On the Brown-Proschan model when repair effects are unknown

A device is repaired after failure. The BrownProschan (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 (C) 2010 John Wiley & Sons, Ltd.