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Resolving an old problem on the preservation of the IFR property under the formation of $k$-out-of-$n$ systems with discrete distributions
Published online by Cambridge University Press: 16 October 2023
Abstract
More than half a century ago, it was proved that the increasing failure rate (IFR) property is preserved under the formation of k-out-of-n systems (order statistics) when the lifetimes of the components are independent and have a common absolutely continuous distribution function. However, this property has not yet been proved in the discrete case. Here we give a proof based on the log-concavity property of the function $f({{\mathrm{e}}}^x)$. Furthermore, we extend this property to general distribution functions and general coherent systems under some conditions.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust