{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T08:28:48Z","timestamp":1765960128852,"version":"build-2065373602"},"reference-count":58,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T00:00:00Z","timestamp":1605571200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004750","name":"Aeronautical Science Foundation of China","doi-asserted-by":"publisher","award":["CAST-BISEE2019-019"],"award-info":[{"award-number":["CAST-BISEE2019-019"]}],"id":[{"id":"10.13039\/501100004750","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["N2023023"],"award-info":[{"award-number":["N2023023"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["E2020501013"],"award-info":[{"award-number":["E2020501013"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51475086"],"award-info":[{"award-number":["51475086"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper discussed the estimation of stress-strength reliability parameter R=P(Y&lt;X) based on complete samples when the stress-strength are two independent Poisson half logistic random variables (PHLD). We have addressed the estimation of R in the general case and when the scale parameter is common. The classical and Bayesian estimation (BE) techniques of R are studied. The maximum likelihood estimator (MLE) and its asymptotic distributions are obtained; an approximate asymptotic confidence interval of R is computed using the asymptotic distribution. The non-parametric percentile bootstrap and student\u2019s bootstrap confidence interval of R are discussed. The Bayes estimators of R are computed using a gamma prior and discussed under various loss functions such as the square error loss function (SEL), absolute error loss function (AEL), linear exponential error loss function (LINEX), generalized entropy error loss function (GEL) and maximum a posteriori (MAP). The Metropolis\u2013Hastings algorithm is used to estimate the posterior distributions of the estimators of R. The highest posterior density (HPD) credible interval is constructed based on the SEL. Monte Carlo simulations are used to numerically analyze the performance of the MLE and Bayes estimators, the results were quite satisfactory based on their mean square error (MSE) and confidence interval. Finally, we used two real data studies to demonstrate the performance of the proposed estimation techniques in practice and to illustrate how PHLD is a good candidate in reliability studies.<\/jats:p>","DOI":"10.3390\/e22111307","type":"journal-article","created":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T07:23:28Z","timestamp":1605597808000},"page":"1307","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Estimation of the Reliability of a Stress\u2013Strength System from Poisson Half Logistic Distribution"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3899-1626","authenticated-orcid":false,"given":"Isyaku","family":"Muhammad","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China"}]},{"given":"Xingang","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Guangdong University of Petrochemical Technology, Maoming 525000, China"},{"name":"School of Control and Engineering, Northeastern University, Qinhunangdao 066004, China"}]},{"given":"Changyou","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China"}]},{"given":"Mingming","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China"}]},{"given":"Miaoxin","family":"Chang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1080\/00031305.1971.10477278","article-title":"On constructing statistics and reporting data","volume":"25","author":"Wolfe","year":"1971","journal-title":"Am. 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