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An unreliable server characterization of the exponential distribution

Part of: Special processes Distribution theory Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Janos Galambos  and
Charles Hagwood
Janos Galambos*
Affiliation:
Temple University
Charles Hagwood*
Affiliation:
National Institute of Standards and Technology
*
∗ Postal address: Department of Mathematics, TU 038–16, Temple University, Philadelphia, PA 19122, USA.
∗∗ Postal address: NIST, Statistical Engineering Division, Div-882, Gaithersburg, MD 20899, USA.
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Abstract

Consider a workstation with one server, performing jobs with a service time, Y, having distribution function, G(t). Assume that the station is unreliable, in that it occasionally breaks down. The station is instantaneously repaired, and the server restarts the uncompleted job from the beginning. Let T denote the time it takes to complete each job. If G(t) is exponential with parameter A, then because of the lack-of-memory property of the exponential, P (T > t) = Ḡ(t) =exp(−γt), irrespective of when and how the failures occur. This property also characterizes the exponential distribution.

Keywords

LACK-OF-MEMORY PROPERTYRELIABILITY

MSC classification

Primary: 60E99: None of the above, but in this section
Secondary: 62E10: Characterization and structure theory 60K10: Applications (reliability, demand theory, etc.)
Type
Short Communications
Information
Journal of Applied Probability , Volume 31 , Issue 1 , March 1994 , pp. 274 - 279
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

Research carried out while this author was visiting NIST as a Faculty Associate.

This paper is not subject to copyright in the United States of Àmerica.

References

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