A Parrondo Paradox in Reliability Theory

TL;DR

This paper demonstrates a Parrondo paradox in reliability theory where combining less reliable systems in a specific way results in a more reliable overall system, challenging intuitive expectations.

Contribution

It introduces a novel reliability model inspired by Parrondo's paradox, showing how mixing distributions can improve system reliability under certain conditions.

Findings

Mixed systems can outperform individual components in reliability.

The paradoxical effect depends on specific distribution mixtures.

Reliability can be enhanced by strategic combination of less reliable units.

Abstract

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.