Stochastic Renewal Process Models for Maintenance Cost Analysis
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The maintenance cost for an engineering system is an uncertain quantity due to uncertainties associated with occurrence of failure and the time taken to restore the system. The problem of probabilistic analysis of maintenance cost can be modeled as a stochastic renewal-reward process, which is a complex problem. Assuming that the time horizon of the maintenance policy approaches infinity, simple asymptotic formulas have been derived for the failure rate and the cost per unit time. These asymptotic formulas are widely utilized in the reliability literature for the optimization of a maintenance policy. However, in the finite life of highly reliable systems, such as safety systems used in a nuclear plant, the applicability of asymptotic approximations is questionable. Thus, the development of methods for accurate evaluation of expected maintenance cost, failure rate, and availability of engineering systems is the subject matter of this thesis. In this thesis, an accurate derivation of any m-th order statistical moment of maintenance cost is presented. The proposed formulation can be used to derive results for a specific maintenance policy. The cost of condition-based maintenance (CBM) of a system is analyzed in detail, in which the system degradation is modeled as a stochastic gamma process. The CBM model is generalized by considering the random repair time and delay in degradation initiation. Since the expected cost is not informative enough to estimate the financial risk measures, such as Value-at-Risk, the probability distribution of the maintenance cost is derived. This derivation is based on an interesting idea that the characteristic function of the cost can be computed from a renewal-type integral equation, and its Fourier transform leads to the probability distribution. A sequential inspection and replacement strategy is presented for the asset management of a large population of components. The finite-time analyses presented in this thesis can be combined to compute the reliability and availability at the system level. Practical case studies involving the maintenance of the heat transport piping system in a nuclear plant and a breakwater are presented. A general conclusion is that finite time cost analysis should be used for a realistic evaluation and optimization of maintenance policies for critical infrastructure systems.