Importance Measures And Reliability Assessment Of Multi-State Systems Under Epistemic Uncertainty

As one of the important reliability methods,importance measures have received considerable concerns from both academia and industry as they are effective tools to identify the weak components in complex engineered systems,especially for those systems,such as the aerospace,power generating systems,and nuclear power plants,which require a high reliability and long lifetime.Nevertheless,as engineered systems become more complex and sophisticated,the traditional reliability methods for binarystate systems,however,fail to characterize the complicated deteriorating process of systems.Multi-state nature becomes one of the typical characteristics of engineered systems.Furthermore,in many engineering practices,due to limited data,imprecise information,and conflicting judgements from experts,parameter estimation for degradation models or state assignment for components may inevitably produce epistemic uncertainties.Hence,it is a challenge to analyze the reliability of multi-state systems and the importance measure under various epistemic uncertainties.Various epistemic uncertainties from multiple sources have to be quantified properly before performing importance analysis and reliability assessment for multi-state systems.In this dissertation,we aim at conducting reliability assessment and importance analysis in the context of three types of epistemic uncertainties,i.e.,the uncertainty associated with the prameters of components' degradation models,the uncertainty associated with state assignment,and the uncertainty associated with vague experts' judgements.The primary research contributions and innovative outcomes are summarized as follows:(1)Development of an extended Birnbaum importance measures for multi-state systems with epistemic uncertainties associated with the parameters of components' degradation models.The proposed methods can quantify epistemic uncertainties of degradation model parameters by the Dempster-Shafer evidence theory,and can also characterize deteriorating processes of components by Markov models.The composite Birnbaum importance measure is then extended and the possibility degree rule is utilized to rank the extended importance.The illustrative examples show that the ranking results vary from the results if the epistemic uncertainties are overlooked.(2)Development of four extended composite importance measures for multi-state systems by taking account of epistemic uncertainties of component state assignment.The proposed methods introduce an uncertain state by the Dempster-Shafer evidence theory to represent the uncertainty among the singletons without any inclination to select a particular state.The evidential Markov chain and evidential network are proposed to calculate system reliability and manipulate uncertainty propagation,respectively.After handling the dependency between the intervals of the inputs of the proposed importance measures,a pair of optimization problems are formulated to compute the lower and upper bounds of the extended importance measures.As demonstrated in two illustrative examples,due to the epistemic uncertainty associated with the component state assignment,the proposed importance measures become interval values,rather than crisp values,and the ranking orders may also vary with respect to different interval ranking rules.(3)Development of a unified framework to fuse multiple sources of imprecise information from experts' judgements to assess multi-state system reliability.The proposed method assumes that the deterioration behaviors of components can be governed by the homogeneous or nonhomogeneous Markov model.With such assumption,the multiple sources of imprecise information can be converted into a set of constraints of an optimization model,and the system reliability function is treated as the objective function.By maximizing and minimizing the objective function,the upper and lower bounds of the system reliability can be identified.Furthermore,a model selection method is developed to select the best degradation model which matches with the multiple sources of imprecise information from experts' judgements to the maximum extent.The results from numerical examples show that,as compared to the existing works,a narrower reliability bound can be produced by the proposed method.Moreover,the imprecise information from different physical levels of a system at different time instants can be fused by the proposed optimization framework.