An Approximation of ARL for Poisson GWMA Using Markov Chain Approach

Authors

  • Yada Phengsalae Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand.
  • Yupaporn Areepong Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand.
  • Saowanit Sukparungsee Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand.

Keywords:

generally weighted moving average, exponentially weighted moving average, monitoring, average run length, markov chain approach, monte carlo simulation

Abstract

The objective of this research is to propose an approximation of Average Run Length (ARL) by Markov Chain Approach (MCA) for Generally Weighted Moving Average Control Chart (GWMA) when observations are from Poisson distribution. The numerical results obtained from MCA are compared with the results obtained from Monte Carlo Simulation (MC). The performance of control charts are compared in term of monitoring of a change in the process mean defined by out-of-control Average Run Length (ARL1). The results found that the numerical results obtained from MCA are as good as from MC, however, MCA is very time saving. Furthermore, the performance of GWMA chart is superior to EWMA chart when the magnitudes of changes are small ( \delta\leq 0.20).

Author Biography

Yada Phengsalae, Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand.

Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand.

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How to Cite

Phengsalae, Y., Areepong, Y., & Sukparungsee, S. (2015). An Approximation of ARL for Poisson GWMA Using Markov Chain Approach. Thailand Statistician, 13(1), 111–124. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/34189

Issue

Vol. 13 No. 1 (2015): JANUARY

Section

Articles