Reliability and Maintenance Modeling of Complex Systems Under Multiple Dependent Competing Failure Processes



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To achieve commercialization and wide acceptance in industrial application, reliability analysis for complex evolving systems with multiple failure processes becomes increasingly important. The common assumption in analyzing reliability of such systems is that these multiple failure processes are independent, which may lead to the miscalculation of system reliability. To assist engineers with design, manufacturing and maintenance of complex systems, new reliability models that account for the dependence among multiple failure processes need to be developed to accurately predict the lifetime of these systems.

This research aims to develop probabilistic reliability models and analytical tools for systems with dependent competing failure processes, and explore cost-effective maintenance policies based on our reliability analysis. Different dependent patterns among competing failure processes are explored for single-component systems. When the arrival of external shocks diminishes the strength of material, we propose reliability and maintenance models for systems with a shifting, dependent hard failure threshold. When shocks impact the degradation process in different manners, we model zoned shock effects on stochastic degradation, and develop reliability functions for such dependent stochastic failure processes. Case studies of micro-electro-mechanical systems and stent devices are used to demonstrate our models, where Monte Carlo importance sampling is used to estimate system reliability.

We extend our models on single-component systems to a broader range of multi-component systems experiencing multiple failure processes, which presents more challenges on modeling the interaction and dependence among different components. A new reliability model and a unique condition-based maintenance model are proposed for complex systems with dependent components subject to respective degradation processes, and the dependence among components is established through environmental factors. Another condition-based maintenance policy is developed for power transformers using Markov decision processes, where a power transformer with multiple components is modeled as a multi-state system.

The proposed reliability and maintenance models can be implemented to address the critical quality and reliability problems of evolving devices and many other systems with multiple dependent competing failure processes and multiple dependent components. The developed models and analytical tools can facilitate product design, manufacturing and maintenance, and enhance system reliability and availability.



Degradation, Shock models, Multiple dependent competing failure processes, Block replacement policy, Age replacement policy, Gamma process, Peaks-over-threshold method, Shock load exceedances, Truncated generalized Pareto distribution, Decomposition of Poisson process, Monte Carlo importance sampling, Dependent degrading components, Environmental factors, Physics-of-failure, Thermodynamics, Arrhenius relationship, Condition-based maintenance, Power transformer, Semi-Markov decision processes


Portions of this document appear in: Jiang, Lei, Qianmei Feng, and David W. Coit. "Reliability and maintenance modeling for dependent competing failure processes with shifting failure thresholds." IEEE Transactions on Reliability 61, no. 4 (2012): 932-948. © 2012 IEEE. Reprinted with permission. In reference to IEEE copyrighted material which is used with permission in this thesis, the IEEE does not endorse any of the University of Houston's products or services. Internal or personal use of this material is permitted. If interested in reprinting/republishing IEEE copyrighted material for advertising or promotional purposes or for creating new collective works for resale or redistribution, please go to to learn how to obtain a License from RightsLink.