{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T05:27:54Z","timestamp":1769750874412,"version":"3.49.0"},"reference-count":52,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,7]],"date-time":"2023-04-07T00:00:00Z","timestamp":1680825600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Base and Basic Applied Study of Guangdong Province","award":["2020A1515011360"],"award-info":[{"award-number":["2020A1515011360"]}]},{"name":"Base and Basic Applied Study of Guangdong Province","award":["71871181"],"award-info":[{"award-number":["71871181"]}]},{"name":"Base and Basic Applied Study of Guangdong Province","award":["72161025"],"award-info":[{"award-number":["72161025"]}]},{"name":"Base and Basic Applied Study of Guangdong Province","award":["72271169"],"award-info":[{"award-number":["72271169"]}]},{"name":"National Natural Science Foundation of China","award":["2020A1515011360"],"award-info":[{"award-number":["2020A1515011360"]}]},{"name":"National Natural Science Foundation of China","award":["71871181"],"award-info":[{"award-number":["71871181"]}]},{"name":"National Natural Science Foundation of China","award":["72161025"],"award-info":[{"award-number":["72161025"]}]},{"name":"National Natural Science Foundation of China","award":["72271169"],"award-info":[{"award-number":["72271169"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In the present academic and engineering fields, every measure function of product reliability is modeled and estimated from the statistical perspective. These indicate that there universally exist differences in the reliabilities of new identical products that survive the burn-in test. On the basis of the differences in the reliabilities of new identical products, designing through-life maintenance models for managing the different reliabilities is a very practical topic for engineering fields. In this study, a random warranty model and a random maintenance model are designed by screening product reliabilities to manage the through-life reliabilities of products. In the random warranty model, the coverage areas of the warranty are set as the different areas for applying flexibility to them to control the warranty costs of new identical products with different reliabilities, and thus this warranty is called a flexible random free repair warranty (FRFRW) model. In the random maintenance model, two random replacement actions are customized by setting different replacement ranges for controlling maintenance costs and lengthening service life. This random maintenance model is called a customized random replacement (CRR), which is used to manage product reliabilities after the FRFRW expiration. These two random models are characterized from the mathematical perspective, and some derivatives of both are provided to model other maintenance problems. The characteristics of every model and the performance of the CRR are explored and illustrated through numerical experiments. The results show that the CRR is superior to random age replacement.<\/jats:p>","DOI":"10.3390\/axioms12040358","type":"journal-article","created":{"date-parts":[[2023,4,10]],"date-time":"2023-04-10T03:24:18Z","timestamp":1681097058000},"page":"358","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Customizing Random Replacement Model and Flexible Warranty Model from the Perspective of Screening Reliability"],"prefix":"10.3390","volume":"12","author":[{"given":"Lijun","family":"Shang","sequence":"first","affiliation":[{"name":"School of Quality Management and Standardization, Foshan University, Foshan 528000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Baoliang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4738-0210","authenticated-orcid":false,"given":"Li","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9711-3084","authenticated-orcid":false,"given":"Kaiye","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Beijing Information Science & Technology University, Beijing 100192, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1016\/j.ejor.2016.10.038","article-title":"Optimal production run length and warranty period for an imperfect production system under selling price dependent on warranty period","volume":"259","author":"Chen","year":"2017","journal-title":"Eur. 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