Statistical Maintenance Modeling for Complex Systems

Abstract

The first part of this chapter provides a brief introduction to statistical maintenance maintenance modeling subject to multiple failure processes. It includes a description of general probabilistic degradation processes. degradation process The second part discusses detailed reliability modeling reliabilitymodeling for degraded systems subject to competing failure processes without maintenance actions. A generalized multi-state degraded system multi-state degraded-system reliability model with multiple competing failure processes including degradation processes and random shocks is presented. The operating condition of the multi-state system is characterized by a finite number of states. A methodology to generate the system states when multi-failure processes exist is also discussed. The model can be used not only to determine the reliability of the degraded systems in the context of multi-state functions but also to obtain the probabilities of being in a given state of the system. The third part describes the inspection–maintenance inspectionmaintenance issues and reliability modeling for degraded repairable systems with competing failure processes. A generalized condition-based maintenance model for inspected degraded systems is discussed. An average long-run maintenance cost rate function is derived based on an expression for degradation paths and cumulative shock damage, which are measurable. An inspection sequence is determined based on the minimal maintenance minimal maintenance cost rate. Upon inspection, a decision will be made on whether to perform preventive maintenance or not. The optimum preventive maintenancethreshold maintenance thresholds for degradation processes and inspection sequences are also determined based on a modified Nelder–Mead downhill simplex method Nelder–Mead downhill simplex method. Finally, the last part is given over to the conclusions and a discussion of future perspectives for degraded-system maintenance modeling.