On estimating the current intensity of failure for the power-law process |
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| Institution: | 1. Nanjing University of Information Science and Technology, School of Marine Sciences, Nanjing 210044, China;2. Chinese University of Hong Kong, Center for Housing Innovations, Shatin, Hong Kong;3. China University of Geosciences, State Key Laboratory for Geological Processes and Mineral Resources, Beijing 100083, China;4. Beijing University of Technology, Faculty of Information Science, Beijing 100124, China;5. Huaihai Institute of Technology, Faculty of Surveying and Mapping, Lianyungang 222005, China;1. University of Maryland, College Park, United States;2. Goddard Space Flight Center, USA;3. Massachusetts Institute of Technology, United States;4. Jet Propulsion Laboratory, United States;5. University of Texas at Austin, United States |
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| Abstract: | We consider the problem of estimating the current failure intensity for the power-law (Weibull) process. Closed-form optimum estimators under the criteria of minimum risks as well as Pitman-closeness are derived for the failure truncated case. A unique Pitman-closest estimator which is also invariant of the choice of the loss function within a very wide class of loss functions is obtained. In the frequentist setup, no admissible estimator under these criteria are available for the time truncated scheme due to the lack of any pivotal quantity. We present a Bayesian approach, which circumvents this problem and provides a uniform solution. In the Bayesian framework, we provide an algorithm based on Markov Chain Monte Carlo (MCMC) technique, which facilitates the evaluation of the estimators. The theoretical findings are supplemented by substantial numerical investigation. |
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