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This article proposes a space‐efficient approximation to empirical tail dependence coefficients of an indefinite bivariate stream of data. The approximation, which has stream‐length invariant error bounds, utilizes recent work on the development of a summary for bivariate empirical copula functions. The work in this paper accurately approximates a bivariate empirical copula in the tails of each marginal distribution, therefore modeling the tail dependence between the two variables observed in the data stream. Copulas evaluated at these marginal tails can be used to estimate the tail dependence coefficients. Modifications to the space‐efficient bivariate copula approximation, presented in this paper, allow the error of approximations to the tail dependence coefficients to remain stream‐length invariant. Theoretical and numerical evidence of this, including a case‐study using the Los Alamos National Laboratory netflow data‐set, is provided within this article. [ABSTRACT FROM AUTHOR]

Administrative strategies to cope with drought are steadily changing, from emergency procedures to day-to-day monitoring. More consideration must be paid to long-term and preventive drought control measures in the future. This paper discusses the risk of hydrological drought in the Yellow River Basin. The standardized runoff index (SRI) was used to characterize hydrological drought, and the run theory was used to identify drought states and quantify drought characteristic variables. Based on the drought severity and duration, a drought development plan was proposed and a three-dimensional copula function was constructed to obtain the joint distribution function of three-dimensional drought characteristic variables. A drought risk assessment system based on the loss × probability risk theory was constructed to explore the spatial and temporal characteristics of hydrological drought risk in the Yellow River Basin. Finally, according to the risk assessment results, the risk level was divided into low, medium and high risk, and a Bayesian network was used to explore the probability of hydrological drought. The main results are as follows: (1) From 1960 to 2018, the severity of hydrological drought in the Yellow River Basin increased, the duration lengthened, and the development speed accelerated. (2) The hydrological drought risk in the Yellow River Basin showed an overall upward trend, with the fastest increase in the HJ region of 0.041/10a. The highest annual average drought risk in the TDG region is 0.598. (3) The spatial transmission of hydrological drought risk is divided into three types: constant, enhanced and mitigation types, of which the constant type is the most common. The transmission probabilities of low, medium and high risk of hydrological drought from the HYK region to the low, medium and high risk of hydrological drought in the LJ region are 0.68, 0.66 and 0.78, respectively. [ABSTRACT FROM AUTHOR]

The subsea control system, a pivotal element of the subsea production system, plays an essential role in collecting production data and real-time operational monitoring, crucial for the consistent and stable output of offshore oil and gas fields. The increasing demand for secure offshore oil and gas extraction underscores the necessity for advanced reliability modeling and effective maintenance strategies for subsea control systems. Given the enhanced reliability of subsea equipment due to technological advancements, resulting in scarce failure data, traditional reliability modeling methods reliant on historical failure data are becoming inadequate. This paper proposes an innovative reliability modeling technique for subsea control systems that integrates a Wiener degradation model affected by random shocks and utilizes the Copula function to compute the joint reliability of components and their backups. This approach considers the unique challenges of the subsea environment and the complex interplay between components under variable loads, improving model accuracy. This study also examines the effects of imperfect maintenance on degradation paths and introduces a holistic lifecycle cost model for preventive maintenance (PM), optimized against reliability and economic considerations. Numerical simulations on a Subsea Control Module demonstrate the effectiveness of the developed models. [ABSTRACT FROM AUTHOR]

The paper analyzes the correlation features between stress strength, multiple failure mechanisms, and multiple components. It investigates the effects of different correlation features on reliability and proposes a method for structural reliability analysis that considers the joint effects of multiple correlation features. To portray the stress–strength correlation structure, the Copula function is utilized and the influence of the correlation degree parameter on reliability is clarified. The text describes the introduction of time-varying characteristics of structural strength and correlation parameters. A time-varying Copula is then constructed to calculate the structural reliability under the stress–strength correlation characteristics. Additionally, a time-varying hybrid Copula is constructed to characterize the intricate and correlation features of multiple failure mechanisms and components. The article proposes the variational adaptive sparrow search algorithm (VASSA) to obtain optimal parameters for the time-varying hybrid Copula. The effectiveness and accuracy of the proposed method are verified through actual cases. The results indicate that multiple correlation features significantly influence structural reliability. Incorporating multiple correlation features into the solution of structural reliability yields safer results that align with engineering practice. [ABSTRACT FROM AUTHOR]

This research aims to investigate the asset allocation performance of three different optimization methods commonly applied in the literature for a portfolio composed of univariate returns generated from Mixed and Elliptic copulas instead of historical data. As a result, returns of five equities traded at the BIST30 index of the Turkish Stock Market were obtained. Dynamics of the univariate return series are modelled with GARCH processes with Student-t distributed innovations. Following the marginal modelling, a five-dimensional dependence structure between the series is modelled with Elliptical and Mixed copulas. From the fitted Mixed and Elliptical copula functions, daily returns of the equities are simulated which are employed by the specified optimization methods in order to find out methodology specific optimal portfolio allocations. Performance of the constructed optimal portfolios are compared according to varying risk and reward to variability ratios yielding results especially in favor of the Mixed and Student t copulas. The main contribution of this research is to be able to fill the gap in the literature on the out-of-sample portfolio allocation performance of copula functions where there are still fewer papers compared to the dependency modelling or the in-sample portfolio allocation performance of copulas. [ABSTRACT FROM AUTHOR]

Traditional univariate drought indices may not be sufficient to reflect comprehensive information on drought. Therefore, this paper proposes a new composite drought index that can comprehensively characterize meteorological and hydrological drought. In this study, the new drought index was established by combining the standardized precipitation index (SPI) and the standardized baseflow index (SBI) for the Jiaojiang River Basin (JRB) using the copula function. The prediction model was established by training random forests on past data, and the driving force behind the combined drought index was explored through the LIME algorithm. The results show that the established composite drought index combines the advantages of SPI and SBI in drought forecasting. The monthly and annual droughts in the JRB showed an increasing trend from 1991 to 2020, but the temporal characteristics of the changes in each subregion were different. The accuracies of the trained random forest model for heavy drought in Baizhiao (BZA) and Shaduan (SD) stations were 83% and 88%, respectively. Furthermore, the Local Interpretable Model-Agnostic Explanations (LIME) interpretation identified the essential precipitation, baseflow, and evapotranspiration features that affect drought. This study provides reliable and valid multivariate indicators for drought monitoring and can be applied to drought prediction in other regions. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient method for quantifying the stratigraphic uncertainties and modeling the geological formations based on boreholes. Two Markov chains are used to describe the soil transitions along different directions, and the transition probability matrices (TPMs) of the Markov chains are analytically expressed by copulas. This copula expression is efficient since it can represent a large TPM by a few unknown parameters. Due to the analytical expression of the TPMs, the likelihood function of the Markov chain model is given in an explicit form. The estimation of the TPMs is then re-casted as a multi-objective constrained optimization problem that aims to maximize the likelihoods of two independent Markov chains subject to a set of parameter constraints. Unlike the method which determines the TPMs by counting the number of transitions between soil types, the proposed method is more statistically sound. Moreover, a random path sampling method is presented to avoid the directional effect problem in simulations. The soil type at a location is inferred from its nearest known neighbors along the cardinal directions. A general form of the conditional probability, based on Pickard's theorem and Bayes rule, is presented for the soil type generation. The proposed stratigraphic characterization and simulation method is applied to real borehole data collected from a construction site in Wuhan, China. It is illustrated that the proposed method is accurate in prediction and does not show an inclination during simulation. [ABSTRACT FROM AUTHOR]

We develop a framework for creating distortion functions that are used to construct new bivariate copulas. It is achieved by transforming non-negative random variables with Lomax-related distributions. In this paper, we apply the distortions to the base copulas of independence, Clayton, Frank, and Gumbel copulas. The properties of the tail dependence coefficient, tail order, and concordance ordering are explored for the new families of distorted copulas. We conducted an empirical study using the daily net returns of Amazon and Google stocks from January 2014 to December 2023. We compared the popular Clayton, Gumbel, Frank, and Gaussian copula models to their corresponding distorted copula models induced by the unit-Lomax and unit-inverse Pareto distortions. The new families of distortion copulas are equipped with additional parameters inherent in the distortion function, providing more flexibility, and are demonstrated to perform better than the base copulas. After analyzing the data, we have found that the joint extremes of Amazon and Google stocks are more likely for high daily net returns than for low daily net returns. [ABSTRACT FROM AUTHOR]

To qualify the risk of extreme weather events for power supply security during the long-term power system transformation process, this paper proposes a risk probability evaluation method based on probabilistic production simulation. Firstly, the internal relationship of extreme weather intensity and duration is depicted using the copula function, and the influences of extreme weather on power security are described using the guaranteed power output ability coefficient, which can provide the extreme scenario basis for probabilistic production simulation. Then, a probabilistic production simulation method is proposed, which includes a typical-year scenario and extreme weather events. Meanwhile, an index system is proposed to qualify the power security level, which applies the loss of load expectation (LOLE) and time of loss of load expectation (TOLE) under different scenarios and other indices to reveal the long-term power security trend. Finally, the long-term power supply risks for the Yunnan provincial power system are analyzed using the proposed method, validating that the proposed method is capable of characterizing the influences of extreme weather on power security. The security level of different long-term power transformation schemes is evaluated. [ABSTRACT FROM AUTHOR]

Increasing the application of renewable energy in the power system is an effective way to achieve the goal of 'Dual Carbon'. At the same time, the high proportion of renewable energy connected to the grid endangers the safe operation of the power system. To solve this problem, this paper proposes the application of a copula function to describe the correlation between wind power and photovoltaic power, and reduce the uncertainty of power-system operation with a high proportion of renewable energy. In order to increase the robustness of the model, this paper proposes the application of the conditional value-at-risk theory to construct the objective function of the model and effectively control the tail risk of power-system operation costs. Through case analysis, it is found that the model proposed in this paper has strong practicality and economy. [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]

The Copula concept has long been used in many applications, especially in the financial field. This concept was first used in 1959 by Sklar in his mathematical work and greatly assisted in the applications of financial and insurance areas. The copula functions have been widely used in dependence modeling. In this study, we look at how the copula began to develop from a basic form to a more advanced form through studies that previous researchers have made. Throughout this study, we find various types of the copula, and each exhibits its own characteristics lying under two main families, Elliptical and Archimedean copulas. Our findings suggest that copula is vital in solving problems in statistical dependence measures and joint marginal distribution functions. This comprehensive study served as a review paper on the development of copulas from their initial existence to their latest evolution. [ABSTRACT FROM AUTHOR]

Traditional methods for diagnosing dam health often rely on single point measurements, which require assumptions about the distributions of these measurements. These approaches fail to integrate multiple measured values for joint diagnosis and overlook the true distribution of the measured values, leading to potential misdiagnosis. This paper proposes a dam health diagnosis method based on kernel density estimation (KDE) and copula functions to address these limitations. The method incorporates a measurement analysis flow that extends from a single point to multiple points and establishes criteria for dam health diagnosis. In addition, this paper proposes to select the optimal copula function based on the Akaike information criterion (AIC). An engineering example is presented to demonstrate the proposed method's effectiveness in diagnosing a dam's health without assuming a specific measurement distribution function. This research contributes to the field of engineering safety management by enabling comprehensive dam health diagnosis from local dam states to the entire dam structure. [ABSTRACT FROM AUTHOR]

Failure correlation is a physical phenomenon observed, for example, in CNC (computer numerical control) lathe applications. Reliability importance measure considering failure correlation is an effective measure to identify the importance of CNC lathe. This paper fully considers the failure correlation among the subsystems of the CNC lathe. Based on the Copula function, the joint reliability model of each subsystem of the CNC lathe is established. Three methods (D‐test, the average cumulative error, and the root mean square error) are used to compare the joint reliability models under different Copula functions. Then ascertained the Clayton Copula model can describe the failure correlation reliability of CNC lathe most accurately. The reliability dynamic importance measure can judge the difference in CNC lathe subsystem importance measure more accurately. In this paper, the reliability dynamic core importance measure is proposed to analyze the potential of the CNC lathe subsystems for improvement. It can determine that the servo subsystem is the crucial part of the CNC lathe for priority improvement. [ABSTRACT FROM AUTHOR]

Long-span bridges in mountainous areas are greatly disturbed by wind, and the wind field at the mountain gorge bridge site is extremely complex. Therefore, it is of great engineering significance to accurately evaluate the wind field characteristics of this kind of terrain. In this paper, to enhance understanding of this kind of wind field, the wind field in a mountainous gorge is measured for a long time using wind radar, and the mean wind parameters are statistically analyzed. The results show that the mean wind parameters vary greatly under different wind directions, and the wind speed profile does not meet the power-law model. Therefore, a mixed model suitable for the wind speed profile in a mountainous gorge is proposed. Additionally, GEV distribution and Logistic distribution are found to be suitable for describing the distribution characteristics of wind speed and angle of attack, respectively. In addition, considering the correlation between wind parameters, this paper also constructs the joint probability model of wind speed and angle of attack at different heights by the Copula function. Thus, a combined wind parameters profile model is developed under different exceedance probabilities based on the inverse first-order reliability method (IFORM). This study can provide a reference for the construction of the joint probability model of wind parameters. [ABSTRACT FROM AUTHOR]

Demand-side flexible load resources, such as Electric Vehicles (EVs) and Air Conditioners (ACs), offer significant potential for enhancing flexibility in the power system, thereby promoting the full integration of renewable energy. To this end, this paper proposes an optimal allocation method for demand-side flexible resources to enhance renewable energy consumption. Firstly, the adjustable flexibility of these resources is modeled based on the generalized energy storage model. Secondly, we generate random scenarios for wind, solar, and load, considering variable correlations based on non-parametric probability predictions of random variables combined with Copula function sampling. Next, we establish the optimal allocation model for demand-side flexible resources, considering the simulated operation of these random scenarios. Finally, we optimize the demand-side resource transformation plan year by year based on the growth trend forecast results of renewable energy installed capacity in Jiangsu Province from 2025 to 2031. [ABSTRACT FROM AUTHOR]

After a transmission line is covered by ice in winter, ice-shedding and vibration occurs under special meteorological and external dynamic conditions, which leads to intense transmission line shaking. Transmission line ice-shedding and vibration often cause line flashover trips and outages. In January 2018, three 500 kV transmission lines, namely, the 500 kV Guanli line, the 500 kV Dushan line, and the 500 kV Guanqiao line, tripped and cut off due to ice-shedding and vibration in Anhui province, seriously threatening the safe operation of a large power grid. Current studies mainly focus on analyzing the influence factors and characteristics of line ice-shedding and investigating suppression measures, but they only analyze the correlation between each influencing factor and icing or shedding, and do not consider the coupling effects between multiple factors. In this paper, the key influencing factors and the probability distribution of transmission line ice-shedding were analyzed, and a multiple-factor coupling fault probability calculation model of line ice-shedding based on Copula function was proposed. The fault probability was calculated directly by considering multiple influence factors at the same time, which effectively overcame the error caused by multi-factor transformation in fuzzy membership degree and other methods. It provided an important decision-making basis for preventing and controlling transmission line ice-shedding faults. [ABSTRACT FROM AUTHOR]

Copulas are well-known tools for describing the relationship between two or more quantitative variables. They have recently received a lot of attention, owing to the variable dependence complexity that appears in heterogeneous modern problems. In this paper, we offer five new copulas based on a common original ratio form. All of them are defined with a single tuning parameter, and all reduce to the independence copula when this parameter is equal to zero. Wide admissible domains for this parameter are established, and the mathematical developments primarily rely on non-trivial limits, two-dimensional differentiations, suitable factorizations, and mathematical inequalities. The corresponding functions and characteristics of the proposed copulas are looked at in some important details. In particular, as common features, it is shown that they are diagonally symmetric, but not Archimedean, not radially symmetric, and without tail dependence. The theory is illustrated with numerical tables and graphics. A final part discusses the multi-dimensional variation of our original ratio form. The contributions are primarily theoretical, but they provide the framework for cutting-edge dependence models that have potential applications across a wide range of fields. Some established two-dimensional inequalities may be of interest beyond the purposes of this paper. [ABSTRACT FROM AUTHOR]

Various random factors in the bridge construction process directly affect the safety of the bridge life cycle. The existing theories on the reliability of bridge structure mainly focus on the reliability of components and the reliability of the bridge structure system in the completion and operation stages, while the research on the reliability of the structure system in the construction stage is relatively lacking. Therefore, this paper proposed using the Copula function to calculate the reliability index of the bridge structure construction process system. The basic theory of the Copula function was introduced in detail, and the formula was improved according to the actual situation of bridge construction. Finally, the sensitivity analysis of bridge system reliability was carried out. The research results showed that the method proposed in this paper based on Copula theory to calculate the reliability index of the bridge structure construction process system has strong applicability, simple calculation, and can be used in conjunction with the "interval estimation method", which is suitable for large and complex bridge structural engineering. At the same time, the conclusion that the influence of failure mode correlation on structural reliability should not be ignored in the actual engineering construction process is confirmed. [ABSTRACT FROM AUTHOR]

In recent years, with the intensification of global warming, extreme weather has become more frequent, intensifying the uncertainty of new energy output and load power, and seriously affecting the safe operation of power systems. Scene generation is an effective method to solve the uncertainty problem of stochastic planning of integrated systems of new energy generation. Therefore, this paper proposes a scenario generation and scenario reduction model of photovoltaic (PV) output and electric vehicle (EV) load power under extreme weather based on the copula function. Firstly, the non-parametric kernel density estimation method is used to fit a large number of sample data. The kernel density estimation expressions of PV and EV powers under extreme weather conditions are obtained and the corresponding goodness of fit tests are carried out. Then, a variety of joint distribution models based on the copula function are established to judge the goodness of fit of each model, and the optimal copula function is selected as the joint probability distribution function by combining the Kendall and Spearman correlation coefficients of each model. Finally, the optimal copula joint probability distribution is used to generate PV and EV power scenarios. The data of extremely hot weather in a certain province were selected for an example analysis. The results show that the output scenario obtained conforms to the correlation under this extreme weather, and has higher accuracy in reflecting the actual PV output and load power in this province under this extreme weather, which can provide a reference for reliability analyses of power systems and power grid planning. [ABSTRACT FROM AUTHOR]

This paper investigated reliability modeling for systems subject to dependent competing risks considering that variation of the failure threshold is not considered in most studies on competing failure reliability. Firstly, the variation of degradation quantity under shocks was analyzed, and the variation of the threshold was considered on this basis. Secondly, the cumulative degradation under the influence of the random shock process was analyzed. The attractive property of Copula functions is symmetry. Then, a linear Wiener process model was applied to model performance degradation failure, and a multi-performance degradation correlated-competition model based on a Copula function was constructed, which considered the correlated competition between multi-performance degradation failures. Lastly, a micromotor system was used to analyze the applicability of the proposed model for bivariate instances, demonstrating the rationality and effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Climate change is a significant environmental challenge that affects water resources, agriculture, health, and other aspects of human life. Bivariate modeling is a statistical method used to analyze the relationship between variables such as rainfall and temperature. The Pearson correlation coefficient, Kendall's tau, or Spearman's rank correlation are some measures used for bivariate modeling. However, copula functions can describe the dependence structure between two or more variables and can be effectively used to describe the relationship between rainfall and temperature. Despite the literature on bivariate modeling of rainfalls and temperature being extensive, finding flexible and sophisticated bivariate models is sometimes difficult. In this paper, we use rotated copula functions that can arrange any type of dependence that is empirically detected, especially negative dependence. The methodology is applied to an Italian municipality's bivariate daily time series of rainfall and temperature. The estimated rotated copula is significant and, therefore, can be used for simulating the effects of extreme events. [ABSTRACT FROM AUTHOR]

The paper introduces a function defined by a power series in the probabilities of multivariate records in a sequence of independent identically distributed random vectors with continuous components. In the univariate case, this function is always the same, but in the multivariate case there exists a broad variety of such functions determined by distribution copulas. The probabilistic meaning of this function and its derivatives is presented. A calculation method using the Kendall distribution function is given. The concepts of favorableness of copulas for records, record time distribution, and mean record time (without taking into account the order) are introduced. Examples are given. [ABSTRACT FROM AUTHOR]

The wind power interval prediction of offshore wind farms and power plan arrangement of conventional thermal power units are of vital importance in the consumption of offshore wind power, the reduction of greenhouse gas impact on the environment, and the electric power system safe and economic operating. With the purpose of selecting the appropriate Copula function on the basis of the results of wind speed and wind power normal test, establish the mathematical model of wind-fire joint optimal scheduling, and optimize coal-fired power units power generation after comparing the convergence performance of particle swarm optimization method and crow search algorithm. Results indicate that the selected Copula function meets the expected criteria, and the optimized thermal unit climbs more smoothly and through the optimization of CSA the complete economic consumption of running is lessened. An idea is presented by this paper, which considers the uncertainties of offshore wind power generation, and the basis for the operational performance of CSA over PSO, and which provides a joint wind-thermal economic optimal dispatch strategy. [ABSTRACT FROM AUTHOR]

In order to present a new estimation approach for multi-parameter distributions without a mean or for heavy tailed distributions, in which the L-moments method proposed by Gumbel, (1960), is invalid due to the absence of theoretical L-moments, Trimmed L-moments were first introduced by Elamir and Seheult (2003). In this paper, a new estimation method based on multi-parameter copulas' Trimmed L-moments is proposed with a simulation study. The consistency and the asymptotic normality of the new estimator also established. [ABSTRACT FROM AUTHOR]

Purpose: In armored vehicles integrated transmissions, residual life prediction based on oil spectrum data is crucial for condition monitoring and reliability assessment. This paper aims to use the advantages of real-time and accurate prediction of binary Wiener process, the residual life prediction of clutch is studied. Design/methodology/approach: First, combined with the wet clutch life test, the indicator elements Cu and Pb and the failure threshold of the residual life prediction of the clutch are extracted through the oil replacement correction of the spectral data of the whole life cycle; second, the correlation characteristics of indicating elements are analyzed by MATLAB Copula function, then the correlation function of residual life will be derived; third, according to the inverse Gaussian principle, the performance degradation mathematical models of the unary and binary Wiener processes of the above two indicator elements are established; finally, the maximum likelihood estimation method is used to estimate the parameters, and the monadic and binary performance degradation mathematical models are used to predict the residual life of the tested clutch. Findings: By comparing the prediction results with the test results, with the passage of time, 81.25% of the predicted value error of the residual life prediction method based on the binary Wiener process is controlled within 20%, while 56.25% of the predicted value error of the residual life prediction method based on the unitary Wiener process is controlled within 20%. At the same time, the prediction accuracy of the binary prediction model is 2%–16.7% higher than that of the unitary prediction model. Originality/value: This paper studies the residual life prediction theory of wet clutch, which can develop the theory and method of comprehensive transmission health monitoring, and provide theoretical and technical support for the construction of a reliable health management system for high-speed tracked vehicles. [ABSTRACT FROM AUTHOR]

Many survival data analyses aim to assess the effect of different risk factors on survival time. In some studies, the survival times are correlated, and the dependence between survival times is related to their spatial locations. Identifying and considering the dependence structure of data is essential in survival modeling. The copula functions are helpful tools for incorporating data dependencies. So, one may use these functions for modelling spatial survival data. This paper presents a model for spatial survival data by the Gumbel-Hougaard copula function. A two-stage estimator using a composite likelihood function is used to estimate regression and dependence parameters. A simulation study investigates the performance of the model. Finally, the proposed model is applied to model a set of COVID-19 data. [ABSTRACT FROM AUTHOR]

This paper is concerned with the optimal number of redundant allocation to n -component coherent systems consisting of heterogeneous dependent components. We assume that the system is built up of L groups of different components, $L\geq 1$ , where there are $n_i$ components in group i , and $\sum_{i=1}^{L}n_i=n$. The problem of interest is to allocate $v_i$ active redundant components to each component of type i , $i=1,\dots, L$. To get the optimal values of $v_i$ we propose two cost-based criteria. One of them is introduced based on the costs of renewing the failed components and the costs of refreshing the alive ones at the system failure time. The other criterion is proposed based on the costs of replacing the system at its failure time or at a predetermined time $\tau$ , whichever occurs first. The expressions for the proposed functions are derived using the mixture representation of the system reliability function based on the notion of survival signature. We assume that a given copula function models the dependency structure between the components. In the particular case that the system is a series-parallel structure, we provide the formulas for the proposed cost-based functions. The results are discussed numerically for some specific coherent systems. [ABSTRACT FROM AUTHOR]

From large-scale aerospace systems to household appliances and other systems in daily life, the application of parallel systems is involved. A parallel system is a typical structural dependence multi-component system, in addition to a series system and hybrid system. This paper takes a parallel system as the research object and minimizes the expected cost rate or maximizes the availability by determining the optimal two-dimensional age replacement interval. The structural dependence of the components is described by the copula function, and the system life model is established. Based on the system life model, the two-dimensional age replacement expected cost rate model and availability model are proposed. In case analysis, the simulated annealing algorithm (SAA), genetic algorithm (GA) and particle swarm optimization (PSO) algorithm are used to find the optimal warranty scheme for the engine fuel fine filter. SAA can converge faster and find a warranty scheme that makes the warranty cost rate lower or the availability higher. Compared with one-dimensional age replacement, two-dimensional age replacement strategy has more advantages in saving warranty costs and improving system availability. Finally, rationalization suggestions are put forward for managers to make maintenance decisions through comparative analysis and sensitivity analysis. [ABSTRACT FROM AUTHOR]

Low-lying coastal urban areas are vulnerable to frequent and chronic flooding due to population growth, urbanization, and accelerated sea level rise originating from climate change. This paper is part one of a 2 paper series, however a detailed literature review on the concept and the technical aspects of both papers is presented. In the 2nd paper, the application of the concepts and the proposed methodology are utilized to set the mitigation strategies for quantification of reliability attributes. The case study is the Hunts Point wastewater treatment plant and its sewershed in Bronx, New York City. The suitability of two major rainfall stations of Central Park and LaGuardia airport in the vicinity of the case study is tested. The copula-based non-stationary 100–year flood frequency analysis of rainfall and storm surge is analyzed to obtain the design values of surge and rainfall. A differential evaluation Markov Chain with Bayesian interface is used in this paper for parameter estimation. In this study, the likelihood of joint probability of co-occurring heavy rainfall and storm surge is determined to illustrate the risk of joint events. Therefore, the copula-based non-stationary 100–year flood frequency analysis of rainfall and storm surge are performed to obtain the design values of surge and rainfall. A multi-criteria decision-making (MCDM) approach that incorporates the load-resistance concept is presented in Part 2 paper to assess the Margin of Safety flood reliability of a wastewater treatment plant (WWTP). The framework presented in this paper is applicable to other coastal sewersheds. [ABSTRACT FROM AUTHOR]

This paper presents an intuitive model for default dependencies in supply networks and its application in firms' capital management. Modern supply chain networks are characterised by horizontal ties between firms within a particular industry or group, which are sequentially arranged based on vertical ties between firms in different layers. The recognition and accounting of these simultaneous interdependencies is crucial for a more advanced understanding of complex inter-organisational relations. Using the state-of-the art vine-copulae, we model these multidimensional interdependencies in the automotive industry, and capture the default tail dependency between alliance partners. Further, we apply our model to determine the optimal economic capital, such that companies can absorb unexpected losses from defaults in supply chain, while avoiding over-capitalisation. Our findings should spur managers to analyse their supplier networks with respect to default dependencies and to take this phenomenon into consideration when making sourcing decisions. [ABSTRACT FROM AUTHOR]

The lack of effective failure correlation analysis is one main reason for the gap between the reliability models and the actual complex systems with mixed static and dynamic characteristics. Takagi and Sugeno (T-S) dynamic fault tree is one powerful tool to analyze the static and dynamic failure logic relationship but it assumes the failure probability of the event is independent. Therefore, this paper proposes a multi-dimensional T-S dynamic fault tree analysis method involving failure correlation. The method integrates the failure probability distribution function of basic events with multi-factors and the multi-dimensional copula function, and the important measure of this method is also deduced. The reliability model expression for systems with failure correlations, both in series and in parallel, is discussed and verified. Compare the proposed method with the assumption that the probability of a failure event is independent. This method solves the problem of a large error when ignoring the failure correlation between parts and the degree of the correlation between variables can be characterized. The reliability analysis can be conducted on complex systems affected both by multi-factors and failure correlations. The proposed method is applied to the reliability analysis of a hydraulic height adjustment system and the correctness and superiority of the method are verified. [ABSTRACT FROM AUTHOR]

Studying the impact of mainshock–aftershock sequences on dam reliability is crucial for effective disaster prevention measures. With this purpose in mind, a new method for stochastic dynamic response analyses and reliability assessments of dams during seismic sequences has been proposed. Firstly, a simulation method of stochastic seismic sequences is described, considering the dependence between mainshock and aftershock based on Copula function. Then, a novel practical framework for stochastic dynamic analysis is established, combined with the improved point selection strategy and the direct probability integration method (DPIM). The DPIM is employed on a nonlinear system with one degree of freedom and compared with Monte Carlo simulation (MCS). The findings reveal that the method boasts exceptional precision and efficiency. Finally, the seismic performance of a practical dam was evaluated based on the above method, which not only accurately estimates the response probability distribution and dynamic reliability of the dam, but also greatly reduces the required calculations. Furthermore, the impact of aftershocks on dam seismic performance is initially evaluated through a probability approach in this research. It is found that seismic sequences will significantly increase the probability of earth dam failure compared with sequences of only mainshocks. In addition, the influence of aftershocks on reliability will further increase when the limit state is more stringent. Specifically, the novel analysis method proposed in this paper provides more abundant and objective evaluation indices, providing a dynamic reliability assessment for dams that is more effective than traditional evaluation methods. [ABSTRACT FROM AUTHOR]

The existing DUS-multivariate inverse Weibull distribution under classical statistics can be applied when all observations in the data are imprecise. In this paper, we introduce DUS-neutrosophic multivariate inverse Weibull distribution that can be used when the observations in the data are imprecise or in intervals. We derive some statistical properties and functions of DUS-neutrosophic multivariate inverse Weibull distribution. We also discuss the maximum likelihood estimation method for estimating the parameters. Monte-Carlo simulation study is performed to study the behavior of maximum likelihood estimates. We compare the efficiency of the proposed DUS-neutrosophic multivariate inverse Weibull distribution with the existing distributions under classical statistics. From the comparison, it is found that the proposed DUS-neutrosophic multivariate inverse Weibull distribution provides smaller values of Akaike's information criteria and Bayesian information criteria than the existing distributions under classical statistics. The proposed study can be extended for other statistical distributions as future research. [ABSTRACT FROM AUTHOR]

In this paper, we propose a correlation-aware probabilistic data summarization technique to efficiently analyze and visualize large-scale multi-block volume data generated by massively parallel scientific simulations. The core of our technique is correlation modeling of distribution representations of adjacent data blocks using copula functions and accurate data value estimation by combining numerical information, spatial location, and correlation distribution using Bayes' rule. This effectively preserves statistical properties without merging data blocks in different parallel computing nodes and repartitioning them, thus significantly reducing the computational cost. Furthermore, this enables reconstruction of the original data more accurately than existing methods. We demonstrate the effectiveness of our technique using six datasets, with the largest having one billion grid points. The experimental results show that our approach reduces the data storage cost by approximately one order of magnitude compared to state-of-the-art methods while providing a higher reconstruction accuracy at a lower computational cost. [ABSTRACT FROM AUTHOR]

In order to explore the relationship between exchange rate fluctuations and oil prices, this paper combines the copula function to study the correlation between exchange rate fluctuations and oil price changes, conducts a more comprehensive study of the copula function, and applies the algorithm to some practical classification problems. Moreover, this paper improves some defects in the algorithm and combines some new learning frameworks in machine learning to generalize the copula function to a variety of learning models. In addition, this paper studies how to use the coverage algorithm to construct classifiers under various problems and proposes corresponding improvement strategies according to the characteristics of various problems. Finally, this paper builds a correlation analysis algorithm model and uses simulation research to verify that there is a relatively obvious correlation between exchange rate fluctuations and oil price changes. [ABSTRACT FROM AUTHOR]

Uncertainty quantification is necessary in wind turbine design due to the random nature of the environmental inputs, through which the uncertainty of structural loads and response under specific situations can be quantified. Specifically, wind turbulence (described by the standard deviation of the longitudinal wind speed over a 10 min time duration) has a significant impact on the extreme and fatigue design envelope of the wind turbine. The wind parameters (mean and standard deviation of longitudinal wind speed over 10 min time duration) are not independent stochastic variables, and structural reliability analysis or uncertainty quantification therefore requires these wind parameters to be correlated stochastic parameters. An accurate probabilistic model should be established to model the correlation among wind parameters. Compared to univariate distributions, theoretical multivariate distributions are limited and not flexible enough to model the wind parameters from different sites or direction sectors. Copula-based models are often used for correlation description, but existing parametric copulas may not model the correlation among wind parameters well, due to limitations of the copula structures. The Gaussian mixture model is widely applied for density estimation and clustering in many domains, but limited studies have been conducted in wind energy and few have used it for density estimation of wind parameters. In this paper, the Gaussian mixture model is used to model the joint distribution of mean and standard deviation of longitudinal wind speed over 10 min time duration, which is calculated from 15 years of wind measurement time series data. As a comparison, the Nataf transformation (Gaussian copula) and Gumbel copula are compared with the Gaussian mixture model in terms of the estimated marginal distributions and conditional distributions. The Gaussian mixture model is then adopted to estimate the extreme wind turbulence (wind parameters for extreme load), which could be taken as an input to design loads used in the ultimate design limit state of turbine structures. The wind parameter contour associated with a 50-year return period computed from the Gaussian mixture model is compared with what is used in the design of wind turbines as given in IEC 61400-1. The Gaussian mixture model is able to model the joint distribution of wind parameters well, where the estimated tail distributions of both the marginal distributions and conditional distribution have good accuracy, and it is a good candidate for extreme turbulence estimation. [ABSTRACT FROM AUTHOR]

AbstractOccurrences of two (or more) types of defects are not uncommon in high quality (or zero-inflated) processes. Bivariate (or multivariate) attribute control charts are required to be developed for monitoring such processes. Fatahi et al. (2012) introduced the idea of applying copula function to derive joint distribution of two correlated zero-inflated Poisson distributions, which can be used to develop bivariate attribute control chart (BACC) for monitoring bivariate zero-inflated Poisson (BZIP) processes. However, the copula-based model often fails to represent bivariate zero-inflated data, which we come across in real-life situations. Li et al. (1999) model for BZIP distribution is quite flexible. Thus, it can overcome the limitations of Fatahi et al. (2012) model. In this paper, BACC is developed based on Li et al. (1999) model. The performances of the proposed BACC, in terms of in-control and out-of-control average run lengths, are evaluated extensively using simulations. The results show that the proposed BACC are well capable of detecting shifts in the parameters of a BZIP process. Further, two case studies on BZIP process data obtained by past researchers reveal that the BACC developed based on Li et al. (1999) model is more effective than the BACC developed based on copula-based model. [ABSTRACT FROM AUTHOR]

Stochastic frontier models commonly assume positive skewness for the inefficiency term. However, when this assumption is violated, efficiency scores converge to unity. The potential endogeneity of model regressors introduces another empirical challenge, impeding the identification of causal relationships. This paper tackles these issues by employing an instrument-free estimation method that extends joint estimation through copulas to handle endogenous regressors and skewness issues. The method relies on the Gaussian copula function to capture dependence between endogenous regressors and composite errors with a simultaneous consideration of positively or negatively skewed inefficiency. Model parameters are estimated through maximum likelihood, and Monte Carlo simulations are employed to evaluate the performance of the proposed estimation procedures in finite samples. This research contributes to the stochastic frontier models and production economics literature by presenting a flexible and parsimonious method capable of addressing wrong skewness of inefficiency and endogenous regressors simultaneously. The applicability of the method is demonstrated through an empirical example. [ABSTRACT FROM AUTHOR]

Redundancy allocations strategies are commonly used in reliability engineering to enhance the performance of reliability systems. This paper makes use the hierarchical copula to characterize the dependence structures among the components and hot/cold standbys in series systems. Optimal allocation policies of hot and cold standbys are presented for series systems with dependent components and redundancies under certain conditions imposed on the hierarchical copula as well as the components and spares reliabilities. It is shown that, under certain mild conditions imposed on the copula function and lifetimes of components and redundancies, the optimal allocations should be following the way that the resultant lifetimes for all nodes should be balanced as much as possible to enhance the system's performance. The results extend some related ones well‐known in the literature from the independent case to the dependent setting. Some numerical examples are presented as illustrations. We also present a real application in optimal allocations of redundant wires for improving the reliability of high‐voltage electricity transmission network systems. [ABSTRACT FROM AUTHOR]

The construction and operation of upstream reservoirs have significantly altered downstream hydrologic regime. Appropriate and quantifiable assessment method for the alteration of hydrologic regime is considerably vital and emergent for ecological protection and restoration. The Range of Variability Approach (RVA) and modified RVA methods have been widely used in practice to assess the hydrological alteration. However, these methods have failed to concurrently describe the distribution of indicator and morphological features in detail, which might inevitably lead to the misjudgment of alteration. This paper proposes a Joint Probability Density Difference Approach (JPDDA) method to address the major drawbacks of these previous methods with the introduction of Gaussian Kernel Density Estimation (KDE) and copula function. The annual average flow is selected as the reference variable to construct a proper joint probability density function between itself and other hydrological alteration indicators. The JPDDA method could describe the marginal distribution in detail through Gaussian KDE and also link the morphological features with copula function. Along with pervious methods, the hydrological alterations at Yichang hydrological station, Yangtze River are estimated based on the measured flow from 1949 to 2022. It is shown that the hydrologic regime has suffered from a moderate or even heavy alteration under the influence of massive upstream cascade reservoirs, and the JPDDA outperforms the other methods in terms of rationality and stability for practical assessments. Thus, the proposed JPDDA method is strongly advised to handle the hydrological alteration and could provide a reasonable reference for ecological operation. [ABSTRACT FROM AUTHOR]