Improving Process Monitoring with a New Modified EWMA Control Chart for ARMA Models: A Case Study on Palm Oil Prices in Thailand

Sittikorn  Khamrod; Yupaporn  Areepong; Saowanit  Sukparungsee; Rapin  Sunthornwat

Authors

Sittikorn Khamrod Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
Yupaporn Areepong Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
Saowanit Sukparungsee Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
Rapin Sunthornwat Industrial Technology Program, Faculty of Science and Technology, Pathumwan Institute of Technology, Bangkok, Thailand

Keywords:

Average run length, zero-state, explicit formula, Gauss-Legendre rule, change point detection

Abstract

This investigation was designed to develop precise formulations for calculating the average run length (ARL) of an autoregressive moving average process, with a particular focus on the ARMA(p,q) process. The accuracy of these formulations was assessed by comparing them to the results of the Gauss-Legendre quadrature rule-based numerical integral equation (NIE) approach, which also considered CPU time. Furthermore, the ARL values derived from explicit formulas were compared across control charts that utilized exponentially weighted moving averages (EWMA), modified EWMA (MEWMA), and new modified EWMA (NMEWMA). Performance was assessed using metrics such as the performance comparison index (PCI), average extra quadratic loss (AEQL), and relative mean index (RMI). The results indicated that the NMEWMA control chart was more effective in identifying changes than the EWMA and MEWMA control charts. The efficacy of our explicit formulae technique was further evaluated by comparing the performance of actual data on palm oil prices in Thailand that weighted over 15 kilograms. The NMEWMA control chart outperforms the others by a significant margin, as evidenced by the results of applying the ARL to this data using the explicit formulas.

References

Chananet C, Areepong Y, Sukparungsee S. A Markov chain approach for average run length of EWMA and CUSUM control chart based on ZINB model. Int J Appl Math Stat. 2015; 53(1): 126-137.

Doktoei P, Areepong Y, Sukparungsee S. Average run length approximation on a double exponentially weighted moving average control chart through the numerical integral equation approach. Thail Stat. 2024; 22(4): 926-938.

Fonseca A, Ferreira PH, Nascimento DC, Fiaccone R, Correa CU, Piña AG, Louzada F. Water particles monitoring in the Atacama desert: SPC approach based on proportional data. Axioms. 2021; 10(3): 154. https://doi.org/10.3390/axioms10030154

Khan N, Aslam M, Jun CH. Design of a control chart using a modified EWMA statistic. Qual Reliab Eng Int. 2017; 33(5): 1095-1104.

Lucas JM, Saccucci MS. Exponentially weighted moving average control schemes: Properties and enhancements. Technometrics. 1990; 32(1): 1-2.

Neammai J, Sukparungsee S, Areepong Y. Explicit analytical form for the average run length of double-modified exponentially weighted moving average control charts through the MA(q) process and applications. Symmetry. 2025; 17(2): 238. https://doi.org/10.3390/sym17020238

Palais RS. A simple proof of the Banach contraction principle. J Fixed Point Theory Appl. 2007; 2(2): 221-223.

Patel AK, Divecha J. Modified exponentially weighted moving average (EWMA) control chart for an analytical process data. J Chem Eng Mater Sci. 2011; 2(1): 12-20.

Peerajit W, Areepong Y, Sukparungsee S. Numerical integral equation method for ARL of CUSUM chart for long-memory process with non-seasonal and seasonal ARFIMA models. Thail Stat. 2018; 16(1): 26-37.

Peerajit W. Gauss-Legendre numerical integrations for average run length running on EWMA control chart with fractionally integrated MAX process. WSEAS Trans Math. 2024; 23: 579-590.

Phanthuna P, Areepong Y. Detection sensitivity of a modified EWMA control chart with a time series model with fractionality and integration. Emerg Sci J. 2022; 6: 1134-1152.

Phanyaem S. Explicit formulas and numerical integral equation of ARL for SARX (P,r)L model based on CUSUM chart. Mathematics and Statistics. 2020; 10(1): 88-99.

Roberts WS. Control chart tests based on geometric moving averages. Technometrics. 1959; 1(3): 239-250.

Saghir A, Aslam M, Faraz A, Ahmad L, Heuchenne C. Monitoring process variation using modified EWMA. Qual Reliab Eng Int. 2020; 36: 328-339.

Serel DA. Economic design of EWMA control charts based on loss function. Math Comput Model. 2009; 49(3-4): 745-759.

Shewhart WA. Economic control of quality of manufactured product. London: Macmillan and Co Ltd; 1931.

Silpakob K, Areepong Y, Sukparungsee S, Sunthornwat R. A new modified EWMA control chart for monitoring processes involving autocorrelated data. Intell Autom Soft Comput. 2023; 36(1): 281-298.

Sunthornwat R, Areepong Y. Average run length on CUSUM control chart for seasonal and non-seasonal moving average processes with exogenous variables. Symmetry. 2020; 12(1): 173. https://doi.org/10.3390/sym12010173

Supharakonsakun Y, Areepong Y, Sukparungsee S. The exact solution of the average run length on a modified EWMA control chart for the first-order moving average process. ScienceAsia. 2020; 46: 109-118.

Suriyakat W, Petcharat K. Exact run length computation on EWMA control chart for stationary moving average process with exogenous variables. Math Stat. 2022; 10(3): 624-635.