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Activity Number:
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189
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Type:
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Contributed
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Date/Time:
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Tuesday, August 10, 2004 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Physical and Engineering Sciences
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| Abstract - #301770 |
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Title:
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Statistical Inference for the Modulated Power-law Process
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Author(s):
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Ananda Sen*+ and Nibedita Bandyopadhyay
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Companies:
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University of Michigan and Oakland University
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Address:
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3550 Rackham , Ann Arbor, MI, 48109,
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Keywords:
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repairable systems ; power-law process ; maximum likelihood ; asymptotics
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Abstract:
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Failure data pertaining to a repairable system is commonly modeled by a nonhomogeneous Poisson process (NHPP). A modulated gamma process evolves as a generalization to a NHPP, where the observed failure epochs correspond to every successive kth event of the underlying Poisson process, k being an unknown parameter to be estimated from the data. We focus on a special class of modulated gamma process, called a modulated power-law process (MPLP) that assumes the Weibull form of the intensity function. The traditional power-law process is a popular stochastic formulation of certain empirical relationships between the time to failure and the cumulative number of failures, often observed in industrial experiments. The MPLP retains this underlying physical basis and provides a more flexible modeling environment potentially leading to a better fit to the failure data at hand. We investigate inference issues related to a MPLP. The maximum likelihood estimators (MLE's) of the model parameters are not in closed form and enjoy the curious property that they are asymptotically normal with a singular variance-covariance matrix.
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