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

摘要

A fast and accurate algorithm to compute the run length probability distribution for a Cusum chart to control process mean is provided. 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 algorithm also provides the probability distribution for the sum of r independent and identically distributed run lengths, where r is a positive integer. Examples are provided to demonstrate the excellent performance of the algorithm, even for very extreme combinations of the design parameters, and to compare this performance with that of previous methods.