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Extreme-value properties of the explosion-time distribution in a pure birth process

Published online by Cambridge University Press:  14 July 2016

Paul D. Feigin  and
Emmanuel Yashchin
Paul D. Feigin*
Affiliation:
Technion — Israel Institute of Technology
Emmanuel Yashchin*
Affiliation:
Technion — Israel Institute of Technology
*
∗ Postal address: Faculty of Industrial Engineering and Management, Technion — Israel Institute of Technology, Haifa 32000, Israel.
∗ Postal address: Faculty of Industrial Engineering and Management, Technion — Israel Institute of Technology, Haifa 32000, Israel.
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Abstract

In each of a large number N of independent cells a breakdown mechanism is under way and proceeds until the first of the cells actually fails. At such a time, in each cell, the situation reverts to some initial state and the mechanism restarts. In this paper we consider those mechanisms for which breakdown may be modelled as the explosion of a pure birth process. Of interest is the distribution of time between failures and the possibility of estimating N and/or model parameters by observing a sequence of failure times. Saddlepoint approximation methods are used in the relevant extreme-value theory analysis for two important cases.

Keywords

SADDLEPOINT APPROXIMATIONBREAKDOWN IN THIN FILM INSULATORSTAIL EQUIVALENCEEXTREME-VALUE THEORYORDER STATISTICS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 500 - 509
Copyright
Copyright © Applied Probability Trust 1982 

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