An accurate algorithm to compute the run length probability distribution, and its convolutions, for a CUSUM chart to control normal mean

摘要

The performance of a CUSUM chart is judged from run length to detect a specified shift in process mean. This article proposes an algorithm that is fast and accurate to compute the run length probability distribution. The algorithm is based on an integral equation for the characteristic function of the run length and uses efficient and accurate formulas based on Gaussian quadrature rules. The probability distribution for the sum of r independent and identically distributed run lengths can also be obtained from the algorithm. The superiority of this algorithm over the previous methods is demonstrated through illustrative examples. (29 refs.)