The optimal age-based replacement policy for systems subject to shocks

In this article, two different systems subject to shocks occurring based on a non-homogeneous poisson process (nhpp) are analyzed. type –i system is consisted of a single unit and type –ii system is consisted of two parallel units in which both units operate identically and simultaneously. in type –i system occurrence of a shock causes system stopping and consequently will be received minimal repairs. also this system is replaced preventively at time ψ, or at time less than ψ due to probable failure. in   type –ii system a shock to each units leads to unit stopping and accordingly the unit receives minimal repairs and other unit receives preventive maintenance services with no system stop. simultaneously, this system is replaced at time ψ or at times less than ψ preventively, due to failure of both units. systems will be replaced with new and the same types when minimizes total expected cost.