A Parrondo Paradox in Reliability Theory

Parrondo's paradox arises in sequences of games in which a winning expectation may be obtained by playing the games in a random order, even though each game in the sequence may be lost when played individually. We present a suitable version of Parrondo's paradox in reliability theory involving two systems in series, the units of the first system being less reliable than those of the second. If the first system is modified so that the distributions of its new units are mixtures of the previous distributions with equal probabilities, then under suitable conditions the new system is shown to be more reliable than the second in the "usual stochastic order" sense.