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http://dx.doi.org/10.5351/KJAS.2017.30.1.001

Average run length calculation of the EWMA control chart using the first passage time of the Markov process  

Park, Changsoon (Department of Applied Statistics, Chung-Ang University)
Publication Information
The Korean Journal of Applied Statistics / v.30, no.1, 2017 , pp. 1-12 More about this Journal
Abstract
Many stochastic processes satisfy the Markov property exactly or at least approximately. An interested property in the Markov process is the first passage time. Since the sequential analysis by Wald, the approximation of the first passage time has been studied extensively. The Statistical computing technique due to the development of high-speed computers made it possible to calculate the values of the properties close to the true ones. This article introduces an exponentially weighted moving average (EWMA) control chart as an example of the Markov process, and studied how to calculate the average run length with problematic issues that should be cautioned for correct calculation. The results derived for approximation of the first passage time in this research can be applied to any of the Markov processes. Especially the approximation of the continuous time Markov process to the discrete time Markov chain is useful for the studies of the properties of the stochastic process and makes computational approaches easy.
Keywords
Markov process; first passage time; average run length; integral equation; transition matrix; Weibull distribution;
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