Analytic and Numerical Solutions of ARL of CUSUM Procedure for Exponentially Distributed Observations

Authors

  • Sophana Somran Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
  • Yupaporn Areepong Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
  • Saowanit Sukparungsee Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand

Keywords:

Average Run Length, CUSUM, exponential distribution, integral equation

Abstract

This paper aims at deriving the explicit expressions of the Average Run Length (ARL) for a negative Cumulative Sum (CUSUM) chart for a lower-sided case when observations are from exponential distribution. ARL is found using two approaches; Integral Equation (IE) and Numerical Integral Equation (NI). The comparison for accuracy of results for explicit expression have been solved with the Integral Equation approach, while, the numerical approximations have been solved with the Numerical Integral equation, which both tend to an acceptable agreement. The computational time obtained from the NI approach is significantly longer than that obtained from the IE approach.

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Published

2016-01-25

How to Cite

Somran, S., Areepong, Y., & Sukparungsee, S. (2016). Analytic and Numerical Solutions of ARL of CUSUM Procedure for Exponentially Distributed Observations. Thailand Statistician, 14(1), 83–91. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/47321

Issue

Vol. 14 No. 1 (2016): January

Section

Articles