A two-unit general parallel system with (n − 2) cold standbys—Analytic and simulation approach

A parallel (2, n − 2)-system is investigated here where two units start their operation simultaneously and any one of them is replaced instantaneously upon its failure by one of the (n − 2) cold standbys. We assume availability of n non-identical, non-repairable units for replacement or support. The system reliability is evaluated by recursive relations with unit-lifetimes T_i (i = 1, … , n) that have a general joint distribution function F(t). On the basis of the derived expression, simulation techniques have been developed for the evaluation of the system reliability and the mean time to failure, useful when dealing with large systems or correlated unit-lifetimes and less mathematically manageable distributions. Simulation results are presented for various lifetime distributions and comparisons are made with derived analytic results for some special distributions and moderate values of n.