Abstract:
In the context of the lifetime data analysis, some models consider the assumption
of the proportional hazard rate or the assumption of the proportional mean
residual life. The foregoing models have developed rapidly in the literature to model
time to event data. The main goal of this thesis is to introduce a new model based on
the concept of the discret Laplace transform of residual lives (dLtrl).
We consider
some examples to demonstrate the usefulness of the obtained results in recognizing
(dLtrl)
ordered
random variables. On the other hand, reversed hazard rates
model are found to be very useful in survival analysis and reliability especially in
study on parallel systems and in the analysis of left censored lifetime data. We
introduced and studied a generalized proportional reversed hazards model defined
by (¤ ) = [ ( )] where ( ) is baseline distribution function and
is a positive real number. The monotonicity of the baseline failure rates in relation
to the monotonicity of the baseline hazard are studied in a general way. A set
of sufficient conditions are provided for ¤ to be ¡increasing failure rate when
is ¡increasing failure rate. We also prove similar preservation results for the
¡new better than used aging properties. Charactrization results for the some generalized
stochastic comparisons are given. Finally, several reliability properties of
order statistics and record values for the proportional failure rate (PFR) model are
introduced. We show that if : is increasing proportional failure rate ( )
