Some properties of the HNBUE and HNWUE classes of life distributions

• The HNBUE (HNWUE) class of life distributions (i.e. for which f F (x)dx< (>)00 t< (>) y exp(-t/y) for t > 0, where y = / F(x)dx) is studied. We prove0that the HNBUE (HNWUE) class is larger than the NBUE (NWUE) class. We alsopresent some characterizations of the HNBUE (HNWUE) property by using theTotal Time on Test (TTT-) transform and the Laplace transform. Further weexamine whether the HNBUE (HNWUE) property is preserved under the reliabilityoperations (1) formation of coherent structure, (2) convolution and(3) mixture. Some bounds on the moments and on the survival function of aHNBUE (HNWUE) life distribution are also presented. The class of distributionswith the discrete HNBUE (discrete HNWUE) property (i.e. for which00 00 00I P. < (>) y(l-l/y)k for k = 0,1,2j=k J "where yi=0 JI p. and P. = E p, )J k=j+l kis also studied.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Life distribution

survival function

survival probability

HNBUE

HNWUE

discrete HNBUE

discrete HNWUE

TTT-transform

Laplace transform

damage model

coherent structure

convolution

mixture

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