Estimating parameters of the power law process with two measures of failure time

Abstract

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.