{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:06:15Z","timestamp":1760144775003,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T00:00:00Z","timestamp":1715558400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["72161025","72271169"],"award-info":[{"award-number":["72161025","72271169"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The number of failures serves as a critical indicator that dynamically impacts the reliability of self-announcing failure products, making it highly practical to incorporate the failure count into reliability management throughout the entire product life cycle. This paper investigates comprehensive methodologies for effectively managing the reliability of self-announcing failure products throughout both the warranty and post-warranty stages, taking into account factors such as the failure count, mission cycles, and limited time duration. Three renewable warranty strategies are introduced alongside proposed models for post-warranty replacements. By analyzing variables like the failure number, mission cycles, and time constraints, these proposed warranties provide practical frameworks for efficient reliability management during the warranty stage. Additionally, the introduced warranties utilize cost and time metrics to extract valuable insights that inform decision making and enable effective reliability management during the warranty stage. Moreover, this study establishes cost and time metrics for key post-warranty replacements, facilitating the development of individual cost rates and model applications in other post-warranty scenarios. Analyses of the renewable free-repair\u2013replacement warranties demonstrate that establishing an appropriate number of failures as the replacement threshold can effectively reduce warranty-servicing costs and extend the coverage duration.<\/jats:p>","DOI":"10.3390\/sym16050603","type":"journal-article","created":{"date-parts":[[2024,5,14]],"date-time":"2024-05-14T08:59:37Z","timestamp":1715677177000},"page":"603","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Modeling Renewable Warranties and Post-Warranty Replacements for Self-Announcing Failure Products Subject to Mission Cycles"],"prefix":"10.3390","volume":"16","author":[{"given":"Lijun","family":"Shang","sequence":"first","affiliation":[{"name":"School of Quality Management and Standardization, Foshan University, Foshan 528225, China"}]},{"given":"Jianhui","family":"Chen","sequence":"additional","affiliation":[{"name":"China North Standardization Center, Beijing 100089, China"}]},{"given":"Baoliang","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Shanxi Datong University, Datong 037054, China"}]},{"given":"Cong","family":"Lin","sequence":"additional","affiliation":[{"name":"AVIC China Areo-Polytechnology Establishment, Beijing 100028, China"}]},{"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"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.ress.2010.09.004","article-title":"On the upper truncated Weibull distribution and its reliability implications","volume":"96","author":"Zhang","year":"2011","journal-title":"Reliab. 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