On the Brown–Proschan model when repair effects are unknown
Article first published online: 5 DEC 2010
Copyright © 2010 John Wiley & Sons, Ltd.
Applied Stochastic Models in Business and Industry
Volume 27, Issue 6, pages 600–618, November/December 2011
How to Cite
Doyen, L. (2011), On the Brown–Proschan model when repair effects are unknown. Appl. Stochastic Models Bus. Ind., 27: 600–618. doi: 10.1002/asmb.869
- Issue published online: 21 DEC 2011
- Article first published online: 5 DEC 2010
- Manuscript Revised: 17 SEP 2010
- Manuscript Accepted: 17 SEP 2010
- Manuscript Received: 9 JUL 2009
- repairable system reliability;
- imperfect repair;
- stochastic intensity;
A device is repaired after failure. The Brown–Proschan (BP) model assumes that the repair is perfect with probability p and minimal with probability (1−p). Theoretical results usually suppose that each repair effect (perfect or minimal repair) is known. However, this is not generally the case in practice. In this paper, we study the behavior of the BP model when repair effects are unknown. In this context, the main features of the failure process are derived: distribution functions of times between failures, failure intensity, likelihood function, etc. We propose to estimate the repair efficiency parameter p and the parameters of the first time to failure distribution with the likelihood function or equivalently the EM algorithm. We also propose to combine a moment estimation of the scale parameter and a maximum likelihood estimation of other parameters. Copyright © 2010 John Wiley & Sons, Ltd.