{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T04:46:28Z","timestamp":1773809188292,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,11,22]],"date-time":"2020-11-22T00:00:00Z","timestamp":1606003200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Funding: This research was supported by the National Research Foundation of Korea (NRF) grant funded by307 the Korea government (NRF-2017R1A2B4004169). Also, this research was funded by the Deanship of Scienti\ufb01c308 Research at Princess Nourah bint Abdulra","award":["(NRF-2017R1A2B4004169"],"award-info":[{"award-number":["(NRF-2017R1A2B4004169"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A load-sharing system is defined as a parallel system whose load will be redistributed to its surviving components as each of the components fails in the system. Our focus is on making statistical inference of the parameters associated with the lifetime distribution of each component in the system. In this paper, we introduce a methodology which integrates the conventional procedure under the assumption of the load-sharing system being made up of fundamental hypothetical latent random variables. We then develop an expectation maximization algorithm for performing the maximum likelihood estimation of the system with Lindley-distributed component lifetimes. We adopt several standard simulation techniques to compare the performance of the proposed methodology with the Newton\u2013Raphson-type algorithm for the maximum likelihood estimate of the parameter. Numerical results indicate that the proposed method is more effective by consistently reaching a global maximum.<\/jats:p>","DOI":"10.3390\/e22111329","type":"journal-article","created":{"date-parts":[[2020,11,23]],"date-time":"2020-11-23T01:28:48Z","timestamp":1606094928000},"page":"1329","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Load-Sharing Model under Lindley Distribution and Its Parameter Estimation Using the Expectation-Maximization Algorithm"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2208-3498","authenticated-orcid":false,"given":"Chanseok","family":"Park","sequence":"first","affiliation":[{"name":"Applied Statistics Laboratory, Department of Industrial Engineering, Pusan National University, Busan 46241, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9233-7844","authenticated-orcid":false,"given":"Min","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Management Science and Statistics, The University of Texas at San Antonio, San Antonio, TX 78249, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9449-7489","authenticated-orcid":false,"given":"Refah Mohammed","family":"Alotaibi","sequence":"additional","affiliation":[{"name":"Mathematical Sciences Department, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7501-7232","authenticated-orcid":false,"given":"Hoda","family":"Rezk","sequence":"additional","affiliation":[{"name":"Mathematical Sciences Department, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"},{"name":"Department of Statistics, Al-Azhar University, Cairo 11884, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,22]]},"reference":[{"key":"ref_1","first-page":"405","article-title":"The Statistical Theory of the Strength of Bundles of Threads I","volume":"83","author":"Daniels","year":"1945","journal-title":"Proc. R. Soc. Lond. Ser. 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