Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-23T18:29:17.404Z Has data issue: false hasContentIssue false
  • English
  • Français

Some multivariate distributions derived from a non-fatal shock model

Published online by Cambridge University Press:  14 July 2016

Thomas H. Savits
Thomas H. Savits*
Affiliation:
University of Pittsburgh
*
∗Postal address: Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

A non-homogeneous Poisson shock model has a continuous mean function Λ(t). The kth shock Sk causes simultaneous failure of the components j ∊ J ∊ {1, ···, n} with probability pJ(Sk). If Tj is the lifetime of component j, it is shown that (T1, · ··, Tn) belongs to various multivariate non-parametric life classes depending on the life class of .

Keywords

IFRIFRANBUNON-HOMOGENOUS POISSON PROCESSESIMPERFECT REPAIR
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 2 , June 1988 , pp. 383 - 390
Copyright
Copyright © Applied Probability Trust 1988 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Research supported by ONR Contract N00014–84-K-0084 and AFOSR Grant AFOSR-84–0113.

References

Barlow, R. E. and Proschan, F. (1981) Statistical Theory of Reliability and Life Testing: Probability Models. To Begin With, Silver Spring, MD.Google Scholar
Block, H. W. and Savits, T. H. (1980) Multivariate IFRA distributions. Ann. Prob. 8, 793–801.Google Scholar
Block, H. W., Borges, W. and Savits, T. H. (1983) A general minimal repair maintenance model. Naval. Res. Log. Quart. To appear.Google Scholar
Block, H. W., Borges, W. and Savits, T. H. (1985) Age dependent minimal repair. J. Appl. Prob. 22, 370–385.Google Scholar
Çinlar, E. (1975) Introduction to Stochastic Processes. Prentice Hall, New York.Google Scholar
Marshall, A. W. and Olkin, I. (1967) A multivariate exponential distribution. J. Amer. Statist. Assoc. 62, 30–44.Google Scholar
Marshall, A. W. and Shaked, M. (1982) A class of multivariate new better than used distributions. Ann. Prob. 10, 259–264.Google Scholar
Neveu, J. (1965) Mathematical Foundations of the Calculus of Probability. Holden Day, New York.Google Scholar
Savits, T. H. (1985) A multivariate IFR class. J. Appl. Prob. 22, 197–204.Google Scholar
Thompson, W. A. Jr. (1981) On the foundations of reliability. Technometrics 23, 1–13.Google Scholar