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We also introduce a novel approach, based on the equilibrium distribution, to handle situations where the techniques of Block and Savits (1980) either fail or involve tedious calculations. Our approach in conjunction with the theory of total positivity yields Vinogradov\u2019s (1973) result for the increasing failure rate class when the distribution function is continuous. We also present simple but elegant proofs for Block and Savits\u2019 results for the decreasing mean residual life, new better than used in expectation, and harmonic new better than used in expectation classes as applications of our approach. We address several other related issues that are germane to our problem. Finally, we conclude with a short discussion on the issue of convolutions.<\/jats:p>","DOI":"10.1017\/jpr.2025.1","type":"journal-article","created":{"date-parts":[[2025,4,22]],"date-time":"2025-04-22T03:48:03Z","timestamp":1745293683000},"page":"1193-1215","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":3,"title":["Block\u2013Savits type characterizations using the Laplace transform and some related issues"],"prefix":"10.1017","volume":"62","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-9050-975X","authenticated-orcid":false,"given":"Lisa","family":"Parveen","sequence":"first","affiliation":[{"name":"Indian Institute of Engineering Science and Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Murari","family":"Mitra","sequence":"additional","affiliation":[{"name":"Indian Institute of Engineering Science and Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2025,4,22]]},"reference":[{"key":"S0021900225000014_ref18","doi-asserted-by":"publisher","DOI":"10.1017\/jpr.2018.82"},{"key":"S0021900225000014_ref37","doi-asserted-by":"crossref","first-page":"666","DOI":"10.1017\/apr.2023.41","article-title":"Preservation of mean inactivity time ordering for coherent systems","volume":"56","author":"Rao","year":"2024","journal-title":"Adv. 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