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As an essential mechanical component, a rolling bearing can exhibit multiple failure modes that may occur independently or in correlation with one another. A reliability analysis method that meticulously accounts for the interdependencies among various bearing failure modes is presented in this paper. The examination of wear and fatigue failure mechanisms in rolling bearings is carried out using the Physics of Failure (PoF) approach. By considering the influence of uncertain variables, the limit state functions for individual failure modes are formulated through the application of stress‐strength interference theory. In the context of wear failure, the limit state function is derived using working clearance as the characteristic quantity. On the other hand, the limit state function for fatigue failure is constructed with a focus on fatigue damage accumulation. The Copula function is used to characterize the relationship between wear failure and fatigue failure, and a reliability calculation model for rolling bearings is developed, considering the correlation between these failure modes. Ultimately, the proposed method is utilized to assess the reliability of bearings under two different sets of test conditions. The feasibility of this method is confirmed through test data, demonstrating its effectiveness in predicting bearing reliability. Through the application of this method, engineers can optimize bearing size parameters, select appropriate initial clearances, and enhance the reliability design of bearing. [ABSTRACT FROM AUTHOR]

A hurricane event can often produce both intense rainfall and a storm tide that can cause a major compound flooding threat to coastlines. This paper examined applications of multivariate copula‐based time series models using data observed during Hurricane Irma (2017) along the coastlines of Florida, Georgia, and South Carolina, United States. Multivariate time series models were developed using bivariate copulas wherein storm tide and rainfall data were modeled using LOWESS‐based autoregressive moving average (ARMA). n samples of observed data were then synthesized using a Monte Carlo approach in which the empirical copula and the parametric estimate of the copula were obtained to approximate two‐sided p‐values using the Rosenblatt probability integral transform method. Analysis suggested that proper selection of the underlying LOWESS‐based ARMA model was the crucial aspect for modeling compound flooding wherein Archimedean, Elliptical, and Extreme Value copulas all offered consistent flexibility in terms of dependence modeling. As a backdrop to compound flood probabilities, this research also outlined both theoretical and applied frameworks for the calculation of non‐exceedance probabilities in a multidimensional environment using classical isofrequency probability assumptions for the "AND" (a bivariate joint probability) and Survival Kendall definitions. Random realizations from storm copulas combined with multivariate non‐exceedance probability definitions ultimately showed there were periods of temporal yet cyclical high intensities that lasted 1–2 hr. Lastly, a discussion is presented on the broader application of the proposed methodology within the field of engineering design and risk management which may serve as a catalyst for the continued research in compound flooding. Plain Language Summary: When a storm tide and intense rainfall simultaneously co‐occur in coastal areas, the potential for flooding is often much greater than from either independent event. Understanding how to assess the probability of these compound events is important in planning for and managing flood risks in coastal communities. This study investigated the temporal dynamics of these two phenomena during a landfalling hurricane across the southeast United States using a multivariate copula‐based time series model. The analysis revealed that storm tide dynamics were more accurately captured in the proposed model when compared to rainfall observations, although temporal rainfall was reasonably described by the model. This study highlights the temporal multivariate probabilistic approach needed to cope with compound flood risk assessment. All outcomes outlined herein are based on the theory of multivariate copula‐based dependence models with three application sites that illustrated the proposed methods. Key Points: The likelihood of joint occurrence of storm tide and intense rainfall is calculated using bivariate copulasMultivariate non‐exceedance probability of rainfall and storm tide was higher using the Survival Kendall (SK) definition when compared to the "AND" definitionCopulas analysis combined with multivariate non‐exceedance probability showed there were periods of temporal yet cyclical high intensities [ABSTRACT FROM AUTHOR]

Managing failure dependence of complex systems with hybrid uncertainty is one of the hot problems in reliability assessment. Epistemic uncertainty is attributed to complex working environment, system structure, human factors, imperfect knowledge, etc. Probability‐box has powerful characteristics for uncertainty analysis and can be effectively adopted to represent epistemic uncertainty. However, arithmetic rules on probability‐box structures are mostly used among structures representing independent random variables. In most practical engineering applications, failure dependence is always introduced in system reliability analysis. Therefore, this paper proposes a developed Bayesian network combining copula method with probability‐box for system reliability assessment. There are four main steps involved in the reliability computation process: marginal distribution identification and estimation, copula function selection and parameter estimation, reliability analysis of components with correlations and Bayesian forward analysis. The benefits derived from the proposed approach are used to overcome the computational limitations of n‐dimensional integral operation, and the advantages of useful properties of copula function in reliability analysis of systems with correlations are adopted. To demonstrate the effectiveness of the developed Bayesian network, the proposed method is applied to a real large piston compressor. [ABSTRACT FROM AUTHOR]

As a relevant topic in reliability theory, the preservation of aging properties under the formation of various coherent structures contributes to improving system performance through better structure design and more effective system maintenance. The classical research in this line usually focuses upon coherent systems with independent component lifetimes. Recently, some authors discussed the preservation of IFR, NBU, and DMRL in the setting of dependent component lifetimes. This paper further investigates sufficient conditions for coherent systems with dependent component lifetimes to preserve aging properties including NBUC, NBU (2), DMRL, and their dual versions. Some examples are presented to illustrate coherent structures and typical copula functions fulfilling the present sufficient conditions as well. [ABSTRACT FROM AUTHOR]

In this paper, we consider non-parametric copula inference under bivariate censoring. Based on an estimator of the joint cumulative distribution function, we define a discrete and two smooth estimators of the copula. The construction that we propose is valid for a large range of estimators of the distribution function and therefore for a large range of bivariate censoring frameworks. Under some conditions on the tails of the distributions, the weak convergence of the corresponding copula processes is obtained in l∞([0,1]2). We derive the uniform convergence rates of the copula density estimators deduced from our smooth copula estimators. Investigation of the practical behaviour of these estimators is performed through a simulation study and two real data applications, corresponding to different censoring settings. We use our non-parametric estimators to define a goodness-of-fit procedure for parametric copula models. A new bootstrap scheme is proposed to compute the critical values. [ABSTRACT FROM AUTHOR]

Most modern products that are highly reliable are complex in their inner and outer structures. This situation indicates quality characterization by the interaction of multiple performance characteristics, which motivates the utilization of robust reliability models to obtain robust estimates. It is paramount to obtaining substantial information about a product's life cycle; therefore, when multiple performance characteristics are dependent, it is important to find models that address the joint distribution of performance degradation of such. In this paper, a reliability model for products with 2 fatigue‐crack growth characteristics related to 2 degradation processes is developed. The proposed model considers the dependence among degradation processes by using copula functions considering the marginal degradation processes as inverse Gaussian processes. The statistical inference is performed by using a Bayesian approach to estimate the parameters of the joint bivariate model. A time‐scale transformation is considered to assure monotone paths of the degradation trajectories. The comparison results of the reliability analysis, under both dependent and independent assumptions, are reported with the implementation of the proposed modeling in a case study, which consists of the crack propagation data of 2 terminals of an electronic device. [ABSTRACT FROM AUTHOR]

Under a climate change, the physical factors that influence the rainfall regime are diverse and difficult to predict. The selection of skilful inputs for rainfall forecasting models is, therefore, more challenging. This paper combines wavelet transform and Frank copula function in a mutual information‐based input variable selection (IVS) for non‐linear rainfall forecasting models. The marginal probability density functions (PDFs) of a set of potential rainfall predictors and the rainfall series (predictand) were computed using a wavelet density estimator. The Frank copula function was applied to compute the joint PDF of the predictors and the predictand from their marginal PDFs. The relationship between the rainfall series and the potential predictors was assessed based on the mutual information computed from their marginal and joint PDFs. Finally, the minimum redundancy maximum relevance was used as an IVS stopping criterion to determine the number of skilful input variables. The proposed approach was applied to four stations of the Nigerien Sahel with rainfall series spanning the period 1950–2016 by considering 24 climate indices as potential predictors. Adaptive neuro‐fuzzy inference system, artificial neural networks, and random forest‐based forecast models were used to assess the skill of the proposed IVS method. The three forecasting models yielded satisfactory results, exhibiting a coefficient of determination between 0.52 and 0.69 and a mean absolute percentage error varying from 13.6% to 21%. The adaptive neuro‐fuzzy inference system performed better than the other models at all the stations. A comparison made with KDE‐based mutual information showed the advantage of the proposed wavelet–copula approach. [ABSTRACT FROM AUTHOR]

This paper presents an intensity-based model of correlated defaults with application to the valuation of defaultable securities. The model assumes that the intensities of the default times are driven by common factors as well as other defaults in the system. A recursive procedure called the “total hazard construction” is used to generate default times with a broad class of correlation structures. This approach is compared to standard reduced-form models based on conditional independence as well as alternative approaches involving copula functions. Examples are given for the pricing of defaultable bonds and credit default swaps of the regular and basket type. [ABSTRACT FROM AUTHOR]

Copula models are becoming increasingly popular for modelling dependencies between random variables. The range of their recent applications includes such fields as analysis of extremes in financial assets and returns; failure of paired organs in health science; reliability studies; and human mortality in insurance. This paper gives a brief overview of the principles of construction of such copula models as Gaussian, Student, and Archimedean. The latter includes Frank, Clayton, and stable (Gumbel–Hougaard) families. The emphasis is on application of copula models to joint last survivor analysis. The main example discussed in this paper deals with the mortality of spouses, known to be associated through such factors as common disaster, common lifestyle, or the broken-heart syndrome. These factors suggest modelling dependence of spouses' lives on both calendar date scale and age-at-death scale. This dependence structure suggests a different treatment than that for problems of survival analysis such as paired organ failure or twins' mortality. Construction of a conditional Bayesian copula model is further generalized in view of the relationship between the joint first life and last surviror probabilities. A numerical example is considered, involving the implementation of Markov chain Monte Carlo algorithms using WinBUGs. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Copyright of Irrigation & Drainage is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Although in the statistical process control (SPC) literature, there are considerable number of researches related to the multivariates variables control charting (focusing on the variable quality characteristics), fewer investigations could be found regarding the multivariate attributes control charts (relying on the attribute quality characteristics). More specifically considering the multivariate attributes control charting, it would be more interesting to monitor the auto-correlated data, since the real-world processes usually include the data based on an auto-correlation structure. Ignoring the auto-correlation structure in developing a multivariate control chart increases the type I and type II errors simultaneously and consequently reduces the performance of the chart. The most important difficulty with developing multivariate attributes control charts is the absence of the joint distribution for the quality characteristics. This deficiency can be dispelled through the use of the copula approach for developing the joint distribution. In this paper, we use the Markov approach for modeling the auto-correlated data. Then, the copula approach is used to make the joint distribution of two auto-correlated binary data series. Finally, based on this joint distribution, we develop a cumulative sum (CUSUM) chart. Hence, the proposed chart is entitled the copula Markov CUSUM chart. The proposed control chart is compared with the most recent and effective existing one in the literature. Based on the average number of observations to signal (ANOS) measure, it is considered that the developed control chart performs better than the other one. In addition, a real case study related to two correlated diseases such as the Type 2 Diabetes Mellitus and the Obesity, in which each has an auto-correlated structure, is investigated to verify the applicability of the control chart. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Copyright of Canadian Journal of Statistics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Light-emitting diode (LED) lamp has received great attention as a potential replacement for the more commercially available lighting technology, such as incandescence and fluorescence lamps. LED which is the main component of LED lamp has a very long lifetime. This means that no or very few failures are expected during LED lamp testing. Therefore, degradation testing and modelling are needed. Because the complexity of modern lighting system is increasing, it is possible that more than one degradation failures dominate the system reliability. If degradation paths of the system's performance characteristics (PCs) tend to be comonotone there is a likely dependence between the PCs because of the system's common usage history. In this paper, a bivariate constant stress degradation data model is proposed. The model accommodates assumptions of dependency between PCs and allows the use of different marginal degradation distribution functions. Consequently, a better system reliability estimation can be expected from this model than from a model with independent PCs assumption. The proposed model is applied to an actual LED lamps experiment data. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This article provides an innovative method for measuring the dependence between pairs of poverty dimensions using a semiparametric copula approach that permits us to account for the importance of extreme low values. The association between pairs of poverty dimensions at the lower tail is easily measured using the parameter estimates of the specified parametric copula, and no further calculations are needed. This approach is used to measure the bivariate lower tail dependence between the dimensions of the AROPE rate in Europe at two time points (2009 and 2018). The findings reveal a statistically significant increase in the lower tail dependence between 2009 and 2018 in several European countries. [ABSTRACT FROM AUTHOR]

Modelling stock prices has been a research topic for many decades and it is still an open question. Different approaches have been used in the literature, the majority of which can be classified within the so‐called econometric framework and sometimes also referred to as the macro‐to‐micro approach. Another strand of literature relies on the modelling of directly observable quantities, the so‐called micro‐to‐macro approach. Based on this second line of research, we propose a new multivariate stochastic process to model simultaneously price returns, trading volumes and the time interval between changes in trades, price and volume. The proposed model is based on a generalization of semi‐Markov chain models and copulas and is motivated by empirical evidence that the three mentioned variables are correlated and long‐range autocorrelated. Utilizing Monte Carlo simulations, we compared our model with real data from the Italian stock market and show that it can reproduce many empirical pieces of evidence. The proposed model can be used in the field of portfolio optimization, development of risk measure and volatility forecasting. [ABSTRACT FROM AUTHOR]

Frequent drought events under climate change are endangering food security and sustainable agricultural development. Quantitative assessment of crop yield anomalies under drought conditions is essential for effective water resources management and adaptative drought risk mitigation strategies. In this study, a copula‐based bivariate probabilistic framework model is developed to assess the impacts of drought events on crop yield, where the correlation of crop yield anomalies and standardized precipitation evapotranspiration index (SPEI) at multi‐month lags are quantified. This model has advantages in quantifying the impacts of drought scales on crop yield through the joint probability of the corresponding series. Then, the model is applied to Xinjiang Province in Northwestern China, an arid region with extensive agricultural activities. SPEI and yield anomalies of wheat, maize and cotton during 1984–2015 are firstly identified, and then copula‐based framework is constructed to quantify probabilistic crop yield losses caused by drought events. Finally, crop water amounts and irrigation requirements under different drought severity conditions are compared and analysed. Our findings are: (a) wheat and maize yield anomalies are vulnerable to long drought time‐scales, with exceedance probabilities of required yield anomalies returning to normal are 19.3% for wheat and 21.1% for maize, while cotton is susceptible to short drought time‐scales, with exceedance probability of 42.3% for drought recovery; (b) response of wheat crop yield anomalies to the SPEI at 1‐, 3‐, 6‐ and 12‐month scales is the most sensitive, followed by maize, and cotton is the least; (c) under extreme drought conditions, the probability of cotton yield reduction is lower than that of wheat and maize. Results may enhance our understanding of the impacts of drought scales on crops during the growing season, thus providing general guidance for rational irrigation management of crops and incentives for irrigation to mitigate drought risk, ultimately promoting sustainable agricultural development. [ABSTRACT FROM AUTHOR]

In this work, a novel learning‐based approach for the design of a compressed sensing measurement matrix is proposed. In contrast with the state‐of‐the‐art methods, the suggested approach takes into account the correlation within entries of each column of the measurement matrix, namely, the inter‐column correlation (ICC). The new method makes use of a rather small number of training sparse signal vectors in a recursive scheme to obtain their corresponding measurement vectors. The latter is exploited to estimate the copula function of measurements which, in turn, is used to generate an arbitrary number of measurement vector ensembles. By using the latter, the autocorrelation of the measurement vectors is estimated precisely and then, the ICC of measurement matrix under design is obtained from the autocorrelation. Given the resulting ICC, the measurement matrix columns are to be generated independently, e.g. by employing a proper random Gaussian vector generator. Performance evaluations using both synthetic and real‐world data confirm the superiority of the proposed approach to the less recent methods. [ABSTRACT FROM AUTHOR]

In this study, an improved prediction model is introduced to assess the residual strength of gear transmission systems. The residual strength and stress‐strength interference theories are then combined to facilitate the study of the reliability of the gears and bearings in these systems. Based on the copula function, the correlation between the gear contact and bending failure is determined. The relationship between the copula function and reliability is used to determine the dynamic reliability of the gears while considering multiple correlated failure modes. In this manner, more accurate and dynamic reliability attenuation characteristics are obtained for the gear transmission system. [ABSTRACT FROM AUTHOR]

ABSTRACT: Instream flooding in coastal areas becomes more severe when heavy precipitation and high tide occur simultaneously. Flood modelling under such conditions requires the joint design of precipitation and tide. Data of 24‐h heavy precipitation and the corresponding daily high tidal level in the Xixiang basin, south China were used. Annual maxima and peaks over threshold sampling methods were applied to construct the precipitation and tidal level series. The joint distribution of precipitation and tide was derived by Archimedean copulas and their joint return period was calculated by the Kendall measure function. Then, equalized frequency and most likely weight function methods were employed for the joint design of precipitation and tide. Results showed that for the peaks over threshold sampling heavy precipitation coincided with more and greater high tidal levels. The general normal distribution was found to fit the marginals of precipitation and tide well, but the location, scale and shape parameters of two sampling methods differed markedly for heavy precipitation and slightly for high tidal level. Although the dependence of heavy precipitation and high tidal level was quite small and positive, Archimedean copulas effectively modelled the joint distribution of precipitation and tide. Based on the equalized frequency method, the joint design precipitation and tide using Gumbel–Hougaard copula for the peaks over threshold sampling was safer than that for the annual maxima sampling. However, for the most likely weight method design pairs remarkably tended to the lower heavy precipitation and the higher high tidal level. If the sampling method and the joint distribution were determined, a reciprocal situation for the design pairs of precipitation and tide occurred for a given joint return period, that is, a greater design value of heavy precipitation corresponded to a smaller design value of high tidal level, and vice versa. Therefore, which design method was safer was underdetermined. [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]

Frequency analysis of streamflow provides an essential ingredient in our understanding of hydrologic events and provides needed guidance in the design and management of water resources infrastructure. However, traditional hydrologic approaches often fail to include important external effects that can result in unpredictable or unforeseen changes in streamflow. Moreover, previous studies investigating multiple characteristics of streamflow do not address a nonstationary approach. This study explores nonstationary frequency analysis of bivariate characteristics, including occurrence and severity, of annual low flow in the Connecticut River Basin, United States. To investigate bivariate low flow frequency, copulas and their marginal distributions are constructed by using stationary and nonstationary approaches. Our study results indicate that streamflow used in this study demonstrate significant nonstationarity. Over time, the occurrence and severity of low flows are shown to be lower with the same probability based on the results of nonstationary copulas. Bivariate low flow frequencies in the years 1970, 2000, and 2030, and their joint return periods are estimated under the nonstationary copulas. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Climate variability modulates spatio-temporal variability of dry spells (DSs) and wet spells (WSs) within a river basin and will affect water resources management practices leading to various impacts on the socio-economic development in river basins. In this study, we evaluated spatio-temporal variability of DS and WS in Huai River basin (HRB), China, by developing copula-based severity-duration-frequency (SDF) curves. The result shows that the upper reach and the southern part of middle reach of HRB are prone to both DS and WS; however, the duration and severity of WS are comparatively higher in comparison to DS. It was observed that DS is more frequent in spring and summer, whereas WS in summer and autumn. The choice of copula plays an important role in deriving the SDF curves, and an inappropriately chosen copula function may result in a large bias of SDF estimation. The arch12 copula was found to be the best choice in the majority of stations for deriving the SDF curves. The constructed SDF curves primarily shows two major patterns for DS and WS, i.e. concave down pattern and convex up pattern. The frequency of extreme DS decreases from 1960s to 1990s, and increases after 2000s, while the frequency of extreme WS increases from 1970s to 1990s and then decreases from 1990s to 2000s. The results in this study can provide useful information for designing conservation structures and to develop water allocation strategies at different temporal scales. [ABSTRACT FROM AUTHOR]

Copyright of Irrigation & Drainage is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)