The cumulative sum (CUSUM) technique is well-established in theory and practice of process control. A comprehensive exposition of the method is given, e.g., by Wetherill and Brown (1991). A question that is seldom treated in the literature is that on the effect of serial correlation of the control variable. Johnson and Bagshaw (1974) investigate the effect of correlation on the run length distribution when the control variable follows a first order autoregressive or moving average process. They also give an approximate expression for the average run length of the CUSUM- technique for correlated control variables. In this paper we derive an exact expression for the average run length of a discretized CUSUM-technique, i.e., a technique that uses a scoring system for the observations of the control variable. The scoring system is that suggested by Munford (1980). Our results are derived for a control variable that is assumed to follow a first order autoregressive process and with normally distributed disturbances. After deriving in Section 2 the expression for the average run length we discuss its dependence on the process parameter and give a numerical illustration. In Section 3 we discuss corrections for the CUSUM-technique in order to keep the nominal risk for an out-of-control decision and compare our results with those given by Johnson and Bagshaw (1974). (author's abstract) / Series: Forschungsberichte / Institut für Statistik

This paper deals with CUSUM tests for monitoring of intensity parameter of a Poisson process if this process can be observed in a restricted manner only at pregiven equidistant time points. In this case the process can be monitored by means of a CUSUM test for the parameter of a corresponding Poisson distribution. For rational reference parameter values the computation of average run length is reduced to that of solving of a system of simultaneous linear equations. The performance of obtained CUSUM tests is discussed by means of corresponding examples.

This paper deals with CUSUM tests based on grouped or classified observations. The computation of average run length is reduced to that of solving of a system of simultaneous linear equations. Moreover a corresponding approximation based on the Wald approximations for characteristics of sequential likelihood ratio tests is presented. The effect of grouping is investigated with a CUSUM test for the mean of a normal distribution based on F-optimal grouping schemes. The considered example demonstrates that hight efficient CUSUM tests can be obtained for F-optimal grouping schemes already with a small number of groups.

This paper deals with CUSUM tests based on grouped or classified observations. The computation of average run length is reduced to that of solving of a system of simultaneous linear equations. Moreover a corresponding approximation based on the Wald approximations for characteristics of sequential likelihood ratio tests is presented. The effect of grouping is investigated with a CUSUM test for the mean of a normal distribution based on F-optimal grouping schemes. The considered example demonstrates that hight efficient CUSUM tests can be obtained for F-optimal grouping schemes already with a small number of groups.

This paper deals with CUSUM tests for monitoring of intensity parameter of a Poisson process if this process can be observed in a restricted manner only at pregiven equidistant time points. In this case the process can be monitored by means of a CUSUM test for the parameter of a corresponding Poisson distribution. For rational reference parameter values the computation of average run length is reduced to that of solving of a system of simultaneous linear equations. The performance of obtained CUSUM tests is discussed by means of corresponding examples.