Inequalities involving the lifetime of series and parallel systems

William E. Stein, Ronald Dattero and Roger C. Pfaffenberger

Naval Research Logistics Quarterly, 1984, vol. 31, issue 4, 647-651

Abstract: Let {Xi} be independent HNBUE (Harmonic New Better Than Used in Expectation) random variables and let {Yi} be independent exponential random variables such that E{Xi}=E{Yi} It is shown that \documentclass{article}\pagestyle{empty}\begin{document}$ E\left[{u\left({\mathop {\min \,X_i}\limits_{l \le i \le n}} \right)} \right] \ge E\left[{u\left({\mathop {\min \,Y_i}\limits_{l \le i \le n}} \right)} \right] $\end{document} for all increasing and concave u. This generalizes a result of Kubat. When comparing two series systems with components of equal cost, one with lifetimes {Xi} and the other with lifetimes {Yi}, it is shown that a risk‐averse decision‐maker will prefer the HNBUE system. Similar results are obtained for parallel systems.

Date: 1984
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https://doi.org/10.1002/nav.3800310413

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Persistent link: https://EconPapers.repec.org/RePEc:wly:navlog:v:31:y:1984:i:4:p:647-651

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