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Cloud and edge computing are necessary elements in the modern distributed network. To reflect the capacity variances of the system, stochastic capacities and costs of components (arcs and nodes) are considered such that stochastic capacity distributed networks (SCDNs) can be formed in the paper. To learn the capability of the SCDN for system monitoring and management, system reliability can be utilized which is defined as the probability of satisfying demands (data) under a budget for an SCDN. An exact-system reliability algorithm for system reliability is derived in advance for prudent management and decision-making. For immediate control and management, a deep neural network (DNN) architecture is proposed to create a prediction model for system reliability. Enough data points about SCDN information are generated and transformed into an appropriate format for training the prediction model. Note that the labels (system reliability) for all the data points would be calculated using the exact-system reliability algorithm. Necessary hyperparameters for determining the DNN of system reliability of the SCDN are also suggested. The model can be used for the future management of the distributed network. [ABSTRACT FROM AUTHOR]

In some settings, systems may not fail completely but instead undergo performance degradation, leading to reduced efficiency. A significant concern arises when a system transitions into a degraded state without immediate detection, with the degradation only becoming apparent after an unpredictable period. Undetected degradation can result in failures with significant consequences. For instance, a minor crack in an oil pipeline might go unnoticed, eventually leading to a major leak, environmental harm, and costly cleanup efforts. Similarly, in the nuclear industry, undetected degradation in reactor cooling systems could cause overheating and potentially catastrophic failure. This paper focuses on reliability modeling for systems experiencing degradation, accounting for time delays associated with undetected degraded states, self-repair mechanisms, and varying operating environments. The paper presents a reliability model for degraded, time-dependent systems, incorporating various aspects of degradation. It first discusses the model assumptions and formulation, followed by numerical results obtained from system modeling using the developed program. Various scenarios are illustrated, incorporating time delays and different parameter values. Through computational analysis of these complex systems, we observe that the probability of the system being in the undetected degraded state tends to stabilize shortly after the initial degradation begins. The model is valuable for predicting and establishing an upper bound on the probability of the undetected, degraded state and the system's overall reliability. Finally, the paper outlines potential avenues for future research. [ABSTRACT FROM AUTHOR]

The convergence of heterogeneous wireless sensor networks provides many benefits, including increased coverage, flexible load balancing capabilities, more efficient use of network resources, and the provision of additional data by different types of sensors, thus leading to improved customer service based on more complete information. However, despite these advances, the challenge of ensuring reliability and survivability remains due to low-cost sensor requirements and the inherent unreliability of the wireless environment. Integrating different sensor networks and unifying protocols naturally leads to the creation of a network with multiple sinks, necessitating the exploration of new approaches to rational reliability assurance. The failure of some sensors does not necessarily lead to a shutdown of the network, since other sensors can duplicate information and deliver data to sinks via an increased number of alternative routes. In this paper, the reliability indicator is defined as the probability that sinks can collect data from a given number of sensors. In this context, a dedicated reliability metric is introduced and examined for its effectiveness. This metric is computed using an algorithm rooted in the modified factoring method. Furthermore, we introduce a heuristic algorithm designed for optimal sink placement in wireless sensor networks to achieve the highest level of network reliability. [ABSTRACT FROM AUTHOR]

The multi-state flow network (MSFN) serves as a fundamental framework for real-life network-structured systems and various applications. The system reliability of the MSFN, denoted as Rd, is defined as the probability of successfully transmitting at least d units of demand from a source to a terminal. Current analytical algorithms are characterized by their computational complexity, specifically falling into the NP-hard problem to evaluate exact system reliability. Moreover, existing analytical algorithms for calculating Rd are basically designed for predetermined values of d. This limitation hinders the ability of decision-makers to flexibly choose the most appropriate based on the specific characteristics of the given scenarios or applications. This means that these methods are incapable of simultaneously calculating system reliability for various demand levels. Therefore, this paper develops a simulation-based algorithm to estimate system reliability for all possible demand levels simultaneously such that we can eliminate the need to rely on repeat procedures for each specified d. An experimental investigation was carried out on a benchmark network and a practical network to validate the effectiveness and performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

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This paper proposes a reliability evaluation method of a distribution network with electric vehicles (EVs) and distributed generations (DGs) based on network equivalence and sequential Monte Carlo. Unlike traditional studies, the proposed method not only can effectively simplify the complexity structure of the distribution network with EVs and DGs, but also can establish a multidimensional reliability evaluation system for the distribution network with EVs and DGs. Firstly, the related models of DGs and EVs are established respectively in our study. Based on the minimum path method, the impact of each component fault on each load point is analyzed, and the failure impact analysis (FIA) table is constructed. Then, a simplified method for the structure of the distribution network with EVs and DGs based on network equivalence is proposed and validated. Moreover, the reliability evaluation method of the distribution network with EVs and DGs is given based on the sequential Monte Carlo. Finally, an illustrative example of the improved IEEE RBTS BUS6 F4 feeder system, as well as multiple dimensions discussions, are elaborated in detail to demonstrate the effectiveness and superiority of the proposed model. [ABSTRACT FROM AUTHOR]

Rural areas with weak distribution networks often suffer from a lack of energy supply reliability, which makes it difficult to widely implement multi-energy complementary systems connected to large-scale photovoltaic. Energy storage systems, as a link to the integration of new energy systems, can effectively improve the reliability of energy supply in such areas. To this end, a cooperative and optimal configuration strategy for rural multi-energy complementary system (RMES) energy storage for weak distribution networks is proposed. Firstly, the RMES architecture including biomass waste energy conversion system is clarified. Secondly, an energy storage configuration evaluation criterion is proposed using the cost of supply deficiency loss of the system as a judgment basis. Finally, the RMES multi-energy storage cooptimal allocation model is established to take into account the total life cycle cost of energy storage. The model is decoupled and transformed into a two-layer optimization model with two stages of planning operation, and solved by a hybrid strategy combining particle swarm algorithm and Gurobi solver. The analysis of the algorithm shows that the proposed energy storage configuration evaluation criteria effectively motivate RMES to deploy energy storage. In addition, the developed multi-variate energy storage configuration model enables RMES to show better economic and environmental benefits, and is superior in improving system reliability.

To consider the complex soil-structure interaction in a pile-slope system, it is necessary to analyze the performance of pile-slope systems based on a three-dimensional (3D) numerical model. Reliability analysis of a pile-slope system based on 3D numerical modeling is very challenging because it is computationally expensive and the performance function of the pile failure mode is only defined in the safe domain of soil stability. In this paper, an efficient hybrid response surface method is suggested to study the system reliability of pile-reinforced slopes, where the support vector machine and the Kriging model are used to approximate performance functions of soil failure and pile failure, respectively. The versatility of the suggested method is illustrated in detail with an example. For the example examined in this paper, it is found that the pile failure can significantly contribute to system failure, and the reinforcement ratio can effectively reduce the probability of pile failure. There exists a critical reinforcement ratio beyond which the system failure probability is not sensitive to the reinforcement ratio. The pile spacing affects both the probabilities of soil failure and pile failure of the pile-reinforced slope. There exists an optimal location and an optimal length for the stabilizing piles.

Flight control system is typical safety critical system, and the reliability of flight control system plays an important role in ensuring the safe operation of aircraft. Traditional reliability analysis methods have a heavy reliance on the experience of analysts, which makes it easy for inconsistencies between reliability models and design models. The fault propagation behavior of the system is thoroughly described by the Architecture Analysis Design Language（AADL）and stochastic Petri nets（SPN）, and a method for model-based reliability analysis is proposed. The nominal model and error model of a lateral fly-by-wire flight control system are constructed using AADL. A method for extracting error propagation information from the AADL model is proposed, and the SPN model described the fault propagation behavior of the system is automatically generated by extracting the information of AADL model. Based on the SPN model, Monte Carlo simulation is used to evaluate the reliability of the lateral fly-by-wire flight control system, compared with the fault tree analysis method, the error is less than 0.018%, which can be neglected in practice. Through the method of this study, the reliability model is automatically generated by the AADL model, which ensures the consistency between the reliability model and the design model and avoids reliance on the experience of designers.

Distributed real time system has developed into an outstanding computing platform for parallel, high-efficiency applications. A real time system is a kind of planning where tasks must be completed with accurate results within a predetermined amount of time. It is well known that obtaining an optimal assignment of tasks for more than three processors is an NP-hard problem. This article examines the issue of assigning tasks to processors in heterogeneous distributed systems with a view to reduce cost and response time of the system while maximizing system reliability. The proposed method is carried out in two phases, Phase Ⅰ provides a hybrid HPSOGAK, that is an integration of particle swarm optimization (PSO), genetic algorithm (GA), and k-means technique while Phase Ⅱ is based on GA. By updating cluster centroids with PSO and GA and then using them like initial centroids for the k-means algorithm to generate the task-clusters, HPSOGAK produces 'm' clusters of 'r' tasks, and then their assignment onto the appropriate processor is done by using GA. The performance of GA has been improved in this article by introducing new crossover and mutation operators, and the functionality of traditional PSO has been enhanced by combining it with GA. Numerous examples from various research articles are employed to evaluate the efficiency of the proposed technique, and the numerical results are contrasted with well-known existing models. The proposed method enhances PIR values by 22.64%, efficiency by 6.93%, and response times by 23.8 on average. The experimental results demonstrate that the suggested method outperforms all comparable approaches, leading to the achievement of superior results. The developed mechanism is acceptable for an erratic number of tasks and processors with both types of fuzzy and crisp time.

Abstract This study addresses the significant problem of Dynamic Economic Emission Dispatch (DEED), a critical consideration in power systems from both economic and environmental protection viewpoints. Reliability stands as another vital facet, impacting maintenance and operation perspectives. The integration of Artificial Neural Network (ANN)-based transmission loss prediction into the DEED model is also essential to address specific limitations and enhance the overall performance of the dispatch process. Traditionally, the DEED model relies on a single B-loss coefficient to estimate transmission losses. While this approach simplifies calculations, it fails to account for the significant variations in demand that occur throughout the dispatch period and it leads to inaccuracies in loss prediction, especially in dynamic environments. Using a single coefficient, the model cannot adequately capture the complex, non-linear relationships between power generation, load, and transmission losses under different operating conditions. To overcome this limitation, this study introduces an ANN-based loss prediction method integrated into the DEED model and uses trained ANN to replace the process of finding B-loss coefficients during each dispatch period. This paper also introduces a strategy leveraging the multi-objective northern goshawk optimizer algorithm, characterized by a non-dominated sorting and crowding distance mechanism, to enhance DEED considerations incorporating reliability (DEEDR). This novel algorithm improves the solution space effectively, maintains high population diversity and enables an even distribution of individuals sharing the same rank in the objective space. The fundamental objective of this study is to balance fuel cost, emission, and system reliability in power system operations. Compared with a few existing multi-objective optimization algorithms, this study demonstrates superior performance in generating a series of non-dominated solutions. The experimental results highlight its competitive and potential as an efficient tool in the DEED and DEEDR problems, promising a synergistic coordination of economy, environmental protection, and system reliability benefits in power system management.

Wireless sensor networks (WSNs) are attracting increasing research interest due to their ability to monitor large areas independently. Their reliability is a crucial issue, as it is influenced by hardware, data, and energy-related factors such as loading conditions, signal attenuation, and battery lifetime. Proper selection of sensor node positions is essential to maximise system reliability during the development of products equipped with WSNs. For this purpose, this paper presents an approach to estimate WSN system reliability during the development phase based on the analysis of measurements, using strain measurements in finite element (FE) models as an example. The approach involves dividing the part under consideration into regions with similar strains using a region growing algorithm (RGA). The WSN configuration is then analysed for reliability based on data paths and measurement redundancy resulting from the sensor positions in the identified measuring regions. This methodology was tested on an exemplary WSN configuration at an aircraft wing box under bending load and found to effectively estimate the hardware perspective on system reliability. Therefore, the methodology and algorithm show potential for optimising sensor node positions to achieve better reliability results. [ABSTRACT FROM AUTHOR]

The aim of this research is to devise a continuous simulation model for predicting ship crane failures to increase their reliability and reduce unplanned downtime during cargo loading and unloading operations. To predict the condition of the hydraulic system, a database from the GALIOT software package was used for carrying out maintenance on cranes at m/v "O" over a period of 120,000 working hours. In the research, fault tree analysis (FTA) was used to identify causal relationships between system failures and basic events, while the Markov mathematical model was used to model the system state and predict transitions between different failure states. A system dynamics simulation model was developed to simulate the behavior of a system using POWERSIM PowerSim Constructor 2.5.d (4002), and regression analysis was performed to analyze the simulation results and understand the relationships between dependent and independent variables. The results show that a model for predicting failures in the hydraulic motors and pumps of ship cranes was developed, and the Markov model makes it possible to estimate the frequency of transitions between states under the condition that the sum of reliability equals one. The simulation model shows high reliability of the cranes and a constant frequency of failures throughout the 120,000 operating hours, while the regression analysis confirms the validity of the simulation model and shows a strong correlation between the analyzed variables. These models are used to improve the planning of ship crane maintenance, reduce unplanned downtime, and predict and promptly detect failures, which overall minimizes maintenance costs and failures. [ABSTRACT FROM AUTHOR]

Fatigue damage can lead to failures of structural systems. To reduce the failure risk and enhance the reliability of structural systems, inspection and maintenance interventions are required, and it is important to develop an efficient inspection strategy. This study, for the first time, develops a system-level reliability growth model to establish efficient inspection planning. System-level reliability growth is defined as an increase in the percentage of the system reliability index with and without inspection. The probabilistic S-N approach is used to obtain the reliability index without inspection. Moreover, advanced risk analysis and Bayesian inference techniques are used to obtain the reliability index with inspection. The optimal inspection planning is obtained by maximizing system-level reliability growth. This model is applied to an offshore wind farm. The results show that inspection efficiency can be improved by increasing the number of repair objects in response to a 'detection' inspection outcome, changing the inspection object for each inspection, and increasing the inspection quality. The maximum system-level reliability growth gained from one additional inspection decreases as the number of inspections increases. This study quantifies the inspection efficiency of offshore wind farms by explicit system-level reliability growth computation, offering valuable insights for promoting sustainable energy solutions. [ABSTRACT FROM AUTHOR]

Bogie is a pivotal system and plays a critical part in the safety and reliability management of high-speed rail. However, the available bogie system reliability analysis methods lack the consideration of multi-state characteristics, and the common multi-state reliability analysis methods, being an NP-hard problem, lead to low efficiency. In order to overcome these drawbacks, this paper proposes a novel multi-state rail train bogie system reliability analysis approach based on the extended d -MC model. Three different function interactions within the bogie system are considered to build the multi-state bogie system flow network model. Meanwhile, an extended d -MC model is established to remove unnecessary d -MC candidates and duplicates, which greatly enhances the computing efficiency. The bogie system reliability is calculated, and examples are provided. Numerical experiments are carried out for the different operational conditions of the bogie system and are used to test the practicability of the method proposed in this article; it is found that this method outperforms a newly developed method in solving multi-state reliability problems. [ABSTRACT FROM AUTHOR]

The parameters of gravity dams and foundation materials objectively exhibit spatial variability due to environmental and load influences, which significantly affect the safety status of dam structures. Therefore, a safety risk analysis method for a gravity dam–foundation system based on random field theory is proposed in this paper. Spatial variabilities in materials are particularly considered by using the finite element method. Then, composite response surface equations for the performance function (PF) of strength and stability failure are established, and then, the system failure risk is obtained using the Monte Carlo method. The proposed method solves the problem wherein the effect of spatial variability on failure risk cannot be reflected accurately by the performance function of multi-element sliding paths, and the difficulties in solving the failure risk of the series–parallel system due to multiple failure paths and their complex correlations. The application of a gravity dam shows that the developed method overcomes the disadvantages of the traditional method, such as the homogenization of the spatially random characteristics of parameters and the overestimation of failure risk in the system due to large variance estimation. [ABSTRACT FROM AUTHOR]

Understanding component criticality in machinery performance degradation is important in ensuring the reliability and availability of ship systems, particularly considering the nature of ship operations requiring extended voyage periods, usually traversing regions with multiple climate and environmental conditions. Exposing the machinery system to varying degrees of load and operational conditions could lead to rapid degradation and reduced reliability. This research proposes a tailored solution by identifying critical components, the root causes of maintenance delays, understanding the factors influencing system reliability, and recognising failure-prone components. This paper proposes a hybrid approach using reliability analysis tools and machine learning. It uses dynamic fault tree analysis (DFTA) to determine how reliable and important a system is, as well as Bayesian belief network (BBN) availability analysis to assist with maintenance decisions. Furthermore, we developed an artificial neural network (ANN) fault detection model to identify the faults responsible for system unreliability. We conducted a case study on a ship power generation system, identifying the components critical to maintenance and defects contributing to such failures. Using reliability importance measures and minimal cut sets, we isolated all faults contributing over 40% of subsystem failures and related events. Among the 4 MDGs, the lubricating system had the highest average availability of 67%, while the cooling system had the lowest at 38% using the BBN availability outcome. Therefore, the BBN DSS recommended corrective action and ConMon as maintenance strategies due to the frequent failures of certain critical parts. ANN found overheating when MDG output was above 180 kVA, linking component failure to generator performance. The findings improve ship system reliability and availability by reducing failures and improving maintenance strategies. [ABSTRACT FROM AUTHOR]

This paper presents a new probability distribution called the DUS Lindley distribution, created by applying the DUS transformation to the traditional Lindley distribution. The study provides an in-depth analysis of the distribution's statistical properties. These properties include a variety of statistical measures such as the probability density function, cumulative distribution function, failure rate, survival function, reverse hazard function, Mills ratio, mean residual life, mean past life, moments, conditional moments, characteristic function, order statistics, entropy measures, likelihood ratio test and Lorenz and Bonferroni curves. Parameter estimation is performed using several methods including weighted least squares, maximum likelihood estimation, Cramer-Von Mises estimation, least squares and Anderson-Darling estimation. The paper also explores the estimation of system reliability and evaluates the performance of maximum likelihood estimators through simulation studies across different sample sizes. Finally, the DUS Lindley distribution is applied to two real-world datasets, demonstrating a better fit than other well-known distributions.

Internet of Things (IoT) based sensor network is largely utilized in various field for transmitting huge amount of data due to their ease and cheaper installation. While performing this entire process, there is a high possibility for data corruption in the mid of transmission. On the other hand, the network performance is also affected due to various attacks. To address these issues, an efficient algorithm that jointly offers improved data storage and reliable routing is proposed. Initially, after the deployment of sensor nodes, the election of the storage node is achieved based on a fuzzy expert system. Improved Random Linear Network Coding (IRLNC) is used to create an encoded packet. This encoded packet from the source and neighboring nodes is transmitted to the storage node. Finally, to transmit the encoded packet from the storage node to the destination shortest path is found using the Destination Sequenced Distance Vector (DSDV) algorithm. Experimental analysis of the proposed work is carried out by evaluating some of the statistical metrics. Average residual energy, packet delivery ratio, compression ratio and storage time achieved for the proposed work are 8.8%, 0.92%, 0.82%, and 69 s. Based on this analysis, it is revealed that better data storage system and system reliability is attained using this proposed work.

A secure and reliable intelligent multi-cloud resource scheduling system in cyberspace is especially important in some industry applications. However, this task has become exceedingly challenging due to the intricate nature of information, the variety of knowledge representations, the compatibility of diverse knowledge reasoning engines, and the numerous security threats found in cloud networks. In this paper, we applied the endogenous security theory to the multi-cloud resource scheduling intelligent system and presented a novel model of the system. The proposed model incorporates various knowledge representations and inference engines, resulting in a multi-cloud resource scheduling intelligent system that ensures endogenous security. In addition, we have devised a scheme for an intelligent system that schedules multi-cloud resources using dual-channels and has an endogenous security mechanism, which we have named Dynamic, Heterogeneous, and Redundant (DHR). Finally, we have used the multi-cloud resource scheduling intelligent run log database to carry out numerous experiments to validate the efficiency of the dual-channel redundant reasoning system with the endogenous security mechanism's DHR property. The results of the experiment demonstrated that the multi-cloud resource intelligent scheduling system model with an endogenous security mechanism was superior to the current single-channel inference system scheme in regards to security and reliability.

Aiming at the problem that the diversity of the current double population algorithm with dynamic population size reduction cannot be guaranteed in real time in iteration and is easy to fall into local optimum, this study presents a dual population collaborative harmony search algorithm with adaptive population size (DPCHS). Firstly, we propose a dual population algorithm framework for improving the algorithm global search capability. Within this framework, the guidance selection strategy and information interaction mechanism are integrated to strengthen the competition and cooperation among populations, and achieving a good balance between exploration and exploitation. A population state assessment method is designed to monitor population changes in real-time for enhancing population real-time self-regulation. Additionally, population size adjustment approach is designed to adopted to effectively streamline population resources and improve population quality. Comprehensive experiment results demonstrate that DPCHS effectively addresses system reliability-redundancy allocation problems with superior performance and robust convergence compared with other HS variants and algorithms from different categories. [ABSTRACT FROM AUTHOR]

Though road authorities have well-defined inspection protocols for evaluating bridge serviceability, gaps remain in understanding optimal timing and the impact of maintenance strategies on an individual bridge and its subsystems and, consequently, on the holistic performance of a road network. This paper proposes an innovative model based on system reliability principles that develops optimized bridge maintenance strategies aimed at enhancing the overall reliability of a bridge-dominated road network by considering the quantified impact of bridge component deterioration. Using the first-order second-moment method, we initially determine the reliability index for each bridge based on condition ratings derived from routine inspections as outlined in the bridge inspection manual. Advanced optimization algorithms then formulate the optimal maintenance strategies for the bridge structures. Finally, we gauge the system reliability of the network using Ditlevsen bounds approximation, considering the impact of maintenance actions on varied bridge structural components. The developed model was implemented on a typical bridge-dominated road network in Chongqing, China. The results demonstrate the model has the capacity to quantify the impact of diverse bridge maintenance strategies on the total road network, offering valuable insights for decision makers to design effective, efficient maintenance strategies aimed at extending the lifespan of bridge-dominated road networks. [ABSTRACT FROM AUTHOR]

This study aims to address the limitations of traditional Failure Mode and Effect Analysis (FMEA) in managing safety and reliability within complex systems characterized by interdependent critical factors. We propose an integrated framework that combines FMEA with the strategic decision-making principles of Game Theory, thereby enhancing the assessment and mitigation of risks in intricate environments. The novel inclusion of the Best Worst Method (BWM) and Pythagorean fuzzy uncertain linguistic variables refines the accuracy of risk evaluation by overcoming the inherent deficiencies of conventional FMEA approaches. Through sensitivity analysis, the framework's efficacy in identifying and prioritizing failure modes is empirically validated, guiding the development of targeted interventions. The practical application of our methodology is demonstrated in a comprehensive healthcare system analysis, showcasing its versatility and significant potential to improve operational safety and reliability across various sectors. This research is particularly beneficial for systems engineers, risk managers, and decision-makers seeking to fortify complex systems against failures and their effects. [ABSTRACT FROM AUTHOR]

A secure and reliable intelligent multi-cloud resource scheduling system in cyberspace is especially important in some industry applications. However, this task has become exceedingly challenging due to the intricate nature of information, the variety of knowledge representations, the compatibility of diverse knowledge reasoning engines, and the numerous security threats found in cloud networks. In this paper, we applied the endogenous security theory to the multi-cloud resource scheduling intelligent system and presented a novel model of the system. The proposed model incorporates various knowledge representations and inference engines, resulting in a multi-cloud resource scheduling intelligent system that ensures endogenous security. In addition, we have devised a scheme for an intelligent system that schedules multi-cloud resources using dual-channels and has an endogenous security mechanism, which we have named Dynamic, Heterogeneous, and Redundant (DHR). Finally, we have used the multi-cloud resource scheduling intelligent run log database to carry out numerous experiments to validate the efficiency of the dual-channel redundant reasoning system with the endogenous security mechanism's DHR property. The results of the experiment demonstrated that the multi-cloud resource intelligent scheduling system model with an endogenous security mechanism was superior to the current single-channel inference system scheme in regards to security and reliability. [ABSTRACT FROM AUTHOR]

In this work, we assess the effect of predictive maintenance on the reliability of repairable systems. In reparable systems, the reliability assessment considering corrective and preventive maintenance is well defined, but not considering predictive one. The effect of predictive maintenance is taken into account through a finite probability that the system is found in degraded condition. If the predictive maintenance evidences the degradation, then the repair is carried out. All the repairs are considered perfects, which means that the system is restored to an as-good-as-new condition each time the repair is carried out. The measure of system reliability under predictive maintenance is found to be between that of a maintenance-free strategy and preventive maintenance. The effect on the system reliability depends on the value of the probability that the system is found in degraded condition. We propose an expression for the reliability that is convenient when values of such probability are less than 15%. By using the proposed expression, one can estimate how much improvement in reliability any system gains by the predictive maintenance.

Functionally graded materials are a class of multifunctional materials that exhibit spatial variation in composition and microstructure. This deliberate variation is designed to effectively manage and manipulate changes in thermal, structural, or functional qualities within the material. The current study explores the system reliability of functionally graded porous beams (FGPB) subjected to buckling, focusing on the interplay of gradient index (0, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10), aspect ratio (5, 10, 15, 20, 25, 30 and 35), porosity index (0, 0.1 and 0.2) and boundary conditions (simply supported, clamped–clamped and clamped-free), with a particular emphasis on the k-out-of-n system reliability assessment, employing three distinct methods such as Evolutionary, GRG Non-linear, and Lagrangian. The results show the system's sensitivity to changes in distribution parameters, with the Lagrangian method being the most robust and stable. The 10-out-of-12 system reliability analysis demonstrates that aspect ratio and even porosity distribution are reliable, while uneven porosity is not. This study enhances structural reliability analysis in FGPBs, enhancing system reliability considerations and paving the way for further advancements in structural reliability analysis.

Wireless sensor networks have become pervasive in various applications, including environmental monitoring, smart cities, precision agriculture, and healthcare. In particular, linear wireless sensor networks that span considerable distances are increasingly deployed for applications such as pipeline monitoring and transportation systems. However, ensuring the reliability of long wireless sensor networks poses significant challenges due to the unique characteristics of the network topology and the constraints imposed by the resource-constrained sensor nodes. There is a notable lack of methods for the analysis and optimization of the reliability of large-scale sensor networks, and in this paper, we partially fill this gap. We propose a method for assessing the tradeoff between redundancy of forward error correction and reliable packet delivery. We also consider approaches to improve the reliability of linear sensor networks based on increasing topology connectivity and provide a corresponding method for the exact calculation of the all-terminal reliability. Numerical experiments demonstrate the relevance and effectiveness of our results. This research contributes to a deeper understanding of the underlying principles governing the reliability of long wireless sensor networks and provides valuable insights for the design, optimization, and management of such networks in real-world applications.

The last few decades have witnessed a dramatic evolution of Artificial Intelligence (AI) algorithms, represented by Deep Neural Networks (DNNs), resulting in AI-enabled systems being significantly dominant in various fields, including robotics, healthcare, and mobility. AI-enabled systems are currently used even for safety-critical applications, including automated driving, where they encounter reliability challenges from both hardware (HW) and software (SW) perspectives. However, there is no effective technique available that can diagnose HW and SW of AI-enabled systems in real-time during operation. Therefore, this paper proposes an intelligent real-time diagnostic technique for detecting HW and SW anomalies of AI-enabled systems and continuously improving the SW quality during operation. The proposed technique can detect HW anomalies to avoid unexpected changes in AI parameters and subsequent AI performance degradation using single context data with a detection accuracy of more than 92%. The proposed technique can also detect SW anomalies and identify edge cases in real-time, which could result in performance degradation by more than 50% compared to normal conditions. The identified edge cases can be used to continuously enhance the SW quality. Experimental results show the effectiveness of the technique for practical applications and thus can contribute to realize reliable and improved AI-enabled systems.

Considering the zoned shock effeteness, a multi-degradation system model subject to dependent competing failure processes is developed in this paper. The multi-degradation is constructed by the degradations in both a soft failure model and a hard failure model. Reliability assessment of the soft failure model has been widely studied, but degradation in a hard failure process with an extreme shock model has been rarely studied. The existing methods adopted approximate approaches to evaluate extreme shock model reliability with threshold degradation, which could not satisfy the accuracy requirement of system reliability calculation. To improve the calculation accuracy, a multi-degradation model subject to stochastic-dependent competing failure processes is investigated in this paper. A distribution-based algorithm is developed to calculate the extreme shock model reliability with threshold degradation. Furthermore, according to the effect of the shock process in the hard failure process, threshold degradation can be divided into degradation caused by both the zoned shock process and general degradation. Consequently, the closed-form formulas for system reliability with the multi-degradation model are derived. A case study is employed to illustrate the developed model, and the effectiveness of the algorithm is validated through Monte Carlo simulations.

Empirical life tests are used for reliability demonstration and determination of the actual reliability of the product. Therefore, engineers are faced with the challenge of selecting the most suitable test strategy out of the possible many and also the optimal parameter setting, e.g. sample size, in order to realize reliability demonstration with limited costs, time and with their available testing resources. It becomes even more challenging due to the stochastic nature of failure times and necessary cost and time being dependent on those. The considerations and guidelines in this paper are intended to simplify this process. Even simple products can fail due to several causes and mechanisms and usually have several components and subsystems. Therefore, this paper provides test planning options for single critical failure mechanisms as well as for systems with multiple failure mechanisms. For this purpose, the Probability of Test Success (Statistical Power of a life test) is used as a central, objective assessment metric. It is capable of indicating the probability of a successful reliability demonstration of a test and thus allows, for example, to answer the question of the required sample size for failure-based tests. The main planning resource is prior knowledge, which is mandatory due to the stochastic lifetime, in order to provide estimates for the Probability of Test Success at all. Therefore, it is also shown how to deal with uncertain prior knowledge and how the underlying information can additionally be used to increase the Probability of Test Success using Bayes’ theorem. The guidelines show how the most efficient test can be identified in the individual case and for individual boundary conditions.

In the dynamic landscape of electronic commerce, the robustness of platforms is a critical determinant of operational continuity and trustworthiness, necessitating innovative approaches to fault tolerance. This study pioneers an advanced strategy for enhancing fault tolerance in e-commerce systems, utilizing non-positional numbering systems (NPNS) inspired by the mathematical robustness of the Chinese Remainder Theorem (CRT). Traditional systems rely heavily on positional numbering, which, despite its ubiquity, harbors limitations in flexibility and resilience against computational errors and system faults. In contrast, NPNS, characterized by their independence, equitability, and residue independence, introduce a transformative potential for system architecture, significantly increasing resistance to disruptions and computational inaccuracies. Our discourse extends beyond theoretical implications, delving into practical applications within contemporary e-commerce platforms. We introduce and elaborate on new terminologies, concepts, and a sophisticated classification system for fault-tolerance mechanisms within the framework of NPNS. This nuanced approach not only consolidates understanding but also identifies underexplored pathways for resilience in digital commerce infrastructure. Furthermore, this research highlights the empirical significance of adopting NPNS, offering a methodologically sound and innovative avenue to safeguard against system vulnerabilities. By integrating NPNS, platforms can achieve enhanced levels of redundancy and fault tolerance, essential for maintaining operational integrity in the face of unforeseen system failures. This integration signals a paradigm shift, emphasizing proactive fault mitigation strategies over reactive measures. Conclusively, this study serves as a seminal reference point for subsequent scholarly endeavors, advocating for a shift towards NPNS in e-commerce platforms. The practical adaptations suggested herein are poised to redefine stakeholders’ approach to system reliability, instigating a new era of confidence in e-commerce engagements.

Scenario: System reliability monitoring focuses on determining the level at which the system works as expected (under certain conditions and over time) based on requirements. The edge computing environment is heterogeneous and distributed. It may lack central control due to the scope, number, and volume of stakeholders. Objective: To identify and characterize the Real-time System Reliability Monitoring strategies that have considered Artificial Intelligence models for supporting decision-making processes. Methodology: An analysis based on the Systematic Mapping Study was performed on December 14, 2022. The IEEE and Scopus databases were considered in the exploration. Results: 50 articles addressing the subject between 2013 and 2022 with growing interest. The core use of this technology is related to networking and health areas, articulating Body sensor networks or data policies management (collecting, routing, transmission, and workload management) with edge computing. Conclusions: Real-time Reliability Monitoring in edge computing is ongoing and still nascent. It lacks standards but has taken importance and interest in the last two years. Most articles focused on Push-based data collection methods for supporting centralized decision-making strategies. Additionally, to networking and health, it concentrated and deployed on industrial and environmental monitoring. However, there are multiple opportunities and paths to walk to improve it. E.g., data interoperability, federated and collaborative decision-making models, formalization of the experimental design for measurement process, data sovereignty, organizational memory to capitalize previous knowledge (and experiences), calibration and recalibration strategies for data sources.

In some settings, systems may not fail completely but instead undergo performance degradation, leading to reduced efficiency. A significant concern arises when a system transitions into a degraded state without immediate detection, with the degradation only becoming apparent after an unpredictable period. Undetected degradation can result in failures with significant consequences. For instance, a minor crack in an oil pipeline might go unnoticed, eventually leading to a major leak, environmental harm, and costly cleanup efforts. Similarly, in the nuclear industry, undetected degradation in reactor cooling systems could cause overheating and potentially catastrophic failure. This paper focuses on reliability modeling for systems experiencing degradation, accounting for time delays associated with undetected degraded states, self-repair mechanisms, and varying operating environments. The paper presents a reliability model for degraded, time-dependent systems, incorporating various aspects of degradation. It first discusses the model assumptions and formulation, followed by numerical results obtained from system modeling using the developed program. Various scenarios are illustrated, incorporating time delays and different parameter values. Through computational analysis of these complex systems, we observe that the probability of the system being in the undetected degraded state tends to stabilize shortly after the initial degradation begins. The model is valuable for predicting and establishing an upper bound on the probability of the undetected, degraded state and the system’s overall reliability. Finally, the paper outlines potential avenues for future research.

The convergence of heterogeneous wireless sensor networks provides many benefits, including increased coverage, flexible load balancing capabilities, more efficient use of network resources, and the provision of additional data by different types of sensors, thus leading to improved customer service based on more complete information. However, despite these advances, the challenge of ensuring reliability and survivability remains due to low-cost sensor requirements and the inherent unreliability of the wireless environment. Integrating different sensor networks and unifying protocols naturally leads to the creation of a network with multiple sinks, necessitating the exploration of new approaches to rational reliability assurance. The failure of some sensors does not necessarily lead to a shutdown of the network, since other sensors can duplicate information and deliver data to sinks via an increased number of alternative routes. In this paper, the reliability indicator is defined as the probability that sinks can collect data from a given number of sensors. In this context, a dedicated reliability metric is introduced and examined for its effectiveness. This metric is computed using an algorithm rooted in the modified factoring method. Furthermore, we introduce a heuristic algorithm designed for optimal sink placement in wireless sensor networks to achieve the highest level of network reliability.

The complexity of large-scale systems has greatly increased and the tools for monitoring complex systems and ensuring their reliability have also been vastly studied. This study presents a tool to improve the understanding of the state-of-health of complex systems with several subsystems and components and partial observability. Many real systems can have issues with monitoring due to the cost of monitoring or physical limitations for constant monitoring. The proposed method in this study tackles this issue by utilizing all available, limited data to better predict system performance. A Multi-scale Multi-Fidelity Bayesian Learning framework is proposed to provide an online tool for component failure prediction as well as system prognostics. A Dynamic Bayesian Network is used to model the dependencies between components in a system and their impact on system failure. Multi-Fidelity Networks is then used to continuously update the parameters in the network to leverage online data to improve the predictive results. A case study of the leakage failure mode of an offshore production well is conducted to highlight the applicability as well as the benefit of the proposed approach. The results show the advantage of accounting for high-fidelity data to inform low-fidelity data for complex systems. • A new Bayesian learning method is developed for reliability analysis. • A dynamic Bayesian network is employed for system modeling. • Multi-fidelity network is integrated with a dynamic Bayesian network for multiscale system failure analysis. • Multi-fidelity data can be used for conditional probability of failure analysis. • A case study is carried out for production well reliability analysis. [ABSTRACT FROM AUTHOR]

The reliability of folding wing deployment performance greatly impacts flight vehicle reliability. Based on the dynamic analysis theory, the deployment dynamic model of folding wing mechanism with joint clearances is established and solved. Considering the failure correlation, the system reliability models are developed for both cases, without considering synchronization and considering synchronization. For the former, a solution method combining saddle point approximation and numerical integration is proposed. For the latter, an estimation method based on a combination of the fourth order moment Pearson distribution family and the numerical integration is proposed. The efficiency and accuracy of the proposed methods are verified through examples. In addition, the trend of the system reliability change when the distribution parameters of random variables are different is also analyzed. From the perspective of improving reliability, the above study can provide theoretical guidance and data support for the design, manufacturing and service process of the folding wing mechanism system. [ABSTRACT FROM AUTHOR]

In the dynamic landscape of electronic commerce, the robustness of platforms is a critical determinant of operational continuity and trustworthiness, necessitating innovative approaches to fault tolerance. This study pioneers an advanced strategy for enhancing fault tolerance in e-commerce systems, utilizing non-positional numbering systems (NPNS) inspired by the mathematical robustness of the Chinese Remainder Theorem (CRT). Traditional systems rely heavily on positional numbering, which, despite its ubiquity, harbors limitations in flexibility and resilience against computational errors and system faults. In contrast, NPNS, characterized by their independence, equitability, and residue independence, introduce a transformative potential for system architecture, significantly increasing resistance to disruptions and computational inaccuracies. Our discourse extends beyond theoretical implications, delving into practical applications within contemporary e-commerce platforms. We introduce and elaborate on new terminologies, concepts, and a sophisticated classification system for fault-tolerance mechanisms within the framework of NPNS. This nuanced approach not only consolidates understanding but also identifies underexplored pathways for resilience in digital commerce infrastructure. Furthermore, this research highlights the empirical significance of adopting NPNS, offering a methodologically sound and innovative avenue to safeguard against system vulnerabilities. By integrating NPNS, platforms can achieve enhanced levels of redundancy and fault tolerance, essential for maintaining operational integrity in the face of unforeseen system failures. This integration signals a paradigm shift, emphasizing proactive fault mitigation strategies over reactive measures. Conclusively, this study serves as a seminal reference point for subsequent scholarly endeavors, advocating for a shift towards NPNS in e-commerce platforms. The practical adaptations suggested herein are poised to redefine stakeholders' approach to system reliability, instigating a new era of confidence in e-commerce engagements. [ABSTRACT FROM AUTHOR]

Hybrid free‐space optical and radio frequency (FSO/RF) systems have attracted much attention for more than a decade because of their enhanced reliability and capacity as comparison to single FSO or RF systems. Existing schemes to construct such a hybrid system are usually to use either switching or encoding/decoding strategies for combination of channels. The proposed scheme, based on packet sharing strategy of Ethernet link aggregation, provides a different way to combine FSO and RF channels. Theoretical analysis and Experimental results show that the proposed scheme does enhance the reliability and utilize both channel capacities for a multi‐channel system. Moreover, this scheme is simple and scalable because more channels can be combined based on such a packet sharing strategy without modifying the physical channel structures, therefore, this scheme may provide a good solution for constructing an efficient and cost‐effective hybrid FSO/RF system. [ABSTRACT FROM AUTHOR]

In order to improve on system reliability, utilities conduct contingency scenarios to determine the impact of component outages to the network. It is usually challenging to conduct this analysis due to the complex grid structure. However, the huge consequences of an equipment outage on the grid and the connected loads are compelling enough for researchers to find ways to mitigate these events. Several blackouts have occurred in various parts of the Southern Interconnected Grid (SIG) of Cameroon due to the transient state of the power system. The most recent was the blackout that kept a greater part of the country's political capital, Yaounde, for several days with no electricity. The paper analyses 44 single line (N-1) contingency scenarios in the SIG using ETAP in order to evaluate the impact of line outage events on grid stability. A combined performance index was calculated from the bus voltage security index (PIV/Vsp), real power flow index (PIΔP), reactive power flow index (PIΔQ) and the branch overloading security index (PIS/Ssp). The results showed that the Mangombe - Oyomabang line outage (scenario 22) was the most severe with the load flow failing to converge, followed by the Oyomabang - Ngousso line 1 (scenario 36) with combined performance indices of 992.6191 and 79.74415 respectively. Other scenarios showed overloaded lines, overloaded transformers, high power losses and under/over bus voltages. This study has identified lines with high vulnerability and should be used by utility operators to enhance the reliability of the transmission network and minimize its susceptibility to cascaded power outages.

Multi-objective design optimization problems offer a set of solution alternatives within a Pareto-front. In structural design, the design variables are typically the section properties. The outcomes of these design variables are usually used in selecting standard sections. However, the properties of the selected standard sections normally have different values from the determined design variables. Accordingly, the values of the objective functions for these solutions will change after selecting standard sections. This change may be different among these solutions. Thus far, only Pareto-optimal solutions have been standardized in the literature. The effects of the inclusion of non-Pareto solutions in the standardization process have never been examined. In this paper, the differences between including the near-optimal solutions and not including them in the final structural design optimization set are explored. The paper investigates the impact of selecting standard sections on both Pareto-front solutions and near-optimal solutions, and it studies the importance of keeping track of the near-optimal solutions. A modified version of a multiple-objective particle swarm optimization method, enhanced with a proposed computationally efficient section standardization algorithm, is used to solve multi-objective system-reliability design optimization problems. The concepts of the paper are applied to examples of bridge structures. The results demonstrate the efficiency of the proposed technique in capturing final design solutions that would have been otherwise missed due to standardization.

For the overall safety evaluation of the tension leg platform (TLP) system, the structural strength reliability analysis is essential. The strength reliability of a typical TLP exposed to combined static and extreme wave loads is the subject of this study. A three-dimensional finite element shell model made up of a pontoon, column, and deck that is assumed to be accurate and efficient with tendon system as the boundary conditions was built using a concrete TLP. By employing the proportional loading method based on the design wave method, failure mechanisms for the platform and were determined. The failure mechanisms were then used to derive limit state expressions. The system reliability indexes of the object platform were calculated using the system reliability assessment framework created by the system reliability model suggested in this paper. This work seeks to advance the application of reliability theory in offshore engineering.

Fatigue damage can lead to failures of structural systems. To reduce the failure risk and enhance the reliability of structural systems, inspection and maintenance interventions are required, and it is important to develop an efficient inspection strategy. This study, for the first time, develops a system-level reliability growth model to establish efficient inspection planning. System-level reliability growth is defined as an increase in the percentage of the system reliability index with and without inspection. The probabilistic S-N approach is used to obtain the reliability index without inspection. Moreover, advanced risk analysis and Bayesian inference techniques are used to obtain the reliability index with inspection. The optimal inspection planning is obtained by maximizing system-level reliability growth. This model is applied to an offshore wind farm. The results show that inspection efficiency can be improved by increasing the number of repair objects in response to a ‘detection’ inspection outcome, changing the inspection object for each inspection, and increasing the inspection quality. The maximum system-level reliability growth gained from one additional inspection decreases as the number of inspections increases. This study quantifies the inspection efficiency of offshore wind farms by explicit system-level reliability growth computation, offering valuable insights for promoting sustainable energy solutions.

The aim of this research is to devise a continuous simulation model for predicting ship crane failures to increase their reliability and reduce unplanned downtime during cargo loading and unloading operations. To predict the condition of the hydraulic system, a database from the GALIOT software package was used for carrying out maintenance on cranes at m/v “O” over a period of 120,000 working hours. In the research, fault tree analysis (FTA) was used to identify causal relationships between system failures and basic events, while the Markov mathematical model was used to model the system state and predict transitions between different failure states. A system dynamics simulation model was developed to simulate the behavior of a system using POWERSIM PowerSim Constructor 2.5.d (4002), and regression analysis was performed to analyze the simulation results and understand the relationships between dependent and independent variables. The results show that a model for predicting failures in the hydraulic motors and pumps of ship cranes was developed, and the Markov model makes it possible to estimate the frequency of transitions between states under the condition that the sum of reliability equals one. The simulation model shows high reliability of the cranes and a constant frequency of failures throughout the 120,000 operating hours, while the regression analysis confirms the validity of the simulation model and shows a strong correlation between the analyzed variables. These models are used to improve the planning of ship crane maintenance, reduce unplanned downtime, and predict and promptly detect failures, which overall minimizes maintenance costs and failures.

Wireless sensor networks (WSNs) are attracting increasing research interest due to their ability to monitor large areas independently. Their reliability is a crucial issue, as it is influenced by hardware, data, and energy-related factors such as loading conditions, signal attenuation, and battery lifetime. Proper selection of sensor node positions is essential to maximise system reliability during the development of products equipped with WSNs. For this purpose, this paper presents an approach to estimate WSN system reliability during the development phase based on the analysis of measurements, using strain measurements in finite element (FE) models as an example. The approach involves dividing the part under consideration into regions with similar strains using a region growing algorithm (RGA). The WSN configuration is then analysed for reliability based on data paths and measurement redundancy resulting from the sensor positions in the identified measuring regions. This methodology was tested on an exemplary WSN configuration at an aircraft wing box under bending load and found to effectively estimate the hardware perspective on system reliability. Therefore, the methodology and algorithm show potential for optimising sensor node positions to achieve better reliability results.

The parameters of gravity dams and foundation materials objectively exhibit spatial variability due to environmental and load influences, which significantly affect the safety status of dam structures. Therefore, a safety risk analysis method for a gravity dam–foundation system based on random field theory is proposed in this paper. Spatial variabilities in materials are particularly considered by using the finite element method. Then, composite response surface equations for the performance function (PF) of strength and stability failure are established, and then, the system failure risk is obtained using the Monte Carlo method. The proposed method solves the problem wherein the effect of spatial variability on failure risk cannot be reflected accurately by the performance function of multi-element sliding paths, and the difficulties in solving the failure risk of the series–parallel system due to multiple failure paths and their complex correlations. The application of a gravity dam shows that the developed method overcomes the disadvantages of the traditional method, such as the homogenization of the spatially random characteristics of parameters and the overestimation of failure risk in the system due to large variance estimation.

Abstract Hybrid free‐space optical and radio frequency (FSO/RF) systems have attracted much attention for more than a decade because of their enhanced reliability and capacity as comparison to single FSO or RF systems. Existing schemes to construct such a hybrid system are usually to use either switching or encoding/decoding strategies for combination of channels. The proposed scheme, based on packet sharing strategy of Ethernet link aggregation, provides a different way to combine FSO and RF channels. Theoretical analysis and Experimental results show that the proposed scheme does enhance the reliability and utilize both channel capacities for a multi‐channel system. Moreover, this scheme is simple and scalable because more channels can be combined based on such a packet sharing strategy without modifying the physical channel structures, therefore, this scheme may provide a good solution for constructing an efficient and cost‐effective hybrid FSO/RF system.

The paper presents an iterative approach based on stochastic simulations and adaptive Kriging metamodels to perform reliability and safety assessments of soil slopes. Two new rules for adaptively selecting support points are proposed, considering an entropy learning function and the closeness to the failure domain defined by a limit state function. In addition, a stopping criterion is proposed based on root-mean-square and mean absolute percentage errors computed with cross-validation at the local level, focusing on regions where the uncertainties are relevant. Finally, the selection rules for support points and the error metrics are implemented in two benchmark problems with a low, moderate, and high probability of failure. Ultimately, the work leads to an adaptive Kriging strategy for slope stability assessment, offering: (1) a fair comparison with other strategies based on a significant number of realizations, (2) a stopping criteria based on a new local error metric, (3) an insight of the behavior across different magnitudes of the probability of failure, and (4) a new selection rule that reduces the total number of support points significantly. The proposed scheme is easily paired with commercial software to compute support points, resulting in an attractive tool for practitioners.

The state of the Ghana Power System reflects a story of progress, challenges, and future potential. Ghana has experienced significant milestones and achievements in its power system, including the development of major infrastructure projects such as the Akosombo Dam and initiatives to expand access to electricity. The country has also made strides in diversifying its energy mix by embracing renewable energy sources. However, challenges exist, including the need to address system reliability, aging infrastructure, financial viability, and rural electrification. The integration of emerging technologies, such as smart grid solutions, energy storage systems, and regional power interconnections, offers opportunities for a sustainable and reliable power system. Recommendations for Ghana's power sector focus on diversification, grid flexibility, infrastructure upgrades, energy efficiency, institutional strengthening, and regional cooperation. Implementing these recommendations holds the promise of building a resilient, affordable, and environmentally sustainable power system for Ghana's future.

In classical survival analysis, it is assumed that all the individuals will experience the event of interest. However, if there is a proportion of subjects who will never experience the event, then a standard survival approach is not appropriate, and cure models should be considered instead. This paper deals with the problem of adapting a machine learning approach for classical survival analysis to a situation when cure (i.e., not suffering the event) is a possibility. Specifically, a brief review of cure models and recent machine learning methodologies is presented, and an adaptation of machine learning approaches to account for cured individuals is introduced. In order to validate the proposed methods, we present an extensive simulation study in which we compare the performance of the adapted machine learning algorithms with existing cure models. The results show the good behavior of the semiparametric or the nonparametric approaches, depending on the simulated scenario. The practical utility of the methodology is showcased through two real-world dataset illustrations. In the first one, the results show the gain of using the nonparametric mixture cure model approach. In the second example, the results show the poor performance of some machine learning methods for small sample sizes. [ABSTRACT FROM AUTHOR]