Main Article Content
The average run length (ARL) is a criterion for measuring the efficiency of a control chart conventionally computed based on the assumption of type I errors for the in-control process and type II errors for the out-of-control process. Still, the eigenvalue approach for the ARL by controlling the direction on its eigenvector is a good alternative. Thus, the objectives of this research are to evaluate the ARL based on the eigenvalue approach on an exponentially weighted moving average (EWMA) control chart and to apply ARL computation to the inflation rate data of the Thai economy. The methods used for ARL evaluation in a comparative study are based on integral equations, a numerical method, the eigenvalue approach, parameter estimation, and fitting of the probability density function. The findings show that the distinct eigenvalues of the ARL on an EWMA control chart monitoring the Thai economy inflation rate with a symmetric kernel are all real and the maximum eigenvalue returns the maximum values of ARL0 (the in-control process) and ARL1 (the out-of-control process). Moreover, an eigenvalue close to zero returns ARL0 and ARL1 values close to one.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
 Areepong Y, Sukparungsee S. An integral equation approach to EWMA chart for detecting a change in lognormal distribution. Thai Stat. 2010;8(1):47-61.
 Bank of Thailand: Report for consumer price index country [Internet]. 2019 [updated 2019 Mar 20; cited 2019 Apr 12]. Available from:https://www.bot.or.th/english/statistics/economicandfinancial/realse
 Champ C, Rigdon S. A comparison of the Markov chain and the integral equation approaches for evaluating the run length distribution of quality control charts. Commu Stat Simu Compu. 1991;20(1):191-203.
 Eke CN. Theoretical distribution fitting of monthly inflation rate in Nigeria from 1997-2014. Int J Inno Fin Eco Res. 2016;4(4):38-49.
 Crowder SV. A simple method for studying run-length distributions of exponentially weighted moving average charts. Technom. 1987;29(4):401-407.
 Diane E, John D, Lawrence L. The distribution of the Kolmogorov-Smirnov, Cramer-Von Mises, and Anderson-Darling test statistics for exponential populations with estimated parameters. Commu Stat Simu Compu. 2008;37(7):1396-1421.
 Kharab A, Guenther B. An introduction to numerical methods a MATLAB approach. 3rd ed. New York:CRC Press;2012.
 Limpanithiwat K, Rungsombudpornkul L. Relationship between inflation and stock prices in Thailand [Master Thesis]. Umeå University; 2010.
 Mititelu G, Areepong Y, Sukparungsee S, Novikov A. Explicit analytical solutions for the average run length of CUSUM and EWMA charts. E W J Math. 2010;Suppl 1:253-265.
 Shewhart WA. Economic control of quality of manufactured product. 8th New York: ASQ Quality Press;1980.
 Roberts SW. Control chart tests based on geometric moving average. Techno. 1959;1(3):239-250.
 Oraee K, Sayadi AR, Tavassoli M. Economic evaluation and sensitivity-risk analysis of Zarshuran gold mine project. SME Ann Meet. 2011;02:1-6.
 Sukparungsee S, Novikov AA. On EWMA procedure for detection of change in observations via martingale approach. An Inter J Sci App Sci. 2006;6(1):373-380.
 Sun T. Forecasting Thailand’s core inflation. Res Econ. 2004;4(90):1-28.
 Sunthornwat R, Areepong Y, Sukparungsee S. Average run length of the long-memory autoregressive fractionally integrated moving average process of the exponential weighted moving average control chart. Cog Math. 2017;4(1):1-11.
 Sunthornwat R, Areepong Y, Sukparungsee S. Analytical and numerical solutions of average run length integral equations for an EWMA control chart over a long memory SARFIMA process. Songkla J Sci Tech. 2018;4(40):885-895.
 Taguchi H, Wanasilp M. Monetary policy rule and its performance under inﬂation targeting: the evidence of Thailand. Munich Pers RePEc Arch. 2018;5(1):1-19.
 Ugaz W, Sáncheza I. Adaptive EWMA control charts with a time varying smoothing parameter. Stat Econ. 2015;15:1-31.