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Inequalities involving the lifetime of series and parallel systems

Author

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  • William E. Stein
  • Ronald Dattero
  • Roger C. Pfaffenberger

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.

Suggested Citation

  • William E. Stein & Ronald Dattero & Roger C. Pfaffenberger, 1984. "Inequalities involving the lifetime of series and parallel systems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(4), pages 647-651, December.
    • Handle: RePEc:wly:navlog:v:31:y:1984:i:4:p:647-651
    DOI: 10.1002/nav.3800310413
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