Generalized Ageing Classes in Terms of Laplace Transforms
نویسنده
چکیده
Kebir (1994) (see also Shaked and Shanthikumar, 1994) has characterized likelihood ratio (LR) ordering, failure rate (FR) ordering, reversed hazard rate ordering and stochastic (ST) ordering with the help of Laplace transform. Using Laplace transform, Nanda (1995) has characterized, by means of necessary and sufficient conditions, the property that two life distributions are ordered in the s-FR and s-ST sense so that the characterization of likelihood ratio, failure rate, mean residual life (MR), variance residual life (VR), stochastic and harmonic average mean residual life (HAMR) orderings follow as particular cases. Vinogradov (1973) has characterized the IFR (Increasing Failure Rate) life distributions in terms of Laplace transform. IFRA (Increasing Failure Rate in Average), DMRL (Decreasing in Mean Residual Life), NBU (New Better than Used), NBUE (New Better than Used in Expectation) and their duals have been characterized by Block and Savits (1980) using the same transform. In Klefsjö (1982), Laplace transform is used in order to give equivalent definition of HNBUE (Harmonically New Better than Used in Expectation) and its dual class. Thus, various reliability classes have been characterized by different researchers by means of Laplace transform. For various definitions of the above ageing classes, one may refer to Bryson and Siddiqui (1969), Deshpande et al. (1986) and the references there in.
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