Determining the Decision Limit of CUSUM Chart for A Fixed Sample Size

When we compare different control charting schemes, the average run length of each control chart is usually used. The use of the average run length implies that there is unbounded number of samples or observations. The regression recursive residuals, however, have been applied to the cumulative sum chart to detect whether the mean or variance changes. To implement choice of decision interval, we calculate the probability that certain fixed number of control statistics stay in the in-control state. This probability can be used as the significance level of a test for detecting the change in the residual mean or variance of the data with a finite number of observations.