NEW STATISTICAL AND RELIABILITY MODELS WITH APPLICATIONS

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 (   )