Explicit analytical solutions for the average run length of CUSUM and EWMA charts

G. Mititelu, Y. Areepong, S. Sukparungsee, A. Novikov

Research output: Contribution to journalArticlepeer-review

Abstract

We use the Fredholm type integral equations method to derive explicit formulas for the Average Run Length (ARL) in some special cases. In particular, we derive a closed form representation for the ARL of Cumulative Sum (CUSUM) chart when the random observations have hyperexponential distribution. For Exponentially Weighed Moving Average (EWMA) chart we solve the corresponding ARL integral equation when the observations have the Laplace distribution. The explicit formulas obviously takes less computational time than the other methods, e.g. Monte Carlo simulation or numerical integration.
Original languageEnglish
Pages (from-to)253-265
Number of pages13
JournalEast-West Journal of Mathematics
Volume2010
Issue numberSpecial edition
Publication statusPublished - 2010

Keywords

  • integral equations
  • CUSUM technique
  • numerical integration

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