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We explored two types of modes: the first type of reliability assessment model integrates a mixed shock process and a single degradation process. Established a soft failure reliability model based on degradation threshold assessment method, a hard failure model using a phase\u2010type distribution survival function is presented. Finally, it constructs the relationship between the shock process and the degradation process using conditional probability. The second type of assessment model is composed of a mixed shock process and multiple degradation paths. In this case, the copula functions were used to analyze the dependency between multiple degradation processes. Last, the effectiveness of the proposed models was demonstrated through two examples involving micro\u2010electro\u2010mechanical system devices and aircraft\u00a0engine.<\/jats:p>","DOI":"10.1002\/qre.3802","type":"journal-article","created":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T13:54:07Z","timestamp":1747144447000},"page":"2647-2663","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Reliability Assessment Models of System Under a Mixed Run Shock With Phase\u2010Type Distribution"],"prefix":"10.1002","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-3904-2426","authenticated-orcid":false,"given":"Yiting","family":"Fan","sequence":"first","affiliation":[{"name":"Department of Statistics School of Mathematics Southwest Jiaotong University Chengdu Sichuan China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiayin","family":"Tang","sequence":"additional","affiliation":[{"name":"Department of Statistics School of Mathematics Southwest Jiaotong University Chengdu Sichuan China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2025,5,13]]},"reference":[{"key":"e_1_2_13_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2016.08.025"},{"key":"e_1_2_13_3_1","doi-asserted-by":"publisher","DOI":"10.1080\/0740817X.2016.1190481"},{"key":"e_1_2_13_4_1","doi-asserted-by":"publisher","DOI":"10.1080\/00207720500032606"},{"key":"e_1_2_13_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2009.10.004"},{"key":"e_1_2_13_6_1","doi-asserted-by":"publisher","DOI":"10.1080\/0740817X.2010.491502"},{"key":"e_1_2_13_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2014.06.020"},{"key":"e_1_2_13_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2017.06.014"},{"key":"e_1_2_13_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/qre.2898"},{"key":"e_1_2_13_10_1","doi-asserted-by":"publisher","DOI":"10.23919\/JSEE.2023.000108"},{"key":"e_1_2_13_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/TR.2009.2033734"},{"key":"e_1_2_13_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/TR.2015.2443858"},{"key":"e_1_2_13_13_1","doi-asserted-by":"publisher","DOI":"10.1080\/08982112.2022.2098043"},{"key":"e_1_2_13_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2014.06.005"},{"key":"e_1_2_13_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/TR.2016.2635149"},{"key":"e_1_2_13_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2008.12.007"},{"key":"e_1_2_13_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2021.107738"},{"key":"e_1_2_13_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2020.107231"},{"key":"e_1_2_13_19_1","doi-asserted-by":"publisher","DOI":"10.2307\/1427554"},{"key":"e_1_2_13_20_1","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1300198148"},{"key":"e_1_2_13_21_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10958-006-0306-4"},{"key":"e_1_2_13_22_1","doi-asserted-by":"publisher","DOI":"10.1002\/qre.2109"},{"key":"e_1_2_13_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2015.06.026"},{"key":"e_1_2_13_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2016.11.017"},{"key":"e_1_2_13_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2018.12.011"},{"key":"e_1_2_13_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2015.06.129"},{"key":"e_1_2_13_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2015.03.037"},{"key":"e_1_2_13_28_1","doi-asserted-by":"publisher","DOI":"10.1080\/08982112.2023.2168202"},{"key":"e_1_2_13_29_1","doi-asserted-by":"publisher","DOI":"10.1080\/16843703.2024.2440250"},{"key":"e_1_2_13_30_1","doi-asserted-by":"publisher","DOI":"10.3390\/math12081191"},{"key":"e_1_2_13_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2018.09.022"},{"key":"e_1_2_13_32_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10985-022-09547-7"},{"key":"e_1_2_13_33_1","doi-asserted-by":"publisher","DOI":"10.2143\/AST.35.1.583170"},{"key":"e_1_2_13_34_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-7330-5"},{"key":"e_1_2_13_35_1","volume-title":"An Introduction to Copulas","author":"Nelsen R. 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