Optimal Grouping Of Heterogeneous Components In Different Systems Under Archimedean Copula Dependence

In this paper,we investigate optimal grouping of heterogeneous components in four systems.such as series systems,parallel system,series-parallel system and parallel-series systems.We investigate the pairs of systems comprising n depen-dent components drawn from a heterogeneous population consisting of m different subpopulations.The components within each subpopulation are assumed to be de-pendent while the subpopulations are independent of each other.We then assume that the subpopulations have different Archimedean copulas to model their depen-dence.Under this setup,we have the following results.In the second chapter,we consider that for a series system.the optimal(maximal)reliability is achieved by drawing all components from a dependent subpopulation,whereas,for a parallel system,the optimal reliability by drawing of all components from the whole mixed populations.In the third chapter,we consider three cases in the series-parallel and parallel-series system:first case is by fixing the number of subsystems and then presenting relationships between allocation vectors,second case is in studying the impact of changes in the number of subsystems,and the last case is in examining the influence of the solection probabilities or the distributions of subpopulations.We also use the theory of stochastic orders and majorization to establish our main results as well as some other related results,and present some numerical examples to illustrate all the results established here.