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The random intrinsic fast initial response of one-sided CUSUM charts

Author

Listed:
  • Alberto Luceno
  • Jaime Puig-Pey

Abstract

This article analyses the performance of a one-sided cumulative sum (CUSUM) chart that is initialized using a random starting point following the natural or intrinsic probability distribution of the CUSUM statistic. By definition, this probability distribution remains stable as the chart is used. The probability that the chart starts at zero according to this intrinsic distribution is always smaller than one, which confers on the chart a fast initial response feature. The article provides a fast and accurate algorithm to compute the in-control and out-of-control average run lengths and run-length probability distributions for one-sided CUSUM charts initialized using this random intrinsic fast initial response (RIFIR) scheme. The algorithm also computes the intrinsic distribution of the CUSUM statistic and random samples extracted from this distribution. Most importantly, no matter how the chart was initialized, if no level shifts and no alarms have occurred before time τ > 0, the distribution of the run length remaining after τ is provided by this algorithm very accurately, provided that τ is not too small.

Suggested Citation

  • Alberto Luceno & Jaime Puig-Pey, 2006. "The random intrinsic fast initial response of one-sided CUSUM charts," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(2), pages 189-201.
    • Handle: RePEc:taf:japsta:v:33:y:2006:i:2:p:189-201
    DOI: 10.1080/02664760500250610
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    Cited by:

    1. Alberto Luceno & Antonio Cofiño, 2006. "The random intrinsic fast initial response of two-sided CUSUM charts," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 505-524, September.

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