Some modified maximum likelihood estimators for the Weibull process

A non-homogeneous Poisson process with Weibull intensity function has been often used to analyze the failure pattern of repairable systems. Simple distributional results for the maximum likelihood estimator of the shape parameter ² are available, so that an unbiased estimator for ² can be introduced. In this paper the effect of using this unbiased estimator in the point estimation of quantities useful in performing reliability analyses, such as the expected number of failures in a given time interval and the failure intensity at a given time t, is analyzed. Moreover an approximately unbiased estimator of the failure intensity at the time of the failure n is introduced.