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Wilasinee Peerajit.. Performance of the CUSUM control chart using approximation to ARL for long- memory fractionally integrated autoregressive process with exogenous variable. (). King Mongkut's University of Technology North Bangkok. Central Library. : , 2023.
Performance of the CUSUM control chart using approximation to ARL for long- memory fractionally integrated autoregressive process with exogenous variable
Name: Direk Bualuang.
Organization :
Uttaradit Rajabhat University. Faculty of Science and Technology
Name: Wilasinee Peerajit.
Organization :
King Mongkut's University of Technology North Bangkok. Faculty of Applied Science
Email :
wilasinee.p@sci.kmutnb.ac.th
keyword:
Average run length.
LCSH:
Quality control
-- Charts, diagrams, etc.
LCSH:
Integral equations
-- Numerical solutions.
Abstract:
The cumulative sum (CUSUM) control chart is a well-known process monitoring tool that is sensitive to small-to-moderate changes in process parameters. In this paper, we propose an approximated average run length (ARL) method based on the numerical integral equation (NIE) method for monitoring the mean of a long-memory autoregressive fractionally integrated process with an exogenous variable (ARFIX) running on a CUSUM control chart. The approximated ARL based on the NIE method is realized by solving a system of linear equations and integration based on the partitioning and summation of the area under the curve of a function derived by using the Gauss-Legendre quadrature. In a comparative study with the ARL based on analytical formulas, the proposed approximated ARL method could detect shifts of various sizes in the process mean of an ARFIX process running on a CUSUM control chart. In addition, the proposed method was compared with their analytical formulas in terms of the relative percentage change (r percent) to verify the accuracy of the ARL results. The results revealed that the ARL results obtained from the NIE method are an approach to analytical formulas with r percent of less than 0.25. Hence, the NIE method is very accurate and in excellent agreement with the analytical formulas approach. Apparently, the NIE method is an alternative as efficiently as the analytical method for this situation. It also performed well in comparison with the approximated ARL for the same process running on an exponentially weighted moving average control chart. In addition, real datasets are also used to demonstrate the efficacy of the proposed method.
King Mongkut's University of Technology North Bangkok. Central Library
Address:
BANGKOK
Email:
library@kmutnb.ac.th
Created:
2023
Modified:
2566-02-12
Issued:
2023-02-12
บทความ/Article
application/pdf
BibliograpyCitation :
APPLIED SCIENCE AND ENGINEERING PROGRESS. vol. 16, no. 2 (Apr.-June 2023), p. 1-13.
eng
©copyrights King Mongkut's University of Technology North Bangkok
RightsAccess:
ใช้เวลา
0.026954 วินาที
Direk Bualuang.
| Title | Contributor | Type |
|---|---|---|
| Performance of the CUSUM control chart using approximation to ARL for long- memory fractionally integrated autoregressive process with exogenous variable
มหาวิทยาลัยเทคโนโลยีพระจอมเกล้าพระนครเหนือ Direk Bualuang.;Wilasinee Peerajit. | บทความ/Article | |
| The performance of DEWMA and EWMA for ZIB model when underlying distribution is the ratio of two poisson means
มหาวิทยาลัยเทคโนโลยีพระจอมเกล้าพระนครเหนือ Direk Bualuang. | บทความ/Article |
Wilasinee Peerajit.
| Title | Contributor | Type |
|---|---|---|
| An approximation to the average run length on a CUSUM control chart with a numerical integral equation method for a long-memory ARFIMAX model
มหาวิทยาลัยเทคโนโลยีพระจอมเกล้าพระนครเหนือ Wilasinee Peerajit. | บทความ/Article | |
| The performance of CUSUM control chart for monitoring process mean for autoregressive moving average with exogenous variable model
มหาวิทยาลัยเทคโนโลยีพระจอมเกล้าพระนครเหนือ Wilasinee Peerajit.;Yupaporn Areepong. | บทความ/Article | |
| Performance of the CUSUM control chart using approximation to ARL for long- memory fractionally integrated autoregressive process with exogenous variable
มหาวิทยาลัยเทคโนโลยีพระจอมเกล้าพระนครเหนือ Direk Bualuang.;Wilasinee Peerajit. | บทความ/Article |