On EWMA procedure for AR(1) observations with exponential white noise

Wannaporn Suriyakat; Yupaporn Areepong; Saowanit Sukparungsee; Gabriel Mititelu

On EWMA procedure for AR(1) observations with exponential white noise

Wannaporn Suriyakat, Yupaporn Areepong, Saowanit Sukparungsee, Gabriel Mititelu

Western Sydney University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	73-83
Number of pages	11
Journal	International Journal of Pure and Applied Mathematics
Volume	77
Issue number	1
Publication status	Published - 2012

Keywords

exponentially weighted moving average
integral equations
stochastic systems

Cite this

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title = "On EWMA procedure for AR(1) observations with exponential white noise",

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.",

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AU - Suriyakat, Wannaporn

AU - Areepong, Yupaporn

AU - Sukparungsee, Saowanit

AU - Mititelu, Gabriel

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - exponentially weighted moving average

KW - integral equations

KW - stochastic systems

UR - http://hdl.handle.net/1959.7/uws:57822

UR - https://ijpam.eu/contents/2012-77-1/7/7.pdf

M3 - Article

SN - 1311-8080

VL - 77

SP - 73

EP - 83

JO - International Journal of Pure and Applied Mathematics

JF - International Journal of Pure and Applied Mathematics

IS - 1

ER -

On EWMA procedure for AR(1) observations with exponential white noise

Abstract

Keywords

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