Stochastic Comparisons of Series and Parallel Systems Comprising Modified Additive Hazard Rate Model

An important semi-parametric model with many applications in reliability theory is the additive hazard rate model, which has key applications in reliability theory.A random variable X is said to follow an AH(, ; F ) model if its survival function is expressed asIt is then easy in this case to see that r(x; , ) = + r(x; ), where r(; ) is the baseline hazard rate function.Finkelstein ( 2008) studied the reliability properties of the AH model and provided some applications of this model. Results and DiscussionThis paper has established stochastic comparisons of parallel and series systems consisting of independent modified additive hazard rate (MAH) components.Establishing hazard rate, reversed hazard rate, and likelihood ratio orders under some conditions on the baseline distribution and the Archimedean copula as joint distribution will be of great interest. ConclusionThis paper introduces a new MAH model that replaces the additive hazard rate distribution in the general proportional add ratio model.Next, when two sets of random variables follow the MAH model, we establish stochastic comparisons between the series and parallel systems comprising these components.