{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:23:12Z","timestamp":1760242992184,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2015,1,26]],"date-time":"2015-01-26T00:00:00Z","timestamp":1422230400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The present paper revolves around two argument points. As first, we have observed a certain parallel between the reliability of systems and the progressive disorder of thermodynamical systems; and we import the notion of reversibility\/irreversibility into the reliability domain. As second, we note that the reliability theory is a very active area of research which although has not yet become a mature discipline. This is due to the majority of researchers who adopt the inductive logic instead of the deductive logic typical of mature scientific sectors. The deductive approach was inaugurated by Gnedenko in the reliability domain. We mean to continue Gnedenko\u2019s work and we use the Boltzmann-like entropy to pursue this objective. This paper condenses the papers published in the past decade which illustrate the calculus of the Boltzmann-like entropy. It is demonstrated how the every result complies with the deductive logic and are consistent with Gnedenko\u2019s achievements.<\/jats:p>","DOI":"10.3390\/e17020502","type":"journal-article","created":{"date-parts":[[2015,1,26]],"date-time":"2015-01-26T13:26:37Z","timestamp":1422278797000},"page":"502-508","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Reshaping the Science of Reliability with the Entropy Function"],"prefix":"10.3390","volume":"17","author":[{"given":"Paolo","family":"Rocchi","sequence":"first","affiliation":[{"name":"IBM, via Shangai 53, Roma 00144, Italy"},{"name":"Research Centre on Information Systems (Cersi), University LUISS, via Salvini 2, Roma 00197, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giulia","family":"Capacci","sequence":"additional","affiliation":[{"name":"Dip. di Medicina Interna Vascolare , University of Perugia, piazza Menghini 1, Perugia 06129, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,1,26]]},"reference":[{"unstructured":"Gnedenko, B.V., Belyaev, Yu. K., and Solovyev, A.D. (1965). Mathematical Methods in Reliability Theory, Nauka. in Russian.","key":"ref_1"},{"unstructured":"Jensen, F. (1996). Electronic Component Reliability, John Wiley & Sons.","key":"ref_2"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1002\/qre.4680050108","article-title":"The roller-coaster curve is in","volume":"5","author":"Wong","year":"1989","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1038\/nature12789","article-title":"Diversity of ageing across the tree of life","volume":"505","author":"Owen","year":"2014","journal-title":"Nature"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1109\/TR.1968.5217523","article-title":"Evaluation of repairable system reliability using the \u201cbad-as-old\u201d concept","volume":"R-17","author":"Ascher","year":"1968","journal-title":"IEEE Trans. Reliab."},{"unstructured":"Kececioglu, D., and Sun, F. (1965). Environmental Stress Screening: Its Quantification, Optimization, and Management, Prentice Hall.","key":"ref_6"},{"unstructured":"Zairi, M. (1991). Total Quality Management for Engineers, Woodhead.","key":"ref_7"},{"unstructured":"Rocchi, P. (2000, January 4\u20137). System reliability and reparability, Bordeaux, France.","key":"ref_8"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"142","DOI":"10.3390\/e4050142","article-title":"Boltzmann-like entropy in reliability theory","volume":"4","author":"Rocchi","year":"2002","journal-title":"Entropy"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"134","DOI":"10.3390\/e8030134","article-title":"Calculations of system aging through the stochastic entropy","volume":"8","author":"Rocchi","year":"2006","journal-title":"Entropy"},{"unstructured":"Rocchi, P. (2005, January 15\u201317). The notion of reversibility and irreversibility at the base of reliability theory, Beer Sheva, Israel.","key":"ref_11"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/2\/502\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:41:59Z","timestamp":1760215319000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/2\/502"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1,26]]},"references-count":11,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,2]]}},"alternative-id":["e17020502"],"URL":"https:\/\/doi.org\/10.3390\/e17020502","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2015,1,26]]}}}