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Laplace ordering and its applications

Published online by Cambridge University Press:  14 July 2016

Abdulhamid Alzaid ,
Jee Soo Kim  and
Frank Proschan
Abdulhamid Alzaid*
Affiliation:
King Saud University
Jee Soo Kim*
Affiliation:
GTE Laboratories
Frank Proschan*
Affiliation:
Florida State University
*
∗Postal address: Department of Statistics, King Saud University, Riyadh 11451, Saudi Arabia.
∗∗Postal address: GTE Laboratories, 40 Sylvan Road, Waltham, MA 02254, USA.
∗∗∗Postal address: Department of Statistics, Florida State University, Tallahassee, FL 32306, USA. Research supported by the Air Force Office of Scientific Research under Grant AFOSR 88–0040.
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Abstract

Two arbitrary life distributions F and G can be ordered with respect to their Laplace transforms. We say is Laplace-smaller than 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.

Keywords

LAPLACE TRANSFORMSURVIVAL FUNCTIONGENERATING FUNCTIONHNBUERANDOM DAMAGECOMPLETELY MONOTONEQUEUEINGTIME SERIESSERIES SYSTEMPARALLEL SYSTEM
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 1 , March 1991 , pp. 116 - 130
Copyright
Copyright © Applied Probability Trust 1991 

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