A New EWMA Control Chart for Monitoring Multinomial Proportions

Abstract

Control charts have been widely used for monitoring process quality in manufacturing and have played an important role in triggering a signal in time when detecting a change in process quality. Many control charts in literature assume that the in-control distribution of the univariate or multivariate process data is continuous. This research develops two exponentially weighted moving average (EWMA) proportion control charts to monitor a process with multinomial proportions under large and small sample sizes, respectively. For a large sample size, the charting statistic depends on the well-known Pearson’s chi-square statistic, and the control limit of the EWMA proportion chart is determined by an asymptotical chi-square distribution. For a small sample size, we derive the exact mean and variance of the Pearson’s chi-square statistic. Hence, the exact EWMA proportion chart is determined. The proportion chart can also be applied to monitor the distribution-free continuous multivariate process as long as each categorical proportion associated with specification limits of each quality variable is known or estimated. Lastly, we examine simulation studies and real data analysis to conduct the detection performance of the proposed EWMA proportion chart.