Numerical Estimation of Expected Number of Failures for Repairable Systems Using a Generalized Renewal Process Model

Abstract

The reliability of repairable systems is important for many engineering applications such as warranty forecasting, maintenance strategies, and durability, among others. A generalized renewal process (GRP) approach, considering the effectiveness of repairs, is commonly used, modeling the concepts of minimal repair, perfect repair, and general repair. The effect of the latter is between the effects of a minimal and a perfect repair. The GRP models the sequence of recurrent failure/repair events for repairable systems by solving the so-called g-renewal equation, which has no analytical solution. This paper proposes a data-driven numerical estimation of the expected number of failures (ENF) for the GRP model without solving the complicated g-renewal equation directly. Instead, it uses an empirical relationship among the cumulative intensity function (CIF) of the GRP, ordinary renewal process (ORP), and nonhomogeneous Poisson process (NHPP). The ORP and NHPP are limiting cases of the generalized renewal process. For practical reasons, it is common to observe only a few units of a repairable system population for only a short time. Using the observed data, the proposed approach creates a reliability metamodel of a renewal process, which is then used to predict the expected number of failures, and assess the average effectiveness of each repair. This increases the usefulness of the method for many practical reliability problems where the collection of a large amount of data is not possible or economical. The good accuracy of the proposed approach is demonstrated with three examples using simulated data, and a real-life example of locomotive braking grids using actual data.