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We introduce a method of combining two time indices, such as mileage and age, into a single index that resembles the Cobb-Douglas production function. Then we present the power law process with this synthesized time index as a model for the reliability of a repairable system, such as an automobile. For the purpose of estimating parameters, we propose two procedures: one is a modified maximum likelihood procedure and the other a least-squares fitting of the mean value function. The performances of the two estimation procedures are compared and analyzed.
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Ahn et al. (1998) studied this question.
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