Orderings of fail-safe systems with components having Marshall-Olkin-Harris lifetime distributions

In this paper, we discuss stochastic comparisons of two fail-safe systems in two different directions. First, we present sufficient conditions for the usual stochastic order between two fail-safe systems have different lifetime distributions but with the same Archimedean copula for their joint distribution. Next, hazard rate orderings of two fail-safe systems with independent components following multiple-outlier models are established. Several illustrative examples are also presented.