Surveillance of Poisson and Multinomial Processes

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Virginia Tech

As time passes, change occurs. With this change comes the need for surveillance. One may be a technician on an assembly line and in need of a surveillance technique to monitor the number of defective components produced. On the other hand, one may be an administrator of a hospital in need of surveillance measures to monitor the number of patient falls in the hospital or to monitor surgical outcomes to detect changes in surgical failure rates. A natural choice for on-going surveillance is the control chart; however, the chart must be constructed in a way that accommodates the situation at hand. Two scenarios involving attribute control charting are investigated here. The first scenario involves Poisson count data where the area of opportunity changes. A modified exponentially weighted moving average (EWMA) chart is proposed to accommodate the varying sample sizes. The performance of this method is compared with the performance for several competing control chart techniques and recommendations are made regarding the best preforming control chart method. This research is a result of joint work with Dr. William H. Woodall (Department of Statistics, Virginia Tech). The second scenario involves monitoring a process where items are classified into more than two categories and the results for these classifications are readily available. A multinomial cumulative sum (CUSUM) chart is proposed to monitor these types of situations. The multinomial CUSUM chart is evaluated through comparisons of performance with competing control chart methods. This research is a result of joint work with Mr. Lee J. Wells (Grado Department of Industrial and Systems Engineering, Virginia Tech) and Dr. William H. Woodall (Department of Statistics, Virginia Tech).

Average Run Length, Cumulative Sum Chart, Exponentially Weighted Moving Average Chart, Statistical Process Control