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Bondesson's functions in reliability theory
Author(s) -
Stein William E.,
Dattero Ronald
Publication year - 1999
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/(sici)1526-4025(199904/06)15:2<103::aid-asmb369>3.0.co;2-c
Subject(s) - reliability theory , reliability (semiconductor) , variance (accounting) , renewal theory , class (philosophy) , sequence (biology) , residual , mathematics , probability theory , stochastic ordering , stochastic process , order (exchange) , computer science , mathematical economics , statistics , algorithm , failure rate , artificial intelligence , economics , power (physics) , physics , accounting , finance , quantum mechanics , biology , genetics
Bondesson's functions in reliability theory are shown to be related to a recursive sequence of probability distributions. These are the ‘higher‐order’ versions of the mean remaining lifetime in an equilibrium renewal process. Based on these functions, classes of distribution functions can be defined. This paper will investigate these classes and place Bondesson's work in the content of the other work done in reliability theory. Connections are made with the decreasing variance residual lifetime class and stochastic ordering. Copyright © 1999 John Wiley & Sons, Ltd.