{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T01:25:46Z","timestamp":1769304346089,"version":"3.49.0"},"reference-count":31,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,17]],"date-time":"2020-09-17T00:00:00Z","timestamp":1600300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A novel methodology for modelling time to failure of systems under a degradation process is proposed. Considering the method degradation may have influenced the failure of the system under the setup of the model several implied lifetime distributions are outlined. Hazard rate and mean residual lifetime of the model are obtained and a numerical situation is delineated to calculate their amounts. The problem of modelling the amount of degradation at the failure time is also considered. Two monotonic aging properties of the model is secured and a characterization property of the symmetric degradation models is established.<\/jats:p>","DOI":"10.3390\/sym12091532","type":"journal-article","created":{"date-parts":[[2020,9,18]],"date-time":"2020-09-18T10:22:23Z","timestamp":1600424543000},"page":"1532","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Dynamic Failure Time Degradation-Based Model"],"prefix":"10.3390","volume":"12","author":[{"given":"Abdulhakim A.","family":"Albabtain","sequence":"first","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11362, Saudi Arabia"}]},{"given":"Mansour","family":"Shrahili","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11362, Saudi Arabia"}]},{"given":"Lolwa","family":"Alshagrawi","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11362, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6363-1246","authenticated-orcid":false,"given":"Mohamed","family":"Kayid","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11362, Saudi Arabia"},{"name":"Department of Mathematics and Computer Science, Faculty of Science, Suez University, Suez 43511, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1080\/07408170590929009","article-title":"Stochastic models for degradation-based reliability","volume":"37","author":"Kharoufeh","year":"2005","journal-title":"IIE Trans."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1109\/TR.2006.874937","article-title":"Stochastic degradation models with several accelerating variables","volume":"55","author":"Park","year":"2006","journal-title":"IEEE Trans. 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