Kotchaporn Karoon, Yupaporn Areepong^*, Saowanit Sukparungsee

Computer Systems Science and Engineering, Vol.44, No.2, pp. 1143-1160, 2023, DOI:10.32604/csse.2023.025420

Abstract The Extended Exponentially Weighted Moving Average (extended EWMA) control chart is one of the control charts and can be used to quickly detect a small shift. The performance of control charts can be evaluated with the average run length (ARL). Due to the deriving explicit formulas for the ARL on a two-sided extended EWMA control chart for trend autoregressive or trend AR(p) model has not been reported previously. The aim of this study is to derive the explicit formulas for the ARL on a two-sided extended EWMA control chart for the trend AR(p) model as well as the trend AR(1)… More >

Kotchaporn Karoon, Yupaporn Areepong^*, Saowanit Sukparungsee

Intelligent Automation & Soft Computing, Vol.33, No.2, pp. 743-759, 2022, DOI:10.32604/iasc.2022.023322

Abstract Extended Exponentially Weighted Moving Average (Extended EWMA or EEWMA) control chart is one of the control charts which can quickly detect a small shift. The average run length (ARL) measures the performance of control chart. Due to the derivation of the explicit formulas for ARL on the EEWMA control chart for the autoregressive AR(p) process has not previously been reported. The aim of the article is to derive explicit formulas of ARL using a Fredholm integral equation of the second kind on EEWMA control chart for Autoregressive process, as AR(2) and AR(3) processes with exponential white noise. The accuracy of… More >

Lan Wu¹, Xue-Yan Chen¹, Muhammet Cihat Dağli², Feng Qi^3,4,*

CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.1, pp. 295-305, 2022, DOI:10.32604/cmes.2022.018778

Abstract In the paper, with the help of the Faá di Bruno formula and an identity of the Bell polynomials of the second kind, the authors define degenerate λ-array type polynomials, establish two explicit formulas, and present several recurrence relations of degenerate λ-array type polynomials and numbers. More >

Piyatida Phanthuna, Yupaporn Areepong^*, Saowanit Sukparungsee

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.1, pp. 23-41, 2021, DOI:10.32604/cmes.2021.013810

Abstract A modified exponentially weighted moving average (EWMA) scheme is one of the quality control charts such that this control chart can quickly detect a small shift. The average run length (ARL) is frequently used for the performance evaluation on control charts. This paper proposes the explicit formula for evaluating the average run length on a two-sided modified exponentially weighted moving average chart under the observations of a first-order autoregressive process, referred to as AR(1) process, with an exponential white noise. The performance comparison of the explicit formula and the numerical integral technique is carried out using the absolute relative change… More >