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On the shape of the mean residual lifetime function
Author(s) -
Finkelstein M. S.
Publication year - 2002
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/asmb.461
Subject(s) - bathtub , mathematics , monotone polygon , reciprocal , residual , function (biology) , failure rate , simple (philosophy) , mixing (physics) , probability density function , statistics , mathematical analysis , geometry , physics , materials science , algorithm , linguistics , philosophy , epistemology , quantum mechanics , evolutionary biology , composite material , biology
Some general properties of the mean residual life (MRL) function are studied. The analysis is based on the shape of the corresponding failure rate. The conditions under which the failure rate and the reciprocal to the MRL function have asymptotically equivalent behaviour as t →∞ are discussed. The simplest non‐monotone shapes of the functions under consideration (bathtub and upside down bathtub) are also considered. The MRL functions for mixtures of distributions are described via the corresponding conditional probability density functions. The direct proportional model of mixing is characterized and some asymptotic results on the shape of the mixture MRL are obtained. Some simple examples are given. Copyright © 2002 John Wiley & Sons, Ltd.