{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,17]],"date-time":"2025-04-17T16:13:07Z","timestamp":1744906387474,"version":"3.37.3"},"reference-count":26,"publisher":"Wiley","license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71401174"],"award-info":[{"award-number":["71401174"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2015]]},"abstract":"<jats:p>For mixed uncertainties of random variables and fuzzy variables in engineering, three indices, that is, interval reliability index, mean reliability index, and numerical reliability index, are proposed to measure safety of structure. Comparing to the reliability membership function for measuring the safety in case of mixed uncertainties, the proposed indices are more intuitive and easier to represent the safety degree of the engineering structure, and they are more suitable for the reliability design in the case of the mixed uncertainties. The differences and relations among three proposed indices are investigated, and their applicability is compared. Furthermore, a technique based on the probability density function evolution method is employed to improve the computational efficiency of the proposed indices. At last, a numerical example and two engineering examples are illustrated to demonstrate the feasibility, reasonability, and efficiency of the computational technique of the proposed indices.<\/jats:p>","DOI":"10.1155\/2015\/365051","type":"journal-article","created":{"date-parts":[[2015,3,2]],"date-time":"2015-03-02T16:01:49Z","timestamp":1425312109000},"page":"1-8","source":"Crossref","is-referenced-by-count":0,"title":["Reliability Analysis in Presence of Random Variables and Fuzzy Variables"],"prefix":"10.1155","volume":"2015","author":[{"given":"Cui","family":"Lijie","sequence":"first","affiliation":[{"name":"School of Equipment Management and Safety Engineering, Air Force Engineering University, Xi\u2019an, Shaanxi 710051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L\u00fc","family":"Zhenzhou","sequence":"additional","affiliation":[{"name":"School of Aeronautics, Northwestern Polytechnical University, Xi\u2019an, Shaanxi 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Guijie","sequence":"additional","affiliation":[{"name":"School of Aeronautics, Northwestern Polytechnical University, Xi\u2019an, Shaanxi 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"4","doi-asserted-by":"publisher","DOI":"10.1126\/science.2255906"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2004.03.001"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2008.06.002"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/0167-4730(90)90012-E"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/s0045-7825(98)00140-6"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.2514\/2.1597"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.2514\/2.599"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(87)90163-1"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1081\/sme-120020293"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7949(03)00147-0"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(03)00424-7"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1080\/02331931003657691"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijmecsci.2007.09.015"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.strusafe.2009.02.001"},{"issue":"6","key":"14","first-page":"712","volume":"16","year":"2003","journal-title":"Progress in Natural Science"},{"issue":"2","key":"25","first-page":"338","volume":"8","year":"1965","journal-title":"Information and Computation"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/0167-4730(88)90020-3"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/0167-4730(89)90003-9"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/s0167-4730(00)00014-x"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.probengmech.2008.01.004"},{"year":"1995","key":"3"},{"year":"1981","key":"12"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/s00466-006-0054-9"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2008.07.006"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.3901\/jme.2009.04.105"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.strusafe.2006.03.002"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/365051.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/365051.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/365051.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,18]],"date-time":"2016-08-18T12:50:09Z","timestamp":1471524609000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2015\/365051\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"references-count":26,"alternative-id":["365051","365051"],"URL":"https:\/\/doi.org\/10.1155\/2015\/365051","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2015]]}}}