Wannaporn Suriyakat, Yupaporn Areepong,
Saowanit Sukparungsee, Gabriel Mititelu
Department of Applied Statistics
Faculty of Applied Science
King Mongkut's University of Technology
North Bangkok, Bangkok, 10800, THAILAND
Department of Mathematical Sciences
University of Technology Sydney
Broadway, NSW 2007, AUSTRALIA

Abstract. In this paper, we use Fredholm second kind integral equations method to solve the corresponding Average Run Length (ARL), when the observations of a random process are serially-correlated. We derive explicit expressions for the ARL of an EWMA control chart, or its corresponding AR(1) process, when the observations follow an exponential distribution white noise. The analytical expressions derived, are easy to implement in any computer packages, and as a consequence, it reduces considerably the computational time comparable with the traditional numerical methods used to solve integral equations.

Received: February 5, 2012

AMS Subject Classification: 60A05

Key Words and Phrases: average Run Length, exponential white noise, exponentially weighted moving average chart, fredholm integral equation

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