Application of Stochastic Modeling Methods for Optimization of Maintenance and Repair Processes
A Systematic Approach
Abstract
The paper presents a systematic approach to optimizing maintenance and repair processes of complex technical systems based on stochastic modeling methods. An extended stochastic model of equipment degradation has been developed, considering multiple factors and nonlinear wear patterns. The model is based on stochastic differential equations with a Poisson component, describing continuous and discontinuous changes in system state. A multi-criteria maintenance optimization problem is formulated, and an adaptive solution method based on stochastic dynamic programming is proposed. An algorithm for calculating residual prediction error using statistical analysis methods is developed. A multi-scale approach to modeling degradation processes is presented, considering various temporal and spatial scales. A feedback optimal control strategy based on the Hamilton-Jacobi-Bellman equation and stochastic filtering methods for system state estimation is proposed. The problem of optimizing maintenance frequency and scope considering probabilistic constraints is examined. Methods for sensitivity analysis and solution robustness are proposed. The proposed approach provides increased efficiency in equipment lifecycle management under stochastic impacts.
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