Methods for Monitoring Multiple Proportions When Inspecting Continuously

Abstract

As technology advances, the need for methods to monitor processes that produce readily-available inspection data becomes essential. In this paper, a multinomial cumulative sum (CUSUM) chart is proposed to monitor in situations where items can be classified into more than two categories, the items are not put into subgroups, and the direction of the out-of-control shift in the parameter vector can be specified. It is shown through examples that the multinomial CUSUM chart can detect shifts in category probabilities at least as quickly and, in most cases, faster than using multiple Bernoulli CUSUM charts. The properties of the multinomial CUSUM chart are determined through a Markov chain representation. If the direction of the out-of-control shift in the parameter vector cannot be specified, we recommend the use of multiple Bernoulli CUSUM charts.