Multi-State Complex System Reliability Modeling And Maintenance Decision

As modern advanced engineering devices and systems designed towards larger size, more complex, and higher precision, as well as the understanding of system failure mechanism and physics developed continuously, it has been observed that multiple states occur during the deterioration process of engineering systems and components. The associated failure mechanism, performance rate, and efficiency vary across different states. Conventional reliability analysis methods are limited by their fundamental assumption that both systems and components can be characterized as one of only two possible states:working perfectly or completely failed. It is inappropriate to describe the complicated failure process using these two states while ignoring the multiple states that possibly exist in engineering systems. Therefore, there is an urgent need for developing reliability theories and reliability analysis methodologies to facilitate the reliability assessment and enhancement in sophisticated multi-state systems.With an increasing demand in industry in recent years, multi-state reliability theory has become an emerging research topic in both industry and academia. It has been applied to a variety of industrial domains, including mechanical engineering, computer and network, grid systems, communication, energy, supply systems, municipal infrastructure, and defense strategy research, etc. The overall objective of this dissertation is to address key challenges and critical issues in multi-state reliability theory, with a special emphasis on two fundamental aspects:complexity and uncertainty. In particular, this dissertation is focused on the reliability modeling and maintenance decision making of multi-state complex systems. The primary research contributions and innovative outcomes are summarized as follows:(1) Development of a selective maintenance optimization strategy for multi-state systems. With the consideration of the limitation of maintenance resources, a selective maintenance optimization methodology based upon the multi-state system reliability theory is proposed. To take into account the imperfect maintenance quality, an imperfect maintenance model for binary state components is incorporated into the maintenance decision model. In addition, a cost-maintenance quality functional relationship is developed to consider the age reduction factor as a function of allocated maintenance cost. Demonstrated by numerical studies and examples, the proposed methodology provides much more flexibility in assigning the maintenance cost and yields better results than the existing methods in literature.(2) Development of an imperfect maintenance model for multi-state components and a "system perspective" replacement policy for multi-state systems. In practice, the maintenance planning of complex systems is usually carried out from the system-level perspective. The existing imperfect maintenance models are applicable only to binary state components. In this work, a novel imperfect maintenance model is proposed to quantify the impact of maintenance activities on the degradation trend of multi-state components. Based upon the proposed imperfect maintenance model, a new system replacement strategy is developed to achieve the maximum expected profit per unit time for the entire multi-state system.(3) Systematic investigation of the component-level maintenance and replacement optimization strategies for multi-state systems. In this dissertation, the optimized component replacement strategy, and the lifecycle-based redundancy design optimization under perfect and imperfect maintenance are studied from the component-level perspective. Building upon a generalized imperfect maintenance model for multi-state components, a flexible and effective repair cost assignment among components is achieved by proposing a set of functional relationships between the assigned repair cost and the imperfect repair quality. Through the study, it has been demonstrated that the proposed method is more economically efficient than conventional methods. In addition, a joint optimization method for redundancy and component replacement strategy is put forth by considering the component maintenance planning in the design stage of multi-state systems. It enables the system reliability design optimization across the entire lifecycle.(4) Development of fuzzy multi-state system reliability modeling methods and fuzzy multi-state component replacement strategy. The multi-state system reliability modeling and assessment methods are developed based on the fuzzy uncertainty theory. A fuzzy Markov model and a fuzzy Markov reward model are proposed to evaluate the dynamic state distribution and the cumulative performance of fuzzy multi-state components. By developing a set of composition rules for the fuzzy universal generation function of different types of systems, the system state distribution can be derived in a computationally efficient manner. In addition, a modified fuzzy multi-state systems availability assessment approach is developed to overcome the drawbacks of the existing methods in assessing the system availability. A replacement strategy for fuzzy multi-state components that are based on the proposed fuzzy multi-state system reliability theory is further investigated. By constructing the formulation of replacement decision and utilizing the existing fuzzy ranking methods, it provides a general framework and guideline of maintenance planning for fuzzy multi-state components.(5) Development of a hierarchical statistical sensitivity analysis method to facilitate uncertainty analysis and reduce complexity in design and reliability assessment of complex multi-level hierarchical systems. Statistical sensitivity analysis is an effective tool to examine the impact of variation in model inputs on the variations in model outputs, and can relieve the computational burden and manage the complexity in complicated system design and reliability analysis under uncertainty. A hierarchical statistical sensitivity analysis method is developed to deal with the shared variable among submodels, which is not addressed in other existing statistical sensitivity analysis methods. The inherited advantages of the proposed method are that the top-down strategy used in the method matches better with a typical design process of complex systems and products. The global statistical sensitivity index is obtained by aggregating the local sensitivity indices of submodels across multi-level hierarchy. The associated computational time is significantly reduced using the concurrent computing fashion. Therefore, the proposed method has a broader range of applicability to complex engineering systems design than other existing sensitivity analysis methods.