The Trend-Renewal Process for Statistical Analysis of Repairable Systems

A repairable system can briey be characterized as a system which is repaired rather than replaced after a failure. The most commonly used models for the failure process of a repairable system are nonhomogeneous Poisson processes (NHPP), corresponding to minimal repairs, and renewal processes (RP), corresponding to perfect repairs. This paper introduces and studies a more general model called the TrendRenewal Process (TRP). The TRP is a time transformed renewal process, having both the ordinary renewal process (RP) and the nonhomogeneous Poisson process (NHPP) as special cases. Parametric inference in the TRP model is studied both for observation of single systems and of several systems, with a possible unobserved heterogeneity between the systems. 1 Introduction Lawless & Thiagarajah (1996) discussed statistical inference for recurrent events which incorporated both time trends and renewal type behaviour. Such models are of interest for example in repairable systems reliability as a ..

Preventive maintenance models for complex systems

Preventive maintenance (PM) of repairable systems can be very beneficial in reducing repair and replacement costs, and in improving system availability, by reducing the need for corrective maintenance (CM). Strategies for scheduling PM are often based on intuition and experience, though considerable improvements in performance can be achieved by fitting mathematical models to observed data; see Handlarski (1980), Dagpunar and Jack (1993) and Percy and Kobbacy (2000) for example