Search Results (19)

This work offers a reliability framework for a five-subsystem hybrid series-parallel system representing smart factory monitoring infrastructure under heat and vibration stressors. A central programmable logic controller (1-out-of-1), pressure and temperature sensors (2-out-of-5), wireless communication units (2-out-of-4), solar power modules (3-out-of-6), and a cold standby database server (1-out-of-2) are connected in series. Unit failures are modeled using exponential distributions with component-specific failure rates and two environmental failure rates for thermal stress (${\alpha }_6$) and vibration stress (${\alpha }_7$) which go beyond the single-parameter models used in prior research. Repair of degraded states is governed by general distributions. The Gumbel–Hougaard copula family deals with total failure states, permitting positive repair time dependence due to common maintenance resources and environmental recovery. The state probabilities are obtained in closed form by using Laplace transforms and the supplementary variable method. Those state probabilities are used to find system availability, reliability, $MTTF$, sensitivity, indices and profit for three cases: copula-based repair, general distribution repair and a reduction technique with parameter $\rho$. Numerical analysis reveals steady state availability of 96.80%when using copula repair, and 99.35% when using the reduction technique ($\rho$ = 0.2). Sensitivity analysis reveals that the solar power module subsystem is the main cause of $MTTF$ degradation, however cost analysis reveals that proactive quality enhancement is more profitable than reactive repair options at all maintenance expenditure levels. Full article

Wireless Sensor Networks (WSNs) deployed in agricultural and industrial environments require high reliability to ensure continuous monitoring and data transmission. This study presents a reliability analysis of a hybrid WSN system comprising four series-connected subsystems: (1) the central processing unit, (2) sensor nodes in cluster A, (3) sensor nodes in cluster B, and (4) communication relay units. The system operates under a k-out-of-n: G mechanism, where subsystems 2 and 3 require at least one operational unit, while subsystem 4 requires at least two. Whereas unit failures follow exponential distributions, repair processes are modeled using either general distributions or Gumbel–Hougaard copula-based approaches to capture dependencies among multiple repair units. Using Laplace transforms and supplementary variable techniques, we evaluate system reliability metrics and demonstrate that copula-based repair strategies significantly improve availability and the expected profit function. Furthermore, we propose a reduction technique governed by a factor $\rho$ that decreases component failure rates, thereby enhancing overall system reliability relative to the baseline configuration. Full article

Rainfall, as the main driving force of natural disasters such as floods and droughts, has strong non-linear and abrupt characteristics, which makes it difficult to predict. As extreme weather events occur frequently in the Yellow River Basin, it is especially critical to reveal the physical mechanism of rainfall in the basin and integrate monthly scale meteorological data to achieve monthly rainfall prediction. In this paper, we propose a rainfall prediction model coupled with a physical mechanism and a temporal convolutional network (TCN) to achieve the prediction of monthly rainfall in the basin, aiming to reveal the physical mechanism between rainfall factors in the basin based on the transfer entropy and the multidimensional Copula function and based on the physical mechanism which is embedded into the TCN to construct a dual-driven prediction model with both physical knowledge and data, while the SHAP is used to analyze the interpretability of the prediction model. The results are as follows: (1) Temperature, relative humidity, and evaporation are key characteristic factors driving rainfall. (2) The physical mechanism features between temperature, relative humidity, and evaporation can be described by the three-dimensional Gumbel–Hougaard Copula function, with a more concentrated data distribution of their joint distribution probability. (3) The PHY-TCN model can accurately fit the extremes of the rainfall series, improving the model accuracy in the training set by 3.82%, 1.39%, and 9.82% compared to TCN, CNN, and LSTM, respectively, and in the test set by 6.04%, 2.55%, and 8.91%, respectively. (4) Embedding physical mechanisms enhances the contribution of individual feature variables in the PHY-TCN model and increases the persuasiveness of the model. This study provides a new research framework for rainfall prediction in the YRB and analyzes the physical relationship between the input data and output results of the deep learning model. It has important practical significance and strategic value for guiding the optimal scheduling of water resources, improving the risk management level of the basin, and promoting the ecological protection and high-quality development of the YRB. Full article

Many applications in health research involve the analysis of multivariate distributions of random variables. In this paper, we review the basic theory of copulas to illustrate their advantages in deriving a joint distribution from given marginal distributions, with a specific focus on bivariate cases. Particular attention is given to the Archimedean family of copulas, which includes widely used functions such as Clayton and Gumbel–Hougaard, characterized by a single association parameter and a relatively simple structure. This work differs from previous reviews by providing a focused overview of applied studies in biomedical research that have employed Archimedean copulas, due to their flexibility in modeling a wide range of dependence structures. Their ease of use and ability to accommodate rotated forms make them suitable for various biomedical applications, including those involving survival data. We briefly present the most commonly used methods for estimation and model selection of copula’s functions, with the purpose of introducing these tools within the broader framework. Several recent examples in the health literature, and an original example of a pediatric study, demonstrate the applicability of Archimedean copulas and suggest that this approach, although still not widely adopted, can be useful in many biomedical research settings. Full article

This paper proposes a system made up of four subsystems connected in sequence. The first and third subsystems each have one unit, the second has two, and the fourth has three. Every subsystem operates in parallel and is governed by the K-Out-of-n:G rule. Nonetheless, each subsystem needs at least one operational unit in order for the system to work. While a unit’s failure has an exponential distribution, repair is simulated using a general distribution and a distribution from the Gumbel–Hougaard family of copula. This study’s primary objective is to assess and contrast the system performance while our system is running under these two different repair policies. The problem is solved by combining the supplementary variable technique with Laplace transforms. We use reliability metrics to assess system performance. The second objective of this study is to present a reduction approach plan aimed at improving the overall reliability metrics of our system. Full article

This research envisages a system composed of three subsystems connected in series. Each subsystem comprises three units connected in parallel. For the system to function, at least one unit per subsystem must remain operational. Unit failure is governed by an exponential distribution, while unit repair is governed by either a general distribution or a Gumbel–Hougaard family copula distribution. The primary goal of this research is to compare the overall performance of our system under these two different regimes for performing repairs. Laplace transforms and supplementary variable methods are employed in solving the system. Our metrics for evaluating system performance are the availability, reliability, mean time to failure, and cost. The second goal of this research is to showcase a strategy for reduction that enhances the overall efficiency and availability of our system. Full article

In reliability studies, we are interested in the behaviour of a system when it interacts with its surrounding environment. To assess the system’s behaviour in a reliability sense, we can take the system’s intrinsic quality as strength and the outcome of interactions as stress. Failure is observed whenever stress exceeds strength. Taking Y as a random variable representing the stress the system experiences and random variable X as its strength, the probability of not failing can be taken as a proxy for the reliability of the component and given as $P(Y<X)=1-P(X<Y)$. This way, in the present paper, it is considered that X and Y follow generalized extreme value distributions, which represent a family of continuous probability distributions that have been extensively applied in engineering and economic contexts. Our contribution deals with a more general scenario where stress and strength are not independent and copulas are used to model the dependence between the involved random variables. In such modelling framework, we explored the proper selection of copula models characterizing the dependence structure. The Gumbel–Hougaard, Frank, and Clayton copulas were used for modelling bivariate data sets. In each case, information criteria were considered to compare the modelling capabilities of each copula. Two economic applications, as well as an engineering one, on real data sets are discussed. Overall, an easy-to-use methodological framework is described, allowing practitioners to apply it to their own research projects. Full article

It is evident that several real-life applications, such as telecommunication systems, call for the establishment of consecutive-type networks. Moreover, some of them require more complex connectors than the ones that exist already in the literature. Thereof, in the present work we provide a signature-based study of a reliability network consisting of identical m-consecutive-k-out-of-n: F structures with exchangeable components. The dependency of the components of each system is modeled with the aid of well-known Archimedean copulas. Exact formulae for determining the expected lifetime of the underlying reliability scheme are provided under different Archimedean copulas-based assumptions. Several numerical results are carried out to shed light on the performance of the resulting consecutive-type design. Some thoughts on extending the present study to more complex consecutive-type reliability structures are also discussed. Full article

China is one of the regions with the most frequent drought disasters and serious social and economic losses. Agricultural drought is the most serious natural disaster. Due to climate change, the regional agricultural drought risk assessment has always been the focus of the academic circle. This study takes Zunyi City as an example, which is the most typical city of karst landform development. The monthly precipitation data set of ground meteorological observation stations in Zunyi City from 1956 to 2020 was selected, and the drought characteristic variables were extracted by the coupled use of the precipitation anomaly percentage (Pa) index and the theory of runs. A copula function was applied to establish the joint distribution model of characteristic variables, obtaining the drought frequency and drought return periods. Combined with the Jensen model, the agricultural drought loss rate under different drought return periods in the target year (2020) was calculated and evaluated. The results showed that the Gumbel-Hougaard copula function was suitable for the joint distribution of drought joint variables in Zunyi City. From 1956 to 2020, fewer droughts occurred in Zhengan and Wuchuan, and the most droughts took place in Fenggang, Meitan, and Yuqing. The average drought duration in each county was about 1.5 months, and the average drought severity was about 0.35 in spatial distribution. Crop loss rate caused by drought increased and the affected area expanded with the increase of drought return periods (5, 10, 20, 50, and 100 years) in temporal distribution. Meanwhile, the drought disaster was most drastic in the eastern region, followed by the south, north, west, and central area. The results were highly consistent with the historical drought in Zunyi City, which verified the validity of the model. This study could provide scientific knowledge for drought resistance and reasonable mitigation programing for the security of the regional agricultural production and the sustainability of social and economic development. Full article

Wind energy is a kind of renewable energy that plays a significant role in remote areas for pumping water. The windmill is also used to generate electricity. The windmill is also known as a wind pump when it is used for pumping water. In this work, the authors proposed a complex hybrid model of an example of combined system (windmill, rechargeable battery and pumping system) to evaluate the system’s performance. System performance was affected by system degradation due to system failure. These factors also affected the profit of the user. Two types of repair facilities for continuous and satisfactory performance of the system were assumed. To illustrate the system modeling using the Gumbel–Hougaard family of the copula, numerical examples were used for the exploration of Markov results of the reliability measures and the profit of the system with the warranty period, with this also being demonstrated graphically. Full article

In the automotive industry, it is important to know whether the failure of some car parts may be related to the failure of others. This project studies warranty claims for five engine components obtained from a major car manufacturer with the purpose of modeling the joint distributions of the failure of two parts. The one-dimensional distributions of components are combined to construct a bivariate copula model for the joint distribution that makes it possible to estimate the probabilities of two components failing before a given time. Ultimately, the influence of the failure of one part on the operation of another related part can be described, predicted, and addressed. The performance of several families of one-parameter Archimedean copula models (Clayton, Gumbel–Hougaard, survival copulas) is analyzed, and Bayesian model selection is performed. Both right censoring and conditional approaches are considered with the emphasis on conditioning to the warranty period. Full article

Against the background of global warming and rising sea levels, the threat of typhoon disasters to marine engineering structures has become increasingly serious. Therefore, the research on the design standards of marine environmental elements has become an important topic. In this study, two-dimensional joint distributions of wave height and surge height, surge height and wind speed, and wave height and wind speed were constructed based on the Gumbel–Hougaard (G-H) Copula function according to the data of marine environmental elements under extreme sea conditions from Naozhou observation station in the sea waters of western Guangdong, and the Kendall return period is introduced. The joint return periods, co-occurrence return periods, and Kendall return periods of joint distributions were calculated, along with the latter’s corresponding design values of environmental elements. The results showed that the Kendall return periods and the corresponding design values are between two kinds of traditional return periods. After analysis, the conclusion is that the Kendall return period can reflect the occurrence regularity of marine hydrological events more accurately, and the design values of marine environmental elements calculated under this standard can reasonably lower the investment under the premise of ensuring structural safety. Therefore, the Kendall return period can serve as the new selection for marine engineering design and risk management. Full article

The Northeast region of Brazil (NRB) is the most populous semiarid area in the world and is extremely susceptible to droughts. The severity and duration of these droughts depend on several factors, and they do not necessarily follow the same behavior. The aim of this work is to evaluate the frequency of droughts in the NRB and calculate the return period of each drought event using the copula technique, which integrates the duration and severity of the drought in the NRB in a joint bivariate distribution. Monthly precipitation data from 96 meteorological stations spatially distributed in the NRB, ranging from 1961 to 2017, are used. The copula technique is applied to the Standardized Precipitation Index (SPI) on the three-month time scale, testing three families of Archimedean copula functions (Gumbel–Hougaard, Clayton and Frank) to reveal which model is best suited for the data. Averagely, the most frequent droughts observed in the NRB are concentrated in the northern sector of the region, with an observed duration varying from three and a half to five and a half months. However, the eastern NRB experiences the most severe droughts, lasting for 14 to 24 months. The probability distributions that perform better in modeling the series of severity and duration of droughts are exponential, normal and lognormal. The observed severity and duration values show that, for average values, the return period across the region is approximately 24 months. Still in this regard, the southernmost tip of the NRB stands out for having a return period of over 35 months. Regarding maximum observed values of severity and duration, the NRB eastern strip has the longest return period (>60 months), mainly in the southeastern portion where a return period above 90 months was observed. The northern NRB shows the shortest return period (~45 months), indicating that it is the NRB sector with the highest frequency of intense droughts. These results provide useful information for drought risk management in the NRB. Full article

Hydropower is an important renewable energy, and Construction Diversion Risk (CDR) should be highlighted and assessed during hydropower development. Since sediment-rich rivers are widely existing around the world and have great hydro-energy potential, assessing CDR for hydropower development on sediment-rich rivers in terms of engineering feasibility is of significance. This paper proposes a CDR assessment method for the sediment-rich hydropower development environment. The method is concise and practical, reflects diversion uncertainties and correlation, and mainly adopts the Gumbel–Hougaard Copula and the Monte Carlo Simulation. Through simulating flood evolution and sediment impact during diversion, the method can assess CDR basing on the cofferdam overtopping probability. Case results show that the proposed method can achieve CDR assessment on a sediment-rich river and highlights sediment impact on the diversion risk. Through results discussion, the risk feature of construction diversion on sediment-rich rivers is revealed, that sediment impact causes the dynamic and yearly-risen CDR. Hence, our conclusions are: (1) the proposed method is feasible, effective and has industrial potential, and (2) a diversion scheme on sediment-rich rivers is suggested that adopts the design with high or yearly-heightening cofferdams, based on the advanced CDR assessment to cope with the risk features of sediment-rich diversion environments. Full article

Flooding from the Indus river and its tributaries has regularly influenced the region of Pakistan. Therefore, in order to limit the misfortune brought about by these inevitable happenings, it requires taking measures to estimate the occurrence and effects of these events. The current study uses flood frequency analysis for the forecast of floods along the Indus river of Pakistan (Tarbela). The peak and volume are the characteristics of a flood that commonly depend on one another. For progressively proficient hazard investigation, a bivariate copula method is used to measure the peak and volume. A univariate analysis of flood data fails to capture the multivariate nature of these data. Copula is the most common technique used for a multivariate analysis of flood data. In this paper, four Archimedean copulas have been tried using the available information, and in light of graphical and measurable tests, the Gumbel Hougaard copula was found to be most appropriate for the data used in this paper. The primary (T^AND, T^OR), conditional and Kendall return periods have been also determined. The copula method was found to be a powerful method for the distribution of marginal variables. It also gives the Kendall return period for the multivariate analysis the consequences of flooding. Full article