On Some Stochastic Orders and their Applications in System Reliability

Stochastic orders are very useful tools to compare the lifetimes of two systems. In literature, many different types of stochastic orders have been developed in order to study different kinds of problems. Here, we consider some important problems in system reliability. We study these problems using different stochastic orders. Further, we also introduce some new generalized stochastic orders based on some generalized functions. We study different stochastic properties of these stochastic orders. Lastly, we discuss some ageing properties of a system with a random number of components.