Computation of the run-length percentiles of CUSUM control charts under changes in variances
In this paper, the run-length distributions of cumulative sum (CUSUM) charts for monitoring mean changes under normal distributions have been investigated thoroughly. However, there are few studies devoted to the analysis of the run-length distributions of CUSUM charts under changes in process variances. Motivated by this, this paper develops a fast and accurate algorithm based on piecewise collocation method for computing the run-length distributions of CUSUM scale charts. It is shown that the proposed method can provide more accurate approximation to the run-length distribution than the conventional Gauss-type quadrature-based methods applied to the CUSUM location charts. Some computational aspects for facilitating computation load are discussed, including the alternative formulation based on matrix decomposition and the geometric approximation to the distribution of large run lengths.
variance average run length integral equation integration kernel statistical process control