On the Monitoring of BINARCH(1) Processes with CUSUM-Type Charts

In this work, we develop and study one-sided cumulative sum (CUSUM) control charts for monitoring correlated counts with finite range. Often in practice, data of this kind can be adequately described by a first-order binomial integer-valued ARCH model. The proposed charts are based on a likelihood ratio type statistic and can be used for detecting upward, or downward shifts in the process mean level as well as changes in autocorrelation structure. We provide the general framework for the development and the practical implementation of the proposed charts, along with empirical rules for their design. Using Monte Carlo simulation, we compare numerically the performance of the proposed CUSUM charts with the corresponding one-sided Shewhart and exponentially weighted moving average (EWMA) charts. The numerical results show that the proposed charts are very effective in the detection of pre-specified shifts in process parameters. In addition, it is possible to apply a post-signaling procedure to determine which of the process parameters has changed. In terms of overall performance, the proposed charts also outperform their direct competitors. Finally, two real applications of the proposed charts are discussed.