{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:11:07Z","timestamp":1760145067182,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T00:00:00Z","timestamp":1718150400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Project of the Education Department of Liaoning Province","award":["JYTMS20230768","22YJC910009","2021-BS-142","LJKZ1161","JYTMS20230767","23kyxm029"],"award-info":[{"award-number":["JYTMS20230768","22YJC910009","2021-BS-142","LJKZ1161","JYTMS20230767","23kyxm029"]}]},{"name":"Research on Humanities and Social Sciences of the Ministry of Education","award":["JYTMS20230768","22YJC910009","2021-BS-142","LJKZ1161","JYTMS20230767","23kyxm029"],"award-info":[{"award-number":["JYTMS20230768","22YJC910009","2021-BS-142","LJKZ1161","JYTMS20230767","23kyxm029"]}]},{"name":"Doctoral Research Start-up Fund of Liaoning Province","award":["JYTMS20230768","22YJC910009","2021-BS-142","LJKZ1161","JYTMS20230767","23kyxm029"],"award-info":[{"award-number":["JYTMS20230768","22YJC910009","2021-BS-142","LJKZ1161","JYTMS20230767","23kyxm029"]}]},{"name":"Education Department of Liaoning Province","award":["JYTMS20230768","22YJC910009","2021-BS-142","LJKZ1161","JYTMS20230767","23kyxm029"],"award-info":[{"award-number":["JYTMS20230768","22YJC910009","2021-BS-142","LJKZ1161","JYTMS20230767","23kyxm029"]}]},{"name":"Natural Science Found of Anshan Normal University","award":["JYTMS20230768","22YJC910009","2021-BS-142","LJKZ1161","JYTMS20230767","23kyxm029"],"award-info":[{"award-number":["JYTMS20230768","22YJC910009","2021-BS-142","LJKZ1161","JYTMS20230767","23kyxm029"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Monitoring the parameter of discrete distributions is common in industrial production. Also, it is often crucial to monitor the parameter of geometric distribution, which is often regarded as the nonconforming item rate. To enhance the detection of nonconforming item, we designed an exponentially weighted moving average (EWMA) scheme based on the weighted likelihood ratio test (WLRT) method, and this scheme is denoted as the EWLRT scheme, specifically designed for monitoring the increase of the parameter in geometric distribution. Moreover, the optimal statistical design of the EWLRT scheme is presented when the shift is known. Results from numerical comparisons through Monte Carlo simulations indicates that the EWLRT scheme performs better than the competing schemes in some scenarios. Additionally, the designed scheme is characterized by its simplicity and ease of use, making it ideally suited for scenarios involving single observation. An example is illustrated to demonstrate the effectiveness of the EWLRT scheme.<\/jats:p>","DOI":"10.3390\/axioms13060392","type":"journal-article","created":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T04:15:27Z","timestamp":1718165727000},"page":"392","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Weighted-Likelihood-Ratio-Based EWMA Schemes for Monitoring Geometric Distributions"],"prefix":"10.3390","volume":"13","author":[{"given":"Yizhen","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Beihang University, Beijing 100191, China"}]},{"given":"Hongxing","family":"Cai","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China"}]},{"given":"Jiujun","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,12]]},"reference":[{"key":"ref_1","first-page":"480","article-title":"Statistical process monitoring: Basics and beyond","volume":"17","year":"2003","journal-title":"J. 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