Comparisons of series and parallel systems with random and non-random components

This paper mainly studies the stochastic comparisons of lifetime for series and parallel systems with positive integer-value random variable N and non-random n components. Utilizing Jensen inequality, some results are proved: under some conditions on the relationship of the expectation E(N) and n, the lifetimes of series systems with random N components is better than the series systems with non-random n components in traditional stochastic order. Analogously, some comparison results of the lifetimes of parallel systems can be obtained.