Trend-Incomplete-Renewal Process Models for Repairable Systems

Repairable systems are characterized by alternation of function times and repair times. The repair times are often neglected, and the investigation of the system is based on sequences of failure times and the corresponding counting processes. Nonhomogeneous Poisson processes describe cases of minimal repair. Renewal processes model perfect repairs. More general models for repair types between the cases of minimal and perfect repair are studied by Kijima and Lindqvist. For different repair levels Kijima introduced the virtual age function, and the failure intensity of the system depends on the virtual age. Trend-renewal processes (TRP) introduced by Lindqvist generalize renewal processes of failure time points and lead to general failure intensities. The paper introduces a new model for repairable systems: a combination of TRP and Kijima virtual age models. The generalization contains most models dealt with in literature as special cases. For special process examples, maximum likelihood and Bayes parameter estimation are considered.