Waiting Time Analysis Using Control Charts Based on Skewness and Kurtosis
Keywords:
Control limits, false alarm rate, kurtosis correction method, skewness correction method, skewness and kurtosis correction method, Shewhart method, weighted standard deviation method, (M/M/1) : (∞/FCFS) queueing system
Abstract
For (M/M/1) : (∞/FCFS) queue, the service or waiting time distribution do not conform to property of symmetry in such situation the traditional chart is improper to give satisfactory performance. In this paper, control charts based on skewness and kurtosis are used to determine the patience limits (i.e. control limits for waiting time) of customers arriving at a system for availing services. A comparative study is carried out and best control chart based on skewness and kurtosis for waiting time for queueing model is evaluated on the basis of performance measure false alarm rate. Also, simulation study is carried out to compare the performances of various control charts using lognormal distribution.
References
K.Derya and H.Canan, Control charts for skewed distributions: Weibull, gamma, and lognormal, Metodoloskizvezki, 9(2)(2012), 95-106.
D.Gross and C.M.Harris, Fundamentals of queueing theory, Third edition. A Wiley-Interscience Publication, (1998).
D.C.Montgomery, Statistical Quality Control: A Modern Introduction, Sixth edition, Wiley-India Edition, India, (2010).
Y.S.Chang and D.S.Bai, Control charts for positively-skewed populations with weighted standard deviations, Quality and Reliability Engineering International, 17(2001), 397-406.
L.K.Chan and H.J.Cui, Skewness correction X and R charts for skewed distributions, Naval Research Logistics 50(6)(2003), 555-573.
S.B.Wang, Skewness and kurtosis correction for X and R control charts, Institute of Statistics, National University of Kaohsiung, Kaohsiung, Taiwan 811 R.O.C,( 2009).
P.R.Tadikamalla and D.G.Popescu, Kurtosis correction method for X and R control chartsfor long-tailed symmetrical distributions, Naval Research Logistics, 54(2007), 371-383.
D.Gross and C.M.Harris, Fundamentals of queueing theory, Third edition. A Wiley-Interscience Publication, (1998).
D.C.Montgomery, Statistical Quality Control: A Modern Introduction, Sixth edition, Wiley-India Edition, India, (2010).
Y.S.Chang and D.S.Bai, Control charts for positively-skewed populations with weighted standard deviations, Quality and Reliability Engineering International, 17(2001), 397-406.
L.K.Chan and H.J.Cui, Skewness correction X and R charts for skewed distributions, Naval Research Logistics 50(6)(2003), 555-573.
S.B.Wang, Skewness and kurtosis correction for X and R control charts, Institute of Statistics, National University of Kaohsiung, Kaohsiung, Taiwan 811 R.O.C,( 2009).
P.R.Tadikamalla and D.G.Popescu, Kurtosis correction method for X and R control chartsfor long-tailed symmetrical distributions, Naval Research Logistics, 54(2007), 371-383.
How to Cite
Nanda Rajput, & Manik Khaparde. (2017). Waiting Time Analysis Using Control Charts Based on Skewness and Kurtosis. International Journal of Current Research in Science and Technology, 3(3), 21-29. Retrieved from https://crst.gfer.org/index.php/crst/article/view/87
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