Inequalities involving the lifetime of series and parallel systems |
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| Authors: | William E Stein Ronald Dattero Roger C Pfaffenberger |
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| Institution: | 1. Department of Business Analysis and Research, College of Business Administration, Texas A & M University, College Station, Texas 77843;2. Texas Christian University, Fort Worth, Texas 76129 |
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| 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. |
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