Stochastic comparisons of series and parallel systems with randomized independent components

Consider a series or parallel system of independent components and assume that the components are randomly chosen from two different batches, with the components of the first batch being more reliable than those of the second. In this note it is shown that the reliability of the system increases, in usual stochastic order sense, as the random number of components chosen from the first batch increases in increasing convex order. As a consequence, we establish a result analogous to the Parrondo’s paradox, which shows that randomness in the number of components extracted from the two batches improves the reliability of the series system.

► Systems of components chosen from two different batches are considered.
► The reliability of the system when components are randomly chosen is investigated.
► Stochastic comparisons results are provided for different random extractions.
► It is shown that series systems improve under randomness in extraction from batches.
► The opposite conclusion holds for parallel systems.