Laplace ordering and its applications.(English)Zbl 0721.60097

Summary: Two arbitrary life distributions F and G can be ordered with respect to their Laplace transforms. We say $$\bar F$$ is Laplace-smaller than $$\bar G$$ if $$\int^{\infty}_{0}e^{-st}\bar F(t)dt\leq \int^{\infty}_{0}e^{-st}\bar G(t)dt$$ for all $$s>0$$. Interpretations of this ordering concept in reliability, operations research, and economics are described. General preservation properties are presented. Using these preservation results we derive useful inequalities and discuss their applications to M/G/1 queues, time series, coherent systems, shock models and cumulative damage models.

MSC:

 60K10 Applications of renewal theory (reliability, demand theory, etc.) 90B25 Reliability, availability, maintenance, inspection in operations research 60K25 Queueing theory (aspects of probability theory)
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