for the number of defects per item. These procedures are reconsidered, and some extensions are examined for monitoring processes with multiple attributes.

Some relevant distribution theory is reviewed, and some new results are given. The distributions considered are multivariate versions of the binomial, Poisson, and chi-squared distributions, plus univariate and multivariate generalized Poisson distributions. All of these distributions prove useful in the discussion of attribute control charts.

When quality standards are known, p-charts and c-charts are shown to have certain optimal properties. Generalized p-charts, for monitoring multinomial processes, and generalized c-charts are introduced. Their properties are shown to depend upon multivariate chi-squared and generalized Poisson distributions, respectively.

Various techniques are considered for monitoring multivariate Bernoulli, Poisson, multinomial, and generalized Poisson processes. Omnibus procedures are given, and some of their asymptotic properties are derived. Also examined are diagnostic procedures based upon both small- and large-sample.