الفهرس 
INTRODUCTION AND SUMMARYOnly 14 pages are availabe for public view
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Abstract
Statisticians have introduced various life criteria to represent the ageing or wear of units or modules in a system or the system itself. In Chapter 2 of this dissertation, we introduced the concepts of positive ageing which describe the adverse effects of age on lifetime of units. Several classes of life distribution based on the notions of ageing have been considered by authors. We consider four forms of reliability operations, namely: (i) Formation of coherent systems using independent components (ii) Addition of independent life length (convolution) (iii) Random selection of a unit from a set of known units (mixture) (iv) Shock models. Chapter 3 of this dissertation presents a new family of positive life distributions which is an extension of the NBUE class. This family is based on the comparisons between the weighted average and the mean life of the parent distribution. We end this chapter by introducing some results of excess time in stochastic orders and families of life distributions. Chapter 4 introduces new orders based on the convex order. These orders are the sign increasing convex order and the increasing convex (concave) average order. Finally, we introduced new families of life distributions based on the increasing convex (concave) average order. Chapter 5, begins by a brief introduction about the bivariate life distributions and then introduces some bivariate families of life distributions such as BIFR, BDMRL and BIFRA properties. We studied the bivariate shock model and its properties with BIFR, BDMRL and BIFRA. Finally, Chapter 6 is devoted for introducing different contributed results to shock models. We introduce and prove some results for the renewal process with geometric distribution. The device which is subjected to shocks randomly as events in a renewal process with geometric distribution is obtained. Finally, we discussed a bivariate geometric distribution.