Estimating the intensity function of a weibull process at the current time: failure truncated case

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Abstract
The Weibull process, a nonhomogeneous Poisson process with intensity functionis often used to model the failure times of complex systems which are repaired after failure. Point estimation of the value of the intensity function at the current time is frequently an important problem and in this paper, two classes of estimators of this quantity are proposed when the data are failure truncated. Several members of these classes are suggested as estimators. Expressions for the bias and the mean squared error of these estimators are derived and are evaluated for several values of β and for samples sizes of 5, 10,20 and 40. Some estimators have smaller mean squared error than the conditional MLE for a wide range of the parameters.

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