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This study addresses the problem of performance reliability degradation and lifetime prediction in complex systems with high reliability but insufficient information. It comprehensively considers the effects of various uncertainties, such as measurement, cognitive, and stochastic uncertainties, and proposes a generalized normal grey cloud Bayesian Wiener process (GNGCBWP) stochastic degradation model. First, based on the historical degradation information of the system, the interval grey number sequence of the degradation increment is constructed, and the performance degradation path of the system is analyzed to determine the degradation model type. Then, combining the normal grey cloud and Bayesian estimation theory, the relevant definitions and theorems of generalized normal grey cloud Bayesian estimation (GNGCBE) are proposed. Finally, the parameter estimation results obtained using the GNGCBE method are substituted into the grey Wiener process degradation model to dynamically analyze performance reliability degradation and predict the remaining useful life (RUL) in real‐time. And the validity and scientificity of the proposed model is verified through a case study of laser equipment. Moreover, the comparison results of the models indicate that the proposed model has advantages in dynamic analysis of performance reliability degradation and real‐time RUL prediction for highly reliable complex systems with limited or poor degradation information. It can significantly reduce the impact of multiple uncertainties on the analysis results and improve the accuracy and reliability of the final prediction results. [ABSTRACT FROM AUTHOR]

The evidential variable shows the powerful ability on the parameter description, so we have cooperated it with the linear Wiener process to model linear degradation processes. However, the degradation paths of some products exhibit two‐phase patterns over the running time, which cannot be modeled by the linear Wiener process. Hence, it is developed into an associated evidential variable‐based two‐phase Wiener process. In order to utilize the proposed model, the related evidence obtaining, evidence fusion and performance inference approaches are constructed. A simulation study and an actual case are performed to verify the superiorities of the proposed method. The proposed method provides higher accuracies of the useful life, degradation, and reliability evaluations, due to utilizing the evidential variable and considering the two‐phase degradation conditions. [ABSTRACT FROM AUTHOR]

This paper presents two Bayesian hierarchical models—one utilizing the life-time data and other using the structural health monitoring (SHM) data, for degradation modeling and reliability assessment of rolling element bearings. The main advantage of the proposed life-time data based model is that, it accounts for the variability in failure times caused due to the difference in material properties, initial degradation, operating and environmental conditions by introducing Bayesian hierarchy in the model parameters. On the other hand, SHM data (such as vibration and strain) based model focuses on stochastic nature of bearing degradation, and models it using a two-phase Wiener process. In this model, the point of phase-transition is the time when the damage initiates. The detection of such a point is undertaken using Bayesian change point algorithms. For both the models, the model parameters and reliability are updated as more data becomes available. In this manner, the prior domain knowledge and life-time data or SHM data collected from the field can effectively be integrated to get updated reliability. Two case studies for rolling element bearings are presented to demonstrate the applicability to life-time as well as SHM data. [ABSTRACT FROM AUTHOR]

• A novel deterioration-integrated failure model with varying environments. • A matrix-based approximation method for health measures calculation. • An adaptive reliability-based maintenance policy with a switchable control chart. • An efficient computational algorithm to find the optimal decision variables. • Considerable better maintenance performance than published results. The performance of mechanical systems is greatly influenced by varying operational environments such as load, temperature, and humidity, which can result in accelerated degradation and failure. To address this issue, this article considers an adaptive maintenance policy based on updated conditional reliability for mechanical systems under variable environments. A model of deterioration-integrated failure process is presented, which integrates degradation process, failure events, and environmental variables of the system. The degradation process is modeled by a random effect Wiener process, with its drift parameter following a general distribution to represent the environmental random effects. The failure events are modeled by a proportional hazards (PH) model with environment-varying covariate. The health of the system is evaluated using a matrix-based approximation method that provides estimates of the system's conditional reliability and mean residual life. Using the prognostic information, an adaptive maintenance model with a switchable control chart is then developed to monitor and maintain system based on the status of system reliability. The decision variables of the adaptive reliability-based maintenance are determined by a computational algorithm formulated in a semi-Markov decision process (SMDP) framework, with the objective of minimizing the long-run expected average cost per unit time. Vibrational data of bearings under varying operational environments are presented to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

We consider degrading engineering systems monitored by degrading sensors. Since accurate information is crucial for predicting system health condition and the subsequent decision-making, considering the effect of sensor degradation is highly important to determine the justified reliability characteristics of systems such as the remaining useful life (RUL). Although the concept of sensor degradation has been introduced previously in the literature, the remaining useful life estimation in this case or parameter estimation in the presence of sensor degradation has not been studied in detail. To fill the gap, this study aims to estimate the RUL of a system that is continuously monitored by a degrading sensor. In this work, to distinguish sensor degradation from that of the main system, an additional calibration sensor is used to accurately inspect the system health condition at certain points of time. Subsequently, maximum-a-posteriori estimation technique is employed to estimate the parameters for the system degradation process and maximum likelihood estimation is used to estimate the parameters of sensor degradation. A Kalman filter is then used to estimate the system and sensor states, followed by system RUL evaluation. A numerical example with simulated data is employed to illustrate the effectiveness of the proposed method. It is shown through the numerical study that neglecting sensor degradation can result in significant errors in RUL estimation, which can further impact the subsequent maintenance decisions. • We evaluate the remaining life of degrading systems monitored by degrading sensors. • We estimate the parameters of the degradation process for the sensor and system. • We estimate the system states with Kalman filter. • We highlight the importance of sensor degradation in system reliability evaluation. [ABSTRACT FROM AUTHOR]

Complex characteristics such as non-linearity and multi-stage are usually presented during the degradation process of aluminum electrolytic capacitors (AECs). Therefore, it is difficult to accurately predict the capacitors' remaining useful life (RUL), which is significant to the system's reliability. Based on the model of Wiener process with linear drift, a simple two-stage RUL predicting method for AECs is proposed in this paper. In the offline stage, the Box–Cox transformation (BCT) is first utilized to linearize the degraded data. Then the model parameters of BCT are identified, and the Shapiro–Wilk test is employed to verify whether the transformed data meet the linearity. In the online stage, based on similarity measurement, the drift coefficient of the Wiener process is updated in real-time. By combining BCT and similarity measurement, the nonlinear and multi-stage problems are effectively solved. Finally, the proposed method is verified on NASA's accelerated degradation data set. Experimental results show that the proposed method can automatically learn the capacitor's complex degradation characteristics and accurately predict its RUL. • The BCT (Box–Cox Transformation) is applied to the degradation of AECs (aluminum electrolytic capacitor), which makes it possible to model the degradation process by Wiener process with linear drift. • Based on similarity measurement, an online updating method of DC is proposed, which can automatically learn the multi-stage degradation characteristics of failure samples. • Based on BCT and similarity measurement, a two-stage RUL prediction method for AECs is proposed. [ABSTRACT FROM AUTHOR]

• Multivariate Wiener processes combining time-scale transformed was proposed. • The correlation of four copula functions and the reliability analysis was studied. • The RUL prediction model combining copula function was proposed. • The degradation failure of the aircraft lock mechanism was studied in detail. The failure mechanism and degradation analysis of an aircraft cabin door lock mechanism are studied. A data-driven degradation analysis is conducted based on the characteristics of two types of degradation data for the lock mechanism. The degradation process of the fluctuating elevation is described by Wiener process, and the lifetime is described using the Inverse Gauss (IG) process. The correlation between the two degradation processes is studied, and the correlation analysis is carried out with four copula functions. Moreover, the optimal model is obtained for reliability analysis using three model selection methods and Bayesian inference based on the Markov chain Monte Carlo (MCMC) method for parameter estimation. Finally, a residual life prediction model is proposed, and the accuracy of the model is tested with the error. The results show that the RUL prediction accuracy can be accepted, which helps to improve the reliability and service life of a type of aircraft lock mechanism. [ABSTRACT FROM AUTHOR]

• Importance measures for components with continuous time degradation are proposed. • The component reliability model is constructed by Wiener process. • The system reliability model is developed within Copula Hierarchical Bayesian Network considering the characteristics of dependency, uncertainty, nonlinearity and randomness. • Relationships among different importance measures are discussed. • A case study on the harmonic gear drive is conducted to demonstrate the use of proposed importance measures. In order to identify the vulnerable components and ensure the required reliability of mechatronics systems, importance measures of critical components are crucially used in the early design of systems. However, complex mechatronics systems have the properties of hierarchy, nonlinearity, dependency, uncertainty, and randomness, which make it difficult to analyze the coupling failure mechanisms, model the system, estimate its reliability, and complete importance measures of its components. This paper proposes importance measures for components with continuous time degradation. The Wiener process model is used to describe the continuous-time degradation process, and the Copula Hierarchical Bayesian Network (CHBN) is developed for system reliability estimation. Six importance measures are proposed for continuous-time degrading components. These importance measures provide a time-dependent analysis of the criticality of components, thus adding insights on the contributions of the components on the system reliability or performance over time. A case study on the harmonic gear drive is then conducted to demonstrate the use of the proposed importance measures. The results of the study show that the CHBN-based importance measures can be a valuable decision-support tool for designers in the early design of systems. [ABSTRACT FROM AUTHOR]

Random effects are ubiquitous in the degradation processes of multiple performance characteristics (PCs) of a complex system, and these PCs are not commonly independent. Neglecting either of the above features will lead to bias in system reliability estimation. Therefore, this study develops a reliability estimation method for the complex systems with multiple PC degradations considering both of the features. First, a Wiener process-based marginal degradation model with random effects (including the random initial PC, unit-to-unit variability, temporal uncertainty, and measurement errors) is proposed to track the degradation path of each PC. A model based on D-vine copulas is put forward to describe the correlation among multiple PCs. Then, a system reliability function is derived based on the two models. Furthermore, a two-step statistical inference is developed to estimate the unknown parameters in the system reliability function. Finally, using a practical case, the effectiveness of the proposed method is illustrated. • A reliability estimation method is proposed for complex systems. • A marginal Wiener process-based degradation model with random effects is proposed. • The correlation among multiple performance characteristics is modeled by D-vine copulas. • A two-step statistical inference is developed to perform the parameter estimation. [ABSTRACT FROM AUTHOR]

• A hybrid WKN-BiGRU and Wiener process model is proposed for reliability evaluation of rolling bearing. • A hybrid WKN-BiGRU model is utilized to deep feature extraction and health index construction. • The Wiener process has been introduced to model the health index for reliability evaluation. Reliability evaluation is highly significant for the safe and reliable service of rolling bearings. It is to accurately reflect degradation states of rolling bearings. However, traditional methods have difficulties in solving the problems resulted from the lack of measured data, while the deep learning techniques are insufficient in dealing with uncertainties. This paper proposes a new reliability evaluation schedule based on the WaveletKernelNet (WKN), bidirectional gated recurrent unit (BiGRU), and Wiener process model. The proposed method consists of two parts: a health index construction model by the WKN-BiGRU and a Wiener process-based reliability evaluation method. The WKN-BiGRU network is to extract deep features and construct the health index of the rolling bearings. The Wiener process is to achieve the reliability evaluation of rolling bearings and to quantify uncertainties. The effectiveness of the proposed methodology is confirmed by a real case study of rolling bearings. Overall, the proposed methodology contributes to effectively deep features extraction and reliability estimation of rolling bearings. [ABSTRACT FROM AUTHOR]

• A new PHM with environmental factors and degradation trend as covariates is built. • The complex integrand in reliability function is solved by the Taylor formula. • A real-time updated reliability prediction method is developed based on the PHM. • Numerical study and real case studies show the superiority of the proposed method. Degradation data and lifetime data have been broadly used for assessing product and system reliability. To utilize the two kinds of data simultaneously, the proportional hazard (PH) model with degradation data as a covariate is proposed for reliability analysis. However, most existing works focus on modeling the PH model with degradation state as a covariate, while the degradation trend is ignored, which makes the PH model unable to carry out reliability prediction directly. Confronted with that, a new PH model with the degradation trend and environmental factor as covariates is developed in this paper. The Wiener process is firstly applied to depict the degradation trend, then the degradation trend and temperature are used as covariates to establish the PH model, and a closed-form of the reliability is derived by the Taylor approximation. Based on the degradation data under actual ambient conditions, the real-time updated reliability prediction is provided to guide the health management of products and systems. The simulation study validates that the proposed model outperforms two existing models in terms of Mean Square Error (MSE). Finally, a real-world example of MOSFET is presented to demonstrate the implementation of the proposed method. [ABSTRACT FROM AUTHOR]

As an effective way to enhance the system reliability, the standby redundancy technique has been widely applied in many industrial systems. Finding methods to determine the maintenance policy and spare-part inventory management is an interesting practical issue. However, due to the imperfect storage and inner mechanism, the spare parts usually deteriorate over time, which not only degrades their performance but also may lead to storage failure. In addition, the immediate burst failure caused by the external shock should not be neglected in storage. These two aspects make the joint optimization of preventive maintenance and inventory policies for a standby system more challenging. Thus, in this study, we first propose a general iterative approach for the lifetime estimation of standby systems with a hybrid spare-part degradation process, which includes both stochastic degradation and immediate burst failure. We then take an example of the Wiener-process-based model to explain how to obtain the analytical results of the lifetime estimation. On this basis, we further establish a joint optimization model, in which the preventive block replacement interval and the inventory number are treated as two decision variables to minimize the expected cost per unit time. Finally, a numerical example and practical case are provided for illustration. • Both spare-part storage degradation and immediate burst storage failure are considered. • A general iterative approach for the lifetime estimation of the standby system is proposed. • A joint optimization model of the maintenance interval and the inventory number is established. [ABSTRACT FROM AUTHOR]