PROJECT TITLE :

New Developments on Stochastic Properties of Coherent Systems

ABSTRACT:

We consider a coherent system consisting of $n$ components where the part lifetimes are assumed to be random variables following a probabilistically exchangeable joint distribution perform, where the likelihood distribution will not change with any permutation of the parts. We tend to study stochastic properties of the residual lifetime of live parts of the system, beneath different conditions. The amount of failed parts of the system are explored, beneath the idea that the system is working at time $t$. We have a tendency to additionally study the probability that the $i$th part failure within the system causes the system failure, given that the system is working at time $t$. The results of the paper extend a number of the existing ends up in the literature.