Evaluation of the Run-Length Probability Distribution for CUSUM Charts: Assessing Chart Performance

Article

Luceno, Alberto; Puig-Pey, Jaime   (2000, ASQ and American Statistical Association)   E.T.S. de Ingenieros de Caminos, University of Cantabria, Santander, Spain

Technometrics    Vol. 42    No. 4
QICID: 14539    November 2000    pp. 411-416
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Article Abstract

[This abstract is based on the author's abstract.] A fast and accurate algorithm for computing the run-length probability distribution for cumulative sum charts to control process mean is provided. The algorithm uses a fast and numerically stable recursive formula that is based on accurate Gaussian quadrature rules over the whole range of the computed run-length distribution. Therefore, it improves the numerical efficiency and accuracy of existing methods. The algorithm may detect whether or not the geometric approximation is adequate and, when possible, allows switching to the geometric recursion. The procedure may be applied to nonsymmetric and long-tailed continuous distributions as well as to the normal distribution. Examples are provided. Consideration is given to methods for assessing chart performance according to the run-length distribution. Some multivariate issues in statistical process control are also considered.

Keywords

Cumulative sum control chart (CUSUM),Decision making,Gaussian curve,Multivariate control charts,Statistical process control (SPC),Run charts,Distributions,Run length,Statistical tests,Probability


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