Petcharat, K, Areepong, Y, Sukparungsee, S & Mititelu, G 2014, 'Exact Solution for Average Run Length of CUSUM Charts for MA(1) Process', Chiang Mai Journal of Science, vol. 41, no. 5.2, pp. 1449-1456.
In this paper we apply Fredhom type integral equations method to derive explicit formula
of the average run length (ARL) for a Cumulative Sum (CUSUM) chart, when observations
are described by a first order moving average MA(1) process, with exponential white noise.
We compare the computational time between our analytical explicit expressions for the ARL
performance with the one obtained via Gauss-Legendre numerical scheme for integral equations.
We found that those methods are in excellent agreement however, the computational time of
the former takes approximately 1 second while the latter method consumes the computational
time 11 minutes approximately.
Phanyaem, S, Areepong, Y, Sukparungsee, S & Mititelu, G 2013, 'Explicit formulas of average run length for ARMA(1,1)', International Journal of Applied Mathematics & Statistics, vol. 43, no. 13, pp. 392-405.
Exponentially weighted moving average control chart (EWMA) is a popular chart used for detecting shift in the mean of parameter of distributions in quality control. The objective of this paper is to derive explicit formulas of Average Run Length (ARL) for Autoregressive and Moving Average (ARMA) models by using Integral Equation technique. We find explicit formulas of ARL for EWMA control chart and compare the result of the proposed expressions with Numerical Integral Equation. The explicit formulas for ARL that we have derived have been found to be accurate, fast and easy to calculate in comparison with Integral Equation technique.
Busaba, J, Sukparungsee, S, Areepong, Y & Mititelu, G 2012, 'Analysis Of Average Run Length For Cusum Procedure With Negative Exponential Data', Chiang Mai Journal of Science, vol. 39, no. 2, pp. 200-208.
The Average Run Length (ARL) is a performance measure that is frequently used in control charts. Cumulative Sum (CUSUM) is a popular procedure in quality control as it is a sensitive detector of small shifts in values of distribution parameters. In this
In a standard formulation, a change-point detection (CPD) problem consists in detecting spontaneous changes in the distribution function of sequential random observations, at some unknown points. In many applications, observations of a random process in discrete or continuous time are received sequentially, and, at a certain moment, random or not but unknown, some probabilistic characteristics of this process are changing. An observer should decide as quickly as possible whether change-points occur or not. Besides, the observer should not raise too many `false alarms, that is, make decisions about detecting change-points when they are not presented.
Petcharat, K, Areepong, Y, Sukparungsee, S & Mititelu, G 2012, 'Fitting pareto distribution with hyperexponential to evaluate the ARL for CUSUM chart', International Journal of Pure and Applied Mathematics, vol. 77, no. 2, pp. 233-244.
Explicit formulas for the Average Run Length (ARL) of Cumulative Sum (CUSUM) chart are very complicated in regarding the analytical derivation when observations are Long-tailed distributions. The objective of this paper is to ?tting Pareto distribution with the hyperexponential distribution to evaluate ARL of CUSUM procedure. The numerical results obtained from analytical solution for the ARL and from numerical approximations are derived and we compared the result with integral equations approach.
Suriyakat, W, Areepong, Y, Sukparungsee, S & Mititelu, G 2012, 'Analytical Method of Average Run Length for Trend Exponential AR(1) Processes in EWMA Procedure', IAENG International Journal of Applied Mathematics, vol. 42, no. 4, pp. 1-4.
The Exponentially Weighted Moving Average (EWMA) procedure are used for monitoring and detecting small shifts in the process mean which performs quicker than the Shewhart control chart. Usually, the common assumption of the Statistical Process Control (SPC) is the observations are independent and identically distributed (IID). In practice, however, the observed data are from industry and finance is serially correlated with trend. In this paper, we extend to use CUSUM procedure to compare with EWMA procedure. The performance of latter is superior to the former when the magnitudes of shift are small to moderate. It is shown that EWMA procedure performs better than the CUSUM procedure for the case of trend exponential AR(1) processes.
Suriyakat, W, Areepong, Y, Sukparungsee, S & Mititelu, G 2012, 'On EWMA procedure for AR(1) observations with exponential white noise', International Journal of Pure and Applied Mathematics, vol. 77, no. 1, pp. 73-83.
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.