Asymmetric Tukey’s Control Chart Robust to Skew and Non-Skew Process Observation

In reality, the process observations are away from the assumption that are normal distributed. The observations could be skew distributions which should use an asymmetric chart rather than symmetric chart. Consequently, this research aim to study the robustness of the asymmetric Tukey’s control chart for skew and non-skew distributions as Lognormal and Laplace distributions. Furthermore, the performances in detecting of a change in parameter of asymmetric and symmetric Tukey’s control charts are compared by Average ARL (AARL). The results found that the asymmetric performs better than symmetric Tukey’s control chart for both cases of skew and non-skew process observation.

• S. Sukparungsee

• Asymmetric control limit
• average of average run length
• Tukey’s control chart and skew distributions.

<p>[1] C.M. Borror, D.C. Montgomery and G.C. Runger, &ldquo;Robustness of the EWMA Control Chart to Non-normality&rdquo;, Journal of Quality Technology, 1999, 31(3), 309-316. [2] Z.G. Stoumbos and M.R. Reynolds, &ldquo;Robustness to non-normality and autocorrelation of individuals control charts for monitoring the process mean and variance&rdquo;, Journal of Statistical Computation and Simulation, 2000, 66, 145-187 [3] G. Mititelu, Y. Areepong, S. Sukpakrungsee and A. Novikov, &ldquo;Explicit Analytical Solutions for the Average Run Length of CUSUM and EWMA Charts&rdquo;, East-West Journal of Mathematics, 2010, Special Volume, 253-265. [4] S. Sukparungsee and A.A. Novikov, &ldquo;On EWMA Procedure for Detection of a Change in Observations via Martingale Approach&rdquo;, KMITL Science Journal: An International Journal of Science and Applied Science, 2006, 6(2b), 373-380. [5] F. Alemi, &ldquo;Tukey&rsquo;s Control Chart&rdquo;, Quality Management in Health Care, 2004, 13, 216-221. [6] C.C.Torng and P.H. Lee, &ldquo;ARL Performance of the Tukey&rsquo;s Control Chart&rdquo;, i in Statistics: Simulation and Computation, 2008, 38(3), 541- 557. [7] C.C. Torng and P.H. Lee, &ldquo;The Performance of Double Sampling x</p>