Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-25T04:08:01.452Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimation of limiting availability for a stationary bivariate process

Part of: Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

B. Abraham  and
N. Balakrishna
B. Abraham*
Affiliation:
University of Waterloo
N. Balakrishna*
Affiliation:
University of Waterloo
*
∗Postal address: Institute for Improvement in Quality and Productivity, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1. Email address: [email protected]
∗∗Visiting from Coching University of Science and Technology, Cochin, 682022 India.
Get access Rights & Permissions [Opens in a new window]

Abstract

We estimate the limiting availability of a system when the operating and repair times form a stationary bivariate sequence. These estimators are shown to be consistent and asymptotically normal under certain conditions. In particular, we estimate the limiting availability for a bivariate exponential autoregressive process.

Keywords

Bivariate geometric distributionconsistent and asymptotically normalergodicityexponential autoregressive modelϕ-mixing

MSC classification

Primary: 62M09: Non-Markovian processes 62M10: Time series, auto-correlation, regression, etc.
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 3 , September 2000 , pp. 696 - 704
Copyright
Copyright © Applied Probability Trust 2000 

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

Baxter, L. A., and Li, L. (1994). Nonparametric confidence intervals for the renewal function and the point availability. Scand. J. Statist. 21, 277–287.Google Scholar
Baxter, L. A., and Li, L. (1996). Nonparametric estimation of the limiting availability. Lifetime Data Anal. 2, 391–402.Google Scholar
Billingsley, P. (1968). Convergence of Probability Measures. John Wiley, New York.Google Scholar
Block, H. W., Langberg, N. A., and Stoffer, D. S. (1988). Bivariate exponential and geometric autoregressive and autoregressive moving average models. Adv. Appl. Prob. 20, 792–821.CrossRefGoogle Scholar
Gut, A., and Janson, S. (1983). The limiting behaviour of some stopped sums and some applications. Scand. J. Statist. 10, 281–292.Google Scholar
Hoyland, A., and Rausand, M. (1994). System Reliability Theory. John Wiley, New York.Google Scholar
Mi, Jie (1995). Limiting behaviour of some measures of system availability. J. Appl. Prob. 32, 482–493.CrossRefGoogle Scholar
Nicholls, D. F., and Quinn, B. G. (1982). Random Coefficient Autoregressive Models: An Introduction (Lecture Notes in Statist., II). Springer, New York.Google Scholar
Serfling, R. J. (1980). Approximation Theorems of Mathematical Statistics. John Wiley, New York.Google Scholar