Power law process models for nonhomogeneous Poisson process change-points

The reliability of a repairable system that is either improving or deteriorating depends on the system's chronological age. If such a system undergoes "minimal repair" at the occurrence of each failure so that the rate of system failures is not disturbed by the repair, then a Nonhomogeneous Poisson Process (NHPP) may be used to model the "age-dependent" reliability of the system. The Power Law Process (PLP) is a model within the class of NHPP models and is commonly used as a model for describing the failure times of a repairable system.;We introduce two new models that are extensions of the PLP model: the Power Law Process Change-Point I (PLPCPI) and the Power Law Process Change-Point II (PLPCPII). These models are capable of describing the failure times of particular types of repairable systems that experience a single change in their rates of occurrence of failures.;For the PLPCPI and the PLPCPII, under the assumption of a known change-point: we develop procedures for estimating the model parameters and the system intensity of failures; and predictive distributions are derived for future system failure times and the number of system failures in a future time interval.;For the PLPCPI, we perform a simulation study to investigate the effect (on the estimation of the system intensity of failures at the current time) of assuming that the failure times of a repairable system follow a PLP when in reality the system failure times follow a PLPCPI.;For the PLPCPI and the PLPCPII, under the assumption of an unknown change-point, we develop procedures for estimating the change-point.