Search

• A new multi-state system model with state transition dependency is developed. • Copula functions are used to implicitly characterize state transition dependency. • Reliability measures for the new multi-state system model are given. • Likelihood functions for continuous and discontinuous inspection data are derived. As multi-state system reliability models are capable of characterizing the multi-state nature of engineered systems in deteriorating process, they have received considerable concerns in the past few decades. Most reported works on multi-state system reliability modeling are, however, based on the premise that transitions among states of a system/component are stochastically independent. Sometimes, a system may experience the same environmental/working conditions when deteriorating from a better state to worse ones, and thus, state transitions of a system/component could be stochastically dependent. In this paper, a new reliability model for multi-state systems/components with state transition dependency is put forth. The dependency among state transitions is implicitly characterized by copula functions which offer a great flexibility of linking arbitrary marginal distributions together to construct a multivariate distribution. The reliability function of a population of multi-state systems/components and the conditional reliability function of each individual multi-state system/component given a set of observations are derived. The likelihood functions for model parameter estimation are formulated for two cases, i.e., continuous and discontinuous inspection strategies, and model selection criteria are customized to identify the most preferable model among candidates. Two illustrative examples, together with comparative studies, are presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Operating high-speed trains imposes excessive vibrations to bridges raising concerns about their safety. In this context, it was shown that some conventional design methods such as those related to the running safety suffer from a vague scientific background questioning their reliability or optimality. Therefore, the current article is devoted to updating the conventional design methodology, using Reliability-Based Design Optimization (RBDO) to propose the minimum allowable mass and stiffness which assures satisfying the target reliability. These proposed minimum design values can conceptually replace the conventional partial safety factor-based design method for running safety without the need for dynamic analysis. If the mass and stiffness resulting from the control of other limit states meet the proposed minimum values, the desired target reliability for running safety will be assured. This is achieved by adaptively training Kriging meta-models as a surrogate for the computational models decoupling the RBDO problem. In this regard, a new stopping criteria is proposed using mis-classification ratio of the cross-validated model; which reduces the generalization error of the trained meta-model and consequently the estimated failure probability. Moreover, due to the dependence of the design variables, the Copula concept is used to refine the augmented space and reformulate the RBDO problem. • A novel and straightforward dynamic design method is proposed for railway bridges. • The Copula concept is adopted to reformulate RBDO problems with dependent variables. • A new stopping criterion is proposed for adaptive training of surrogate models. • An extensive data is collected for variables in dynamic behavior of railway bridges. • Proper PDFs are assigned for contributing random variables of railway bridges. [ABSTRACT FROM AUTHOR]

Consider a complex k -out-of- n system consisting of n independent elements each having some dependent components. This paper investigates the reliability of such complex systems based on degradation data systematically. A flexible class of multivariate stochastic processes is proposed to describe the dependence structure of the components by a copula function. Assuming the degradation of each component is modeled by a stochastic process, the reliability of a complex system is derived. A two-step Bayesian approach is used to estimate the unknown parameters of the model and it is implemented with the Hamiltonian Monte Carlo algorithm. Also, Bayesian bootstrap method is applied to estimate system reliability and its credible interval. Moreover, a Markov chain Monte Carlo simulation is conducted to validate our statistical approach. Finally, the applicability of the proposed modeling framework of system reliability is illustrated using two real examples. • The reliability of a new complex k -out-of- n : ℓ system is evaluated. • A multivariate degradation model is proposed to describe the dependence structure. • A two-step Bayesian approach is suggested to estimate the unknown parameters. • A MCMC simulation is conducted to study the performance of the proposed approach. • The results of the paper are illustrated using two real examples. [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]

• An effective reliability analysis method for kinematic trajectory accuracy of industrial robots is proposed. • A new copula function-based method is developed to quantify the intercorrelations among discrete points on the kinematic trajectory. • The effectiveness and robustness of the proposed method are verified by different trajectories of industrial robots. • The proposed method quantifies the intercorrelations within the system, which paves a new avenue for system reliability analysis. The kinematic trajectory accuracy reliability is an essential index to evaluate the service performance of industrial robots. This study proposes a new kinematic trajectory accuracy reliability analysis method for industrial robots by integrating the sparse grid technique, the saddlepoint approximation method and copula functions. The novelty of this study lies in comprehending the intercorrelations among single point three-coordinate directional positioning errors and multiple points positioning errors on the kinematic trajectory. To start with, the statistical moments of the positioning errors at an arbitrary point on the trajectory of industrial robots are calculated by the extended sparse grid (SPGR) technique. The single-point positioning accuracy reliability is then evaluated by the saddlepoint approximation (SPA) method. The joint failure probability of positioning accuracy between any two points and the matrix of correlation coefficients of positioning errors among multiple points are subsequently calculated by copula functions. Two methods, namely the boundary theory and the multivariate normal distribution theory, are employed in the current study to calculate the failure probability of kinematic trajectory accuracy. Three examples are implemented to demonstrate the proficiency of the currently proposed methods. [ABSTRACT FROM AUTHOR]

The reliability of complex systems consisting of n independent elements each having two dependent components is investigated based on degradation data. A copula-based model is used to describe the dependence structure of the components. Considering gamma, Wiener and inverse Gaussian processes for degradation of each component, the reliability of a complex system is derived for some various copula functions. Also, reliability bounds are obtained by assuming that the components are positively associated for special cases of series and parallel systems. When the model parameters are unknown, a two-step method is proposed to derive the maximum likelihood estimators. A simulation study is conducted to evaluate the performance of the estimators. Also, the sensitivity of the system reliability is analyzed using simulation. Finally, the results of the paper are illustrated using two real examples. • The reliability of multi-element systems is evaluated based on degradation data. • Some copulas are used to describe the dependence structure of the components. • A two-step method is proposed to estimate the unknown parameters. • The performance of the proposed estimators is discussed using simulation. • The results of the paper are illustrated using two real data sets. [ABSTRACT FROM AUTHOR]

• The failure correlation with time progressing is illustrated and quantified. • The time-variant reliability estimation method is presented based on the time-varying copula function and subset simulation. • The time-variant reliability prediction framework with partial information is proposed. • The time-variant reliability prediction method is provided. Efficient time-variant reliability prediction for dynamic systems is a challenging problem to reduce the risk because large amounts of information is needed for the prediction. In this paper, a physics-based reliability prediction method is presented with partial information. The cumulative probabilities of failure are first estimated for the given time intervals with complete information based on the subset simulation with splitting and time-variant copula function. An appropriate probability distribution is then selected for fitting the estimated cumulative probabilities of failure. The partial information, which can be collected from mathematical models or the physical experiments during the later time intervals, is used to effectively update the distribution parameters to improve the prediction accuracy. A case study of a vibratory system representing the quarter car model is employed to testify the proposed method. [ABSTRACT FROM AUTHOR]

• A flexible class of bivariate degradation process models are proposed. • The system reliability of a degrading system with dependent failures is analyzed. • The effects of environment stress variables are quantified. • A Hamiltonian Monte Carlo algorithm is applied to perform Bayesian inference. Consider a coherent system, in which the degradation processes of its performance characteristics are positively correlated, this paper systematically investigates a bivariate degradation model of such a system. To analyze the accelerated degradation data, a flexible class of bivariate stochastic processes are proposed to incorporate the effects of environmental stress variables and the dependency between two degradation processes is modeled by a copula function. A two-step system reliability analysis approach is developed and it is implemented with the Hamiltonian Monte Carlo algorithm. Simulation studies validate this approach and the consequences of model misspecification are evaluated too. Furthermore, two real-world examples are presented to demonstrate the applicability of the proposed modeling framework of system reliability on correlated degradation processes. [ABSTRACT FROM AUTHOR]