Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T00:30:27.686Z Has data issue: false hasContentIssue false
  • English
  • Français

Limiting behavior of some measures of system availability

Part of: Special processes Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

Jie Mi
Jie Mi*
Affiliation:
Florida International University
*
∗Department of Statistics, Florida International University, University Park, Miami FL 33199, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

Availability is an important characteristic of a system. Different types of availability are defined. For the case when a sequence of bivariate random variables of lifetime and repair time are i.i.d. certain properties have been established previously. In practice, however, we need to consider the situation where these bivariate random variables are independent but not identically distributed. Properties of two measures of availability for the i.i.d. case are extended to this more general case.

Keywords

STABLE AVAILABILITYAVERAGE AVAILABILITYDOMINATED SEQUENCE OF RANDOM VARIABLESSTRONG LAW OF LARGE NUMBERSASYMPTOTIC NORMALITY

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 62N05: Reliability and life testing
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 2 , June 1995 , pp. 482 - 493
Copyright
Copyright © Applied Probability Trust 1995 

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.)

References

Barlow, R. E. and Proschan, F. (1981) Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring, MD.Google Scholar
Bergman, B. (1985) On reliability theory and its applications. Scand. J. Statist. 12, 1–41.Google Scholar
Chow, Y. S. and Teicher, H. (1978) Probability Theory: Independence, Interchangeability, Martingales. Springer-Verlag, New York.Google Scholar
Gut, A. and Janson, S (1983) The limiting behaviour of certain stopped sums and some applications. Scand. J. Statist. 10, 281–292.Google Scholar
Rényi, A. (1957) On the asymptotic distribution of the sum of a random number of independent random variables. Acta Math. Acad. Sci. Hungar. 8, 193–199.Google Scholar
Rise, J. (1979) Compliance test plans for reliability. Proceedings of the 1979 Annual Reliability and Maintenance Symposium.Google Scholar
Takács, L. (1957) On certain sojourn time problems in the theory of stochastic processes. Acta Math. Acad. Sci. Hungar. 8, 169–191.Google Scholar