PROJECT TITLE :
Stochastic Comparisons of Series and Parallel Systems With Generalized Exponential Components
This paper examines the matter of the stochastic comparison of series and parallel systems with $s$-independent heterogeneous generalized exponential parts. The results established here are developed in 3 directions. Initial, we have a tendency to take into account a system with possibly totally different form and scale parameters, and get some ordering results when its matrix of parameters changes to a different matrix, in the bound mathematical sense. Next, by using the concept of vector majorization and related orders, we establish numerous ordering results for the comparisons of series and parallel systems, when their element's lifetimes have either the same shape parameters with probably totally different scale parameters, or the identical scale parameters with possibly different form parameters. Finally, some of the known results on various stochastic orderings between parallel systems within the exponential case are extended to the case when the lifetimes of elements follow the generalized exponential distributions. The results of this paper can be used in sensible things to exchange parts of series and parallel systems by new parts, or to seek out varied bounds for the vital aging characteristics of these systems.
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