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• Uncertain process is adopted for degradation modeling accounting for epistemic uncertainty. • A novel similarity based-uncertain weighted least squares estimation method is proposed. • A denoising method is proposed to deal with the noises caused by recovery phenomenon. • The proposed framework is applied to real lithium-ion battery degradation dataset for demonstration. Remaining useful life prediction based on degradation modeling is of great importance to condition-based maintenance, for which epistemic uncertainty due to the lack of sufficient knowledge needs to be characterized. For certain components, such as the batteries, the recovery phenomenon during degradation has to be considered, and the epistemic uncertainty associated with it is inevitable. This paper proposes a systematic method for degradation modeling and remaining useful life prediction based on uncertain process for degradation with recovery phenomenon. First, uncertain process is adopted for degradation modeling accounting for epistemic uncertainty. Then, a novel similarity based-uncertain weighted least squares estimation method is proposed to update the model parameters with real-time monitoring data. Afterwards, a denoising method is used to deal with the noises caused by recovery phenomenon. Finally, remaining useful life is calculated by uncertain simulation. A case study on real lithium-ion battery degradation dataset is performed to illustrate the effectiveness of the proposed method in comparison with traditional stochastic process. [ABSTRACT FROM AUTHOR]

• This paper proposes a new uncertain accelerated degradation model. • The model considers the epistemic uncertainties in time and unit dimensions. • This paper presents the uncertain statistical method for parameter estimations. • The model is suitable for limited data sizes in time and unit dimensions. Accelerated degradation testing (ADT) has been widely used for the reliability and lifetime evaluations of highly reliable products. Generally speaking, the obtained ADT data are composed of two parts - the deterministic degradation trend and uncertainties. When only limited ADT data can be obtained, there will be a lack of knowledge on recognizing the population and lead to epistemic uncertainties. However, current accelerated degradation models fail to clearly distinguish and properly quantify the epistemic uncertainties in time and unit dimensions. Motivated by this problem, this paper constructs a new uncertain accelerated degradation model based on uncertainty theory and belief reliability theory, and presents the uncertain statistical method for parameter estimations. An application case is used to illustrate the proposed methodology and conduct discussions for the deterministic degradation trend and uncertainty analyses of the proposed methodology and the analyses of the proposed methodology to the data sizes in time and unit dimensions. Results show that under limited data sizes in time and unit dimensions, the proposed model can clearly distinguish and properly quantify the epistemic uncertainties in time and unit dimensions and is more suitable for the ADT modeling and analysis than the other two widely used accelerated degradation models. [ABSTRACT FROM AUTHOR]

• Uncertainty theory is used to express the epistemic uncertainty. • Uncertainty expressions considering analyst's knowledge stages are developed. • Propagations methods corresponding to knowledge stages are developed. • A knowledge-increasing process is simulated based on the proposed methods. Uncertainty analysis plays a significant role in risk assessment, which consists of two tasks: uncertainty expressions of input variables in the model and their propagations through the model built. We aim to provide, in fault tree analysis context, suitable methods of expression and propagation of uncertainty corresponding to different stages of knowledge that the risk analyst own, where frequentist probability is used to express the aleatory uncertainty and uncertainty theory is used to represent the epistemic uncertainty. To do so, we divide the analyst's knowledge state into five different stages, and develop the correct expression of uncertainty corresponding to each stage, where different combinations of probability and uncertainty are considered. Methods of propagation of these uncertainties through fault trees are further developed, where we introduce probability distributions, uncertainty distributions, newly-developed level-2 distributions, and the varying time t into the operational law for Boolean uncertain random system to better address the needs of practical risk assessments. A case study is conducted to show the differences in the propagation methods corresponding to various knowledge stages, and the results highlight that the proposed methods are effective and could deliver clear messages to decision makers. [ABSTRACT FROM AUTHOR]

Due to economic and technical reasons, in accelerated degradation testing (ADT) there are usually limited ADT data, which embody lots of epistemic uncertainties that cannot be depicted well by probability theory. Noting these facts, several uncertain processes based accelerated degradation models (UADMs) are proposed under the framework of uncertainty theory. However, these UADMs described uncertainties from a macro perspective which ignored the characteristic of performance degradation in small time scales and failed to describe the essence of nonlinear degradation. What is more, to estimate unknown parameters, these models used empirical distribution functions, which may have a great impact on the estimation results with limited samples. Motivated by these problems, based on uncertainty theory this paper builds up an uncertain differential equation based accelerated degradation model (UDEADM), which considers the dynamic cumulative change process of performance in small space–time scale, and explains the essence of nonlinear for uncertainties in degradation trend. Unknown parameters are estimated using uncertain generalized moment estimations. Furthermore, reliability and lifetime are analyzed under the normal operating condition based on belief reliability theory. A simulation study and a real data analysis are conducted to illustrate the effectiveness and advantages of the proposed methodology in details. • An uncertain differential equation based accelerated degradation model is proposed. • Dynamic cumulative change of performance in small space–time scale is considered. • Unknown parameters are estimated by uncertain generalized moment estimations. [ABSTRACT FROM AUTHOR]

• Dataset discrepancies and epistemic uncertainties are considered in the integration. • The evaluation index system for an ADT dataset is constructed. • Relative qualities of multi-source ADT datasets are quantified. • A statistical method is given for dataset discrepancies and epistemic uncertainties. • Uncertainties in the degradation evaluation are notably decreased. Degradation data collected from a single accelerated degradation testing (ADT) are usually non-sufficient, which causes a lack of knowledge and leads to epistemic uncertainties. So multi-source ADT datasets are usually integrated for degradation analysis and reliability evaluations. Nevertheless, the discrepancies among multi-source ADT datasets are ignored in current integration methods, which cannot make full use of all information in the integration process. To address these problems, an integration method of multi-source ADT datasets is developed for degradation analysis and reliability evaluations. Firstly, the evaluation index system for an ADT dataset is constructed. Then, the relative qualities of ADT datasets are computed through an additive model and a weight formula. After that, the degradation process is described by an uncertain accelerated degradation model to quantify epistemic uncertainties, and the related statistical analysis is given through a proposed uncertain least weighted squared error to consider dataset discrepancies. A simulation study and an application case are utilized to illustrate the proposed method. Results show that the proposed method can well capture the discrepancies among multi-source ADT datasets and make a quantitative comparison; additionally, it can notably decrease uncertainties in the degradation analysis. [ABSTRACT FROM AUTHOR]

• The epistemic uncertainty of trigger effect in reliability evaluation is analyzed. • Uncertain theory is applied to quantify the PoF model-form uncertainty. • The uncertain degradation model of failure mechanism is built. • Belief reliability of the system with failure trigger effect is deduced. • The advantages of the new method are discovered in the engineering case. Reliability evaluation of system with dependent failure processes is a problem that draws more research attention. It is essential to quantify the epistemic uncertainty in the system for high evaluation accuracy. Trigger is one of the typical dependent failure processes. Trigger effect indicates that some events occur because of the trigger of other events. This paper studies the epistemic uncertainties in the reliability evaluation of the system with trigger effect based on uncertainty theory. The model-form uncertainty of physics of failure (PoF) model, the failure process uncertainty due to lack of knowledge and the propagation of them in the system are quantified with Belief Adjustment Factors Method (BAFM) and the Liu process. System belief reliability is evaluated by decoupling the correlations between the trigger failure mechanism and triggered failure mechanisms. A conductive slip ring in electromechanical orientation device is introduced as a case. The trigger effect and system belief reliability are analyzed. Results show that, compared with probability method, evaluation values with uncertainty method are more conservative and stable in the case.. [ABSTRACT FROM AUTHOR]

• URADM is proposed to integrate aleatory and epistemic uncertainties from multiple dimensions in ADTs. • Aleatory and epistemic uncertainties are divided and quantified separately in the URADM. • Integration of aleatory and epistemic uncertainties is measured through chance theory. • A dynamic uncertain random simulation algorithm is proposed to approximate reliability. • More accurate and stable degradation predictions are achieved under multiple situations. Accelerated degradation testing (ADT) is commonly employed for degradation analysis and reliability evaluations. Due to limitations in practical ADTs, aleatory and epistemic uncertainties are simultaneously embodied in time, unit, and stress dimensions but they are not considered comprehensively and integrated scientifically currently. To address such problems, we focus on the most common situation in ADTs that test time is relatively long (reflecting aleatory uncertainties in time dimension) while the numbers of test units and stress levels are quite small (reflecting epistemic uncertainties in unit and stress dimensions), and establish an uncertain random accelerated degradation model (URADM). In the URADM, aleatory and epistemic uncertainties are quantified using probability theory and uncertainty theory, respectively, and they are integrated using chance theory. Then, first passage time and reliability evaluations are derived. Next, a three-step uncertain random statistical method is presented for parameter estimations, where aleatory and epistemic uncertainties are divided carefully and quantified separately. A simulation study and a practical case are conducted to show the effectiveness of the URADM. Results reveal that the URADM can not only predict deterministic degradation trends with high accuracy as existing methods do, but contribute degradation boundaries well covering ADT data with narrower boundaries and higher stability. [ABSTRACT FROM AUTHOR]

• The hybrid uncertainty includes the aleatory uncertainty and epistemic uncertainty is analyzed in DCFP. • The uncertainty random renewal reward process and arithmetic Liu process are used to describe the shock and degradation process. • The analytic formulas of system reliability models considering three types of DCFPs are derived. • A combinational algorithm is proposed to calculate system reliability. • The proposed method is proved to be an appropriate method to qualify the hybrid uncertainty in the case. Dependent competing failure process (DCFP) has been widely studied in recent years. When evaluating the reliability of DCFP system, the aleatory uncertainty due to randomness and the epistemic uncertainty due to lack of data and knowledge should be considered. In this paper, the hybrid uncertainty of DCFP system is analyzed and quantified with chance theory. The uncertainty random renewal reward process and the arithmetic Liu process are used to describe the shock and degradation process. The quantification of uncertainty propagation is realized by decoupling DCFP from the physical correlation aspect. Reliability of DCFP system considering two kinds of unilateral dependencies and mutual dependency is modeled and a combinational algorithm is proposed to solve it. Finally, the DCFP effect in control system of an aircraft is studied as a case, aleatory uncertainty and epistemic uncertainty are modeled, and the system reliability is evaluated. Meanwhile, the effects of key parameters on system reliability are discussed. Results show that the chance theory is an appropriate method to qualify the hybrid uncertainty for engineering systems when data is insufficient. The mutual dependency of soft failure and hard failure will reduce the system reliability. The smaller the parameter of hard failure, the greater the influence of mutual dependency on the results. [ABSTRACT FROM AUTHOR]

• A general ADT modeling framework considering uncertainties are presented. • A 3-Dimensional ADT model and a practical application procedure are developed. • A bidirectional Liu process is utilized to describe the epistemic uncertainty. • A new statistical method is presented for parameter estimations. • Cases show the accuracy and practicability of the proposed model and framework. Accelerated degradation testing (ADT) has been widely used to identify the performance degradation law so as to evaluate the reliability and lifetime. During this process, there are aleatory and epistemic uncertainties in the unit, time and stress dimension. However, the current studies do not have a comprehensive modeling framework and a general ADT model that fully considers and properly quantifies all sources and types of uncertainties. Aiming at these problems, this paper proposes a 3-Dimesional modeling framework and a general ADT model, and gives a new uncertain ADT model considering epistemic uncertainties in the unit, and stress dimension. Furthermore, considering the weights of observed degradation data under different stress levels, this paper proposes a new parameter estimation method, uncertain weighted least squares, to well predict degradation law and control uncertainties. Finally, a microwave case, a rubber seal case and two simulation cases are conducted to show the practicability of the proposed framework and model. The results show that the proposed framework can guide the construction of different models according to different situations; and compared with current methods, the proposed model are more appropriate for performing ADT model and quantifying uncertainties when uncertainty in the stress dimension cannot be ignored. [ABSTRACT FROM AUTHOR]