The design of CUSUM quality control charts
Journal of Quality Technology
Computational Statistics & Data Analysis
Approximate distribution of demerit statistic-A bounding approach
Computational Statistics & Data Analysis
Optimization designs of the combined Shewhart-CUSUM control charts
Computational Statistics & Data Analysis
Computation of the ARL for CUSUM-S2 schemes
Computational Statistics & Data Analysis
Evaluation of the run-length distribution for a combined Shewhart-EWMA control chart
Statistics and Computing
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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.