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The Effects of Skewed Distributions on the Performance of Variable Sample Size X Chart

Wei Lin Teoh 1, Michael B. C. Khoo 2, Zhi Lin Chong 3, and Sin Yin Teh 4
1. School of Mathematical and Computer Sciences, Heriot-Watt University Malaysia, Putrajaya, Malaysia
2. School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia
3. Department of Physical and Mathematical Science, Faculty of Science, Universiti Tunku Abdul Rahman, Kampar, Perak, Malaysia
4. School of Management, Universiti Sains Malaysia, Penang, Malaysia

Abstract—The variable sample size (VSS)  chart is one of the adaptive control charts that gains prestige in the field of statistical process control during the last decade. Traditionally, the design of the VSS  chart is based on the assumption of normally distributed data or measurements. However, in many real-life applications, the normality assumption may be violated. This paper investigates the effects of skewed distributions on the performance of the VSS  chart. Two VSS schemes are considered in this paper, i.e. (i) the small sample size ( ns ) or (ii) the large sample size (nL), is predetermined for the first sample (n1). Monte Carlo simulation is adopted to evaluate the run-length performances of these two VSS  schemes for different levels of skewness corresponding to Weibull, lognormal and gamma distributions. The results show that the in-control average run lengths for the VSS  chart with n1 = ns are closer to the desired value and have a lower false alarm rate compared to that of the VSS  chart with n1 = nL. 
 
Index Terms—average run length, skewed distribution, standard deviation of the run length, statistical process control, variable sample size  chart

Cite: Wei Lin Teoh, Michael B. C. Khoo, Zhi Lin Chong, and Sin Yin Teh, "The Effects of Skewed Distributions on the Performance of Variable Sample Size  Chart," International Journal of Electrical and Electronic Engineering & Telecommunications, Vol. 8, No. 3, pp. 171-176, May 2019. Doi: 10.18178/ijeetc.8.3.171-176
 

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