الفهرس 
Contributions to discrete mean residual life and mean inactivity orderings, with applications
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Abstract
The concepts of mean residual time and mean inactivity time play an important role in reliability and life testing. Several research articles have studied these two concepts for continuous distributions. However, to the best of our knowledge, not much has been published on their discrete analog. The objective of this thesis is to fill in this gap in the statistical literature, keeping in mind their importance to reliability studies. In this thesis, based on the comparison of mean inactivity times of a certain function of two lifetime random variables, we introduce and study a new stochastic order. This new order lies between the reversed hazard rate and the mean inactivity time orders. Several characterizations and preservation properties of the new order under reliability operations of monotone transformation, mixture, and shock models are discussed. In addition, a new class of life distributions called strong increasing mean inactivity time is proposed, and some of its reliability properties are investigated. Finally, to illustrate the concepts, some applications in the context of reliability theory are included. Moreover, we introduce, study and analyze a new stochastic order that lies in the framework of the discrete mean residual life and the convexity orders. Several preservation properties of the new order under reliability operations of monotone transformation, mixture, weighted distributions and shock models are discussed. In addition, two characterization properties of the new order based on the concept of discrete residual life at random time and the concept of excess lifetime in discrete renewal processes are given. Finally, we introduce some new applications of this order in the context of reliability theory