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In engineering practice, some weighted-k-out-of-n: G systems often show multiple performance levels, resulting in multi-failure-mode mechanism. For these complex degradation systems, a novel reliability model with heterogeneous components is proposed on account of the number of working components, the total weight, and the sojourn time in some a stage, where different weights and thresholds are taken into account in different stages, and so do failure modes. After presenting the indispensable definitions of first passage time and the system lifetime, the system reliability indexes are derived by the Copula method to depict the dependence between components. Furthermore, maximum likelihood estimation of the Copula parameters is adopted and a Copula-based expression for component importance in each type is obtained. Finally, the reliability of the overall supercharging subsystem of an advanced fighter air energy system, as an example of weighted-k-out-of-n: G system with multi-failure modes is analyzed by the suggested model, which offers the comparison of independent and dependent cases. Meanwhile, sensitivity analysis is available to point out the effects on the system. [ABSTRACT FROM AUTHOR]

The study introduced the transformed copula models and a D-vine structure for three variables. The numerical applications of the models are evaluated using two different sets of real-life data that exhibit nearly no dependence, highly dependent, over, and under dispersed characteristics. We examined only the volatilities of the first data using the exponentiated weighted moving average (EWMA). The parameter estimates of the models were obtained based on the maximum likelihood estimation method for the bivariate copula models and the Dissmann algorithm for sequential top-down estimation for the D-vine structure. The results showed that the introduced copula models outperformed some existing copula models in terms of their fit statistics for both real-life and simulated data sets. In addition, the Gaussian copula model gave a better fit to the D-vine structure than some existing copula models and could be recommended for modeling a D-vine structure comprising of variables that are positively weak correlated and highly correlated. [ABSTRACT FROM AUTHOR]

In this paper, a functionality unit named as meta-action unit (MAU) is proposed to correlate the system function with the part actions and assess reliability of mechanical system. Firstly, the function of system is decomposed into multiple MAUs by function-movement-action (FMA). Then, the lifetime of MAU is fitted by Weibull distribution, and its parameters are estimated by support vector regression (SVR). In addition, taking the distributions of MAU as marginal distributions, the lifetime distribution of mechanical system is constructed by copula function to assess system reliability, and its parameters are estimated using the maximum likelihood estimator (MLE). Further, the reliability assessment accuracy based on MAU is compared with that from traditional method based on mechanical part failure modes. Finally, the reliability assessment of the indexing turntable (IT) is performed as an example to illustrate the feasibility and reasonability of the proposed method. [ABSTRACT FROM AUTHOR]

In order to accurately calculate the reliability of mechanical components and systems with multiple correlated failure modes and to reduce the computational complexity of these calculations, the Copula function is used to represent related structures among failure modes. Based on a correlation analysis of the failure modes of parts of a system, a life distribution model of components is constructed using the Copula function. The type of Copula model was initially selected using a binary frequency histogram of the life empirical distribution between the two components. The unknown parameters in the Copula model were estimated using the maximum likelihood estimation method and the most suitable Copula model was determined by calculating the square Euclidean distance. The reliability of series, parallel, and series–parallel systems was analyzed based on the Copula function, where life was used as a variable to measure the correlation between components. Thus, a reliability model of a system with life correlations was established. Reliability calculation of a particular diesel crank and connecting rod mechanism was taken as a practical example to illustrate the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

In order to solve the problem of aero-engines' reliability evaluation of multi-degraded systems under competitive failure, a reliability evaluation method of related competitive failure between multi-degraded failure and sudden failure is proposed. The non-linear Wiener process and Gamma process with random effects are used to describe the degenerate failure process of the system, the appropriate Copula function is chosen to model the failure correlation of the multivariate degenerate system, and parameter of multivariate degradation-related failure model is estimated by Markov chain Monte Carlo method. The Weibull distribution is introduced to describe the sudden failure time, the proportional hazard model is used to construct the sudden failure rate function about the performance degradation, and the two-step maximum likelihood estimation method is used to identify the model parameters. Combined with the performance degradation data of aero-engines, the reliability evaluation of the multivariate degradation system under competitive failure is realized, and the validity and accuracy of the model are verified through the analysis results. [ABSTRACT FROM AUTHOR]

The reliability of concrete in complex environments is the basis for improving the reliability of concrete structures. A concrete reliability assessment based on multiple degradation factor is proposed. First, chloride penetration and fatigue damage are selected as two degradation parameters for concrete, and series tests are developed to investigate the surface chloride concentration, diffusion coefficient, and degradation of residual strength under coupled effect of chloride penetration and fatigue. Then, two marginal distribution functions of the durability reliability of the concrete are deduced based on two failure modes. Subsequently, fatigue loading the parameters of different typical copula functions are obtained by using the maximum likelihood method (MLM), and copula function selection is carried out according to the Akaike information criterion (AIC) criterion. The joint distribution function is then derived by fusing the two marginal distribution functions using the selected copula function, and a remaining durability reliability model is obtained. Finally, the proposed model is verified by experimental data. This method should be considered as a reference for the evaluation and reliability calculation of concrete structures. [ABSTRACT FROM AUTHOR]

In recent years, the use of copulas has grown rapidly, especially in survival analysis. In this paper, we introduce a bivariate modified Weibull distribu-tion derived from the Farlie{Gumbel{Morgenstern (FGM), a copula function commonly used to model very weak linear dependences. Considering the presence of non censored data and censored data, an extensive simulation study was developed to check the performance of the maximum likelihood method in estimating the parameters of the proposed model. Maximum like-lihood and Bayesian approaches for the estimation of the model parameters are presented. In the Bayesian analysis, the posterior distributions of the pa-rameters are estimated using Markov chain Monte Carlo (MCMC) method-ology. An example, considering a real data set, is introduced to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

This article considers statistical analysis of dependent competing risks model from Weibull distribution in accelerated life testing, in which copula function is used to examine the dependence structure between competing failure modes. We derive the maximum likelihood estimates, the approximate, and Bootstrap confidence intervals of the parameters. The effects of different dependence structures on the estimates of parameters are investigated. The simulation is given to compare the performance of the estimates when the competing failure modes are dependent with those when the failure modes are independent. Finally, one dataset was used for illustrative purpose in conclusion. [ABSTRACT FROM AUTHOR]

This study focuses on the simulation of automotive warranty data, using a two-dimensional (2D) parametric approach based on copulas. We start with the description of a real automotive warranty database and follow it through to the building of 2D parametric model for warranty prediction. The task of parameter fitting and measuring the quality of the fit is also addressed. The accuracy of the model proposed is compared with previously published non-parametric models. Finally, using this 2D parametric model, data are generated and compared with the original data. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A detailed account on environment and its related problems often requires a study on variables, some of which may be linear and others, circular in nature. Specialized techniques are required to analyze circular variables and also, the interrelationship between circular and linear variable. In this paper, estimation methods of joint density of a circular and linear variable have been compared with the aid of three real life examples. Therein, we have computed the maximum likelihood estimates of the l-modal circular normal distribution and used the Monte Carlo approximation method to approximate its distribution function. Finally, the theory of Copula function has been put to use for exploring the association between the two variables. The study reveals the superiority of one of the methods over the others, as exemplified by all the three data sets. [ABSTRACT FROM AUTHOR]

In this study, methods of copula estimation are used and the temperature measurement data of the four regions located at the same positions in the range of 01.01.2008 - 30.04.2009 was modeled with copula functions. For dependence structures of the data sets, it is calculated Kendall Tau and Spearman Rho values which are nonparametric. Based on this method, parameters of copula are obtained. A clear advantage of the copula-based model is that it allows for maximum-likelihood estimation using all available data. The main aim of the method is to find the parameters that make the likelihood functions get its maximum value. With the help of the maximum-likelihood estimation method, for copula families, it is obtained likelihood values. These values, Akaike information criteria (AIC) are used to determine which copula supplies the suitability for the data set. [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]

Copula theories have obtained rapid development with respect to the dependent analysis of financial markets. The widely adopted technique for estimating Copula is maximum likelihood. In distinction, this paper proposes weighted average quantile regression to estimate Copula, which shares robustness from quantile regression and achieves nearly the same efficiency as the maximum likelihood. Consistency and asymptotic normality of the suggested estimators are established under regularity conditions. Through solving a quadratic programming, we obtain the expression of optimal weights. Monte Carlo simulations are conducted to compare the performance of different estimators. The proposed approach is used to investigate the dependent structure and risk measurement of Chinese financial markets. [ABSTRACT FROM AUTHOR]

Evidence theory contains powerful features for uncertainty analysis and can be effectively employed to address the epistemic uncertainty, which is attributed to a lack of information in complex engineering problems. This paper presents an evidence theory model based on the copula function and the related structural reliability analysis method. It is an effective tool for uncertainty modeling and reliability analysis with dependent evidence variables. In the evidence theory model, a canonical maximum likelihood (CML) method was adopted to estimate the correlation parameter, and the Akaike information criterion (AIC) was utilized to select a reasonable Archimedean copula function and whereby construct the joint basic probability assignment (BPA) for the multidimensional evidence variables. Based on the joint BPA function, a procedure for reliability analysis was formulated to compute the reliability interval on the structure with evidence uncertainty. Four numerical examples were provided to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Modern highly reliable products usually have complex structure and many functions. This means that they may have two or more performance characteristics. All the performance characteristics can reflect the product's performance degradation over time, and they may be independent or dependent. If the performance characteristics are independent, they can be modelled separately. But if they are not independent, it is very important to find the joint distribution function of the performance characteristics for estimating the reliability of the product as accurately as possible. Here, we suppose that a product has two performance characteristics and the degradation paths of these two performance characteristics can be governed by a Wiener process with a time-scale transformation, and that the dependency of the performance characteristics can be described by a copula function. The parameters of the two performance characteristics and the copula function can be estimated jointly. The model in such a situation is very complicated and analytically intractable and becomes cumbersome from a computational viewpoint. For this reason, the Bayesian Markov chain Monte Carlo method is developed for this problem that allows the maximum-likelihood estimates of the parameters to be determined in an efficient manner. For an illustration of the proposed model, a numerical example about fatigue cracks is presented. [ABSTRACT FROM PUBLISHER]

Cross-sectional dependence is often encountered in study. The MLE estimators are inefficient when cross section independence is assumed. Therefore, Copula-based log-likelihood functions are introduced to consider the cross section dependence. To avoid the nuisance parameters problem, a method called two-step MLE is proposed. The consistency and the asymptotic normality of the estimator are proved. And the asymptotic covariance matrix is given as well. Monte Carlo experiments show that the two-step MLE improves the efficiency of the estimators significantly. This model is applied to study the characters that affect the cash dividend policies of the listed companies, and it is shown that the sale growth rate becomes more significant relatively. [ABSTRACT FROM AUTHOR]

Extreme weather conditions put heavy environmental loads on systems and may cause catastrophic failure. Classification societies such as Lloyd's Register, DNV GL and the American Bureau of Shipping recommend methods for environmental load calculations. These methods do not consider dependencies among parameters when calculating environmental loads. This paper proposes a novel methodology to consider the copula-based bivariate failure function to evaluate the dependence structure of parameters and minimize uncertainty in load calculations. It also presents a robust operational failure assessment model that considers real-time environmental parameters along with their dependencies. The proposed methodology and models are tested on a semi-submersible mobile unit (SMU). The failure probability corresponding to the wind and wave loads imposed on the SMU is calculated using a physical reliability model and Bayesian network. The copula-based bivariate failure function defines the dependence using the parameters δ , which are estimated using maximum likelihood estimation. A detailed case study illustrates the advantage of the proposed methodology. The proposed method is of vital significance to developing a safe operating envelope for offshore assets likely to face extreme weather conditions. • A novel methodology to estimate load using the copula-based bivariate failure function. • The methodology also evaluates the dependence structure and uncertainty in the load calculations. • A robust operational failure assessment model is also proposed. • This work will assist in developing a safe operating envelope for offshore assets in extreme weather conditionss. [ABSTRACT FROM AUTHOR]