The Economic Model of x̄ Control Chart Using Shewhart Method for Skewed Distributions

Authors

  • Adisak Pongpullponsak Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand.
  • Wichai Suracherkeiti Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand.
  • Chaowalit Panthong Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand.

Keywords:

control chart, economic model, skewness, variations of production

Abstract

The purposes of this research were to present economic model and to compare the efficiency of \inline \dpi{80} \bar{X} Control Chart using Shewhart Method for Skewed Distributions. The experiment data sets were Weibull Distribution, Lognormal Distribution, and Burr’s Distribution using the expected value of all expenses per one single unit of time as standard.  The coefficients of skewness (\inline \dpi{100} \alpha _{3}) were 0.1, 0.5, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, and 9.0.  The variations of production level were 0.5σ, 1.0σ, 1.5σ, 2.0σ, 2.5σ, and 3.0σ, obtained by Monte Carlo Simulation Technique. Using an application program with PHP, a total number of 10,000 samples were repeatedly looped. The results indicated that the production level begin to vary from 3.0σ of Lognormal Distribution. The lowest expense was observed at the coefficient of skewness at (\inline \dpi{100} \alpha _{3}) 6.    

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How to Cite

Pongpullponsak, A., Suracherkeiti, W., & Panthong, C. (2015). The Economic Model of x̄ Control Chart Using Shewhart Method for Skewed Distributions. Thailand Statistician, 7(1), 81–99. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/34324

Issue

Vol. 7 No. 1 (2009): JANUARY

Section

Articles