{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T08:46:56Z","timestamp":1778575616440,"version":"3.51.4"},"reference-count":38,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T00:00:00Z","timestamp":1682294400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004242","name":"Princess Nourah bint Abdulrahman","doi-asserted-by":"publisher","award":["PNURSP2023R443"],"award-info":[{"award-number":["PNURSP2023R443"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004242","name":"Princess Nourah bint Abdulrahman","doi-asserted-by":"publisher","award":["PSAU\/2023\/R\/1444"],"award-info":[{"award-number":["PSAU\/2023\/R\/1444"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009392","name":"Prince Sattam bin Abdulaziz Universities","doi-asserted-by":"publisher","award":["PNURSP2023R443"],"award-info":[{"award-number":["PNURSP2023R443"]}],"id":[{"id":"10.13039\/100009392","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009392","name":"Prince Sattam bin Abdulaziz Universities","doi-asserted-by":"publisher","award":["PSAU\/2023\/R\/1444"],"award-info":[{"award-number":["PSAU\/2023\/R\/1444"]}],"id":[{"id":"10.13039\/100009392","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Due to the complexity of the data being generated day in and day out in many practical domains, as a result of the development of scales for rating the success or failure of reliability, a new domain of reliability called the classes of life and determinant probability distributions has been presented. This article introduces novel statistical probability models for the reliability class of life test under different reliability processes in the age range t\u2218. Several probabilistic properties and features were derived and rigorously screened to test the new reliability class. According to the U-statistic, a novel hypothesis test was created to evaluate the exponentiality property. The comparative efficiency of the test according to Pitman\u2019s asymptotic efficiency was examined and compared with other reliability classes. To prove the superiority of the new reliability class, some probability models were utilized, including the Weibull, Makeham, gamma, and linear failure rate models. Moreover, critical point simulations of the null Monte Carlo distribution and some applications of the censored and uncensored data were implemented to validate the class test listed by the reliability analysis.<\/jats:p>","DOI":"10.3390\/axioms12050414","type":"journal-article","created":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T06:20:42Z","timestamp":1682317242000},"page":"414","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Reliability Class Testing and Hypothesis Specification: NBRULC\u2212t\u2218 Characterizations with Applications for Medical and Engineering Data Modeling"],"prefix":"10.3390","volume":"12","author":[{"given":"Hana","family":"Alqifari","sequence":"first","affiliation":[{"name":"Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed S.","family":"Eliwa","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia"},{"name":"Department of Statistics and Computer Science, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"},{"name":"Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Walid B. H.","family":"Etman","sequence":"additional","affiliation":[{"name":"Faculty of Computer and Artificial Intelligence, Modern University for Technology and Information, Cairo 12613, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7585-5519","authenticated-orcid":false,"given":"Mahmoud","family":"El-Morshedy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Laila A.","family":"Al-Essa","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7828-3536","authenticated-orcid":false,"given":"Rashad M.","family":"EL-Sagheer","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science, Al-Azhar University, Naser City 11884, Egypt"},{"name":"High Institute of Computer and Management Information System, First Statement, New Cairo 11865, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,24]]},"reference":[{"key":"ref_1","unstructured":"Stoyan, D. (1983). Comparison Methods for Queues and Other Stochastic Models, Wiley."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ross, S.M. (1983). Stochastic Processes, Wiley.","DOI":"10.1016\/B978-0-12-598420-1.50011-8"},{"key":"ref_3","unstructured":"Barlow, R.E., and Proschan, F. (1981). 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