{"title":"在 CUSUM 控制图上近似运行指数白噪声季节时间序列模型均值变化的 ARL","authors":"W. Peerajit","doi":"10.37394/23203.2023.18.39","DOIUrl":null,"url":null,"abstract":"Control charts comprise an excellent statistical process control tool for monitoring industrial processes. Especially, the CUSUM control chart is very sensitive to small-to-moderate process parameter changes. The proposed approach utilizes the numerical integral equation (NIE) method to approximate the average run length (ARL) of changes in the mean of a seasonal time series model with underlying exponential white noise running on a CUSUM control chart. This was achieved by solving a system of linear equations and integration through partitioning and summation using the area under the curve of a function obtained by applying the Gauss-Legendre quadrature. A numerical study was conducted to compare the capabilities of the ARL derivations obtained using the NIE method and explicit formulas to detect changes in the mean of a long-memory model with exponential white noise running on a CUSUM control chart. The results reveal that the performances of both were comparable in terms of the accuracy percentage, which was greater than 95%, meaning that the ARL values were highly consistent. Thus, the NIE method can be used to validate ARL results for this situation.","PeriodicalId":39422,"journal":{"name":"WSEAS Transactions on Systems and Control","volume":"28 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Approximating the ARL of Changes in the Mean of a Seasonal Time Series Model with Exponential White Noise Running on a CUSUM Control Chart\",\"authors\":\"W. Peerajit\",\"doi\":\"10.37394/23203.2023.18.39\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Control charts comprise an excellent statistical process control tool for monitoring industrial processes. Especially, the CUSUM control chart is very sensitive to small-to-moderate process parameter changes. The proposed approach utilizes the numerical integral equation (NIE) method to approximate the average run length (ARL) of changes in the mean of a seasonal time series model with underlying exponential white noise running on a CUSUM control chart. This was achieved by solving a system of linear equations and integration through partitioning and summation using the area under the curve of a function obtained by applying the Gauss-Legendre quadrature. A numerical study was conducted to compare the capabilities of the ARL derivations obtained using the NIE method and explicit formulas to detect changes in the mean of a long-memory model with exponential white noise running on a CUSUM control chart. The results reveal that the performances of both were comparable in terms of the accuracy percentage, which was greater than 95%, meaning that the ARL values were highly consistent. Thus, the NIE method can be used to validate ARL results for this situation.\",\"PeriodicalId\":39422,\"journal\":{\"name\":\"WSEAS Transactions on Systems and Control\",\"volume\":\"28 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"WSEAS Transactions on Systems and Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37394/23203.2023.18.39\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"WSEAS Transactions on Systems and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37394/23203.2023.18.39","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Approximating the ARL of Changes in the Mean of a Seasonal Time Series Model with Exponential White Noise Running on a CUSUM Control Chart
Control charts comprise an excellent statistical process control tool for monitoring industrial processes. Especially, the CUSUM control chart is very sensitive to small-to-moderate process parameter changes. The proposed approach utilizes the numerical integral equation (NIE) method to approximate the average run length (ARL) of changes in the mean of a seasonal time series model with underlying exponential white noise running on a CUSUM control chart. This was achieved by solving a system of linear equations and integration through partitioning and summation using the area under the curve of a function obtained by applying the Gauss-Legendre quadrature. A numerical study was conducted to compare the capabilities of the ARL derivations obtained using the NIE method and explicit formulas to detect changes in the mean of a long-memory model with exponential white noise running on a CUSUM control chart. The results reveal that the performances of both were comparable in terms of the accuracy percentage, which was greater than 95%, meaning that the ARL values were highly consistent. Thus, the NIE method can be used to validate ARL results for this situation.
期刊介绍:
WSEAS Transactions on Systems and Control publishes original research papers relating to systems theory and automatic control. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with systems theory, dynamical systems, linear and non-linear control, intelligent control, robotics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.