Distribution network reconfiguration is a key strategy for achieving a secure, reliable, and economically efficient electricity supply. This paper proposes an optimization-based reliability enhancement framework for distribution systems through network reconfiguration and distributed generation (DG) integration using a Hybrid Tunicate Swarm Bat Algorithm (TSBA). The proposed approach simultaneously minimizes active power losses while improving the operational reliability of the distribution network. A comprehensive reliability evaluation framework is incorporated to address the uncertainties and imprecision associated with reliability data by considering multidimensional reliability assessment indicators. The proposed optimization and reliability evaluation framework is validated on the IEEE 33-bus and IEEE 69-bus distribution systems. The simulation results demonstrate substantial improvements in network performance, achieving 66% and 92% reductions in active power losses for the IEEE 33-bus and IEEE 69-bus systems, respectively. Furthermore, the proposed framework significantly enhances system reliability, improves the voltage profile, and reduces voltage deviation while maintaining secure network operation. These results confirm the effectiveness of the TSBA-based optimization framework as a robust and practical solution for improving the efficiency, reliability, and operational performance of modern distribution networks with DG integration.
In reliability analysis, product lifetime is a critical quality characteristic, particularly in industries where durability defines performance. Since monitoring every unit is costly, censored life tests are commonly used, followed by control charts to evaluate lifetime behavior. However, failure-time data often contain uncertainty arising from measurement errors, device limitations, or operator variability. This research proposes two new statistical monitoring tools - the Fuzzy Mixed EWMA-CUSUM (Fuzzy MEC) and the Neutrosophic Mixed EWMA-CUSUM (Neutrosophic MEC) charts - to address lifetime monitoring under uncertainty. The charts are developed for failure-censored life tests without replacement, assuming a Weibull distribution with a fixed shape parameter and variable scale. Control limits and performance measures such as average out-of-control run lengths are obtained using Monte Carlo simulation. In the fuzzy framework, triangular fuzzy numbers model imprecise failure times, and alpha-cuts of 0.65 and 1 are examined using the fuzzy midrange transformation. Results indicate that the Fuzzy MEC chart with midrange at alpha = 0.65 provides superior detection capabilities compared with the fuzzy mode. The Neutrosophic MEC chart further improves performance, demonstrating better sensitivity than both the classic and fuzzy MEC charts when uncertainty is high.
This study investigates multi-class production systems in which products are categorized according to a key quality characteristic, namely their primary function, to satisfy diverse customer requirements. Unlike traditional models that treat all conforming products as fulfilling a single, homogeneous demand, the proposed approach explicitly considers distinct demand requirements for each class, thereby ensuring that products from one class cannot substitute for those of another. To assess the performance of production systems with product classification, system reliability is adopted as the performance metric, defined as the probability of successfully fulfilling the demands of all product classes. The production system is modeled as a multi-state production network (MPN), which captures uncertainties in workstation capacities and represents the manufacturing configuration through a network-based structure. An efficient algorithm is developed to assess system reliability based on the concept of the lower boundary vector. System reliability serves as a quantitative basis for decision-making in order acceptance and production planning under uncertainty.
This paper investigates the complexity of inactivity times of the failed components in coherent systems through the lens of cumulative residual extropy and its divergence-based extension, Jensen–cumulative residual extropy. Unlike classical reliability metrics that focus on system inactivity or mean residual life, our framework quantifies the hidden informational structure of inactivity times of the failed components at the coherent system still functioning though some of its components have failed. We derive closed-form expressions for the cumulative residual extropy of inactivity times of the failed components using system signatures and establish stochastic bounds and comparisons that highlight the impact of structural configuration. A novel divergence measure, the Jensen–cumulative residual extropy, is introduced to capture discrepancies between coherent systems and benchmark [Formula: see text]-out-of-[Formula: see text] structures. Numerical illustrations with Weibull-distributed lifetimes demonstrate the sensitivity of cumulative residual extropy and Jensen–cumulative residual extropy to redundancy patterns and dependence structures. Furthermore, by integrating cost considerations into the divergence framework, we provide a rigorous optimization scheme for selecting system signatures that jointly minimize informational complexity and economic expenditure. The proposed approach enriches the theoretical foundation of reliability analysis and offers practical guidelines for designing resilient, cost-effective, and information-efficient engineering systems.
This paper introduces a two-dimensional warranty policy that accounts for both product age and usage with failure interactions considering preventive maintenance actions. The policy jointly specifies the warranty coverage as well as the period during which a refund or replacement may be offered for a repairable product whose failure rate increases over time. Coverage depends on the product's age and usage, and it ends as soon as either a prescribed age limit or a prescribed usage limit is reached, whichever occurs first. A distinctive aspect of the proposed framework is its incorporation of a lemon period motivated by lemon law, under which the manufacturer is obligated to provide a refund. Importantly, a refund is provided only when a failure satisfies predefined criteria related to either the number of failures or the duration of each repair. The lemon period is typically assumed to be shorter than the overall warranty period. After the refund window closes, any subsequent failures are addressed only through minimal repairs until the warranty expires. The study further models a multicomponent system by considering preventive maintenance actions, their effectiveness on system reliability, and the failure interactions between critical and noncritical components. Given a specified cost structure, we investigate the expected total warranty cost rate over the age-based warranty horizon and determine the optimal age-based warranty length from the manufacturer's perspective. A numerical example is provided to illustrate and evaluate the applicability of the proposed warranty policy.
Accelerated life testing is used to measure the lifetime of highly reliable products. These products can work for a long time under normal use conditions; however, the producers want to know their lifetime before marketing. To accelerate the lifetime of a product, the high stress is applied. In this study, we assumed that the lifetime of a product at constant stress level follows exponentiated Pareto distribution. To estimate the parameters of the model, the maximum likelihood, the least squares, the weighted least squares, the maximum product of spacing, minimum spacing absolute-long distance and the minimum distance methods, namely, the Cram & eacute;r-von Mises, the Anderson-Darling and right-tail Anderson-Darling methods are used. The performances of the proposed estimates are compared via the Monte-Carlo simulation study. A real data set is analyzed for illustrative purposes.
Multivariate process capability analysis aims to assess the ability of a manufacturing process to meet the specification limits of multiple quality characteristics (QCs). Most of the existing multivariate process capability analysis approaches rely on modifications of tolerance or process region and/or restrictive assumptions, are computationally intensive and provide few cues for process improvement. This paper aims to address these issues by proposing a max-operator-based capability analysis approach for a process with multiple QCs. The proposed approach first transforms the measurement data into dimensionless data with a common upper specification limit of one, and then aggregates the transformed QCs into an overall performance indicator using the max-operator aggregation model, which ensures that all the specification limits are exactly met and considerably simplifies the analysis. The overall performance indicator is modeled by an appropriate distribution, and the process capability is assessed from the fitted right-tail distribution. When the process is deemed to be incapable, a root cause analysis is carried out to provide the information useful for process improvement. A real dataset is analyzed, and a case study on gear grinding is included to illustrate the appropriateness and usefulness of the proposed approach.
In engineering reliability and safety studies, accurately modeling lifetime data that are strictly positive and integer-valued is critical for understanding failure mechanisms and improving system performance. This paper introduces a novel zero-truncated discrete transmuted Gompertz–Makeham distribution aimed at enhancing the flexibility and applicability of discrete lifetime models encountered in reliability engineering. The proposed model extends existing discrete distributions by incorporating a transmutation mechanism that enables more versatile hazard rate behavior and improved fit to complex failure patterns. We derive key distributional and reliability properties of the model, including closed-form expressions for the probability mass function, survival function, hazard rate, and other dynamic reliability measures, and illustrate their behavior through comprehensive graphical analysis. Parameter estimation is conducted using the maximum likelihood method to ensure robust and efficient inference. The practical utility of the proposed distribution is demonstrated through applications to two real engineering datasets: Aircraft windshield failure times and the number of stress cycles until failure. These empirical studies, drawn from critical engineering contexts, show that the model provides superior fit and enhanced interpretability compared to established zero-truncated discrete alternatives. The results confirm the model’s capability to effectively capture the underlying lifetime characteristics of engineering systems where only positive outcomes are observed. The findings emphasize the potential of the proposed distribution as a valuable tool for reliability practitioners and researchers concerned with lifetime and safety analysis in engineering domains.
We investigate a retrial [Formula: see text]-out-of-[Formula: see text]:[Formula: see text] system that includes both cold and warm standbys and [Formula: see text] reliable repairers through generalized stochastic Petri nets (GSPNs). The system comprises [Formula: see text] active units, [Formula: see text] warm units in standby, and [Formula: see text] cold units in standby. The failures of both primary and warm standby components are modeled as a Poisson process. Failed components immediately undergo repair if a repairer is available; otherwise, they join an FCFS orbit. The tangible marking process of the GSPN model can serve to generate a Markov chain with continuous-time (CTMC). After solving the statistical equilibrium equations in matrix form, various performance measures are obtained. From the reliability viewpoint, using the Laplace transform method, the expression for the reliability function and the mean-time to failure (MTTF) are derived. The influence of the system parameters on performance measures, [Formula: see text], reliability function, and MTTF is clarified with numerical examples.
Addressing the reliability challenges faced by wind turbine planetary gearboxes - such as strength degradation and coupled multi-failure modes under complex operating conditions - this study proposes a reliability optimization method that integrates dynamic degradation modeling and multi-failure correlation analysis. A strength degradation model is established by combining the Probability-Stress-Life (P-S-N) curve with the Wiener process. A dynamic reliability framework, which adopts the quadratic fourth-order moment method to improve accuracy compared with traditional second-order approaches, is developed to evaluate the bending and contact fatigue reliability over a 15-year service life. A novel mixed Copula function is utilized to quantify the time-dependent correlations between different failure modes. An optimization model is formulated to minimize the joint failure probability, with constraints including transmission parameters, modulus, tooth width, volume, and deformation, and solved using the Dung Beetle Optimizer (DBO) algorithm. Optimization results show that the system volume is reduced by 4.2% (to 1.13 & times; 10(9)mm(3)) and the deformation of critical components is decreased by over 75%. After 15 years of service, the bending fatigue reliability reaches 0.9568 (sun gear), 0.9414 (planetary gear), and 0.9671 (ring gear), while the contact fatigue reliability achieves 0.9504, 0.9316, and 0.9377, respectively. This approach overcomes the limitations of static models by addressing strength degradation and failure coupling, providing a theoretical and technical basis for designing lightweight, high-stiffness, and long-life gearboxes, thereby enhancing the reliability of wind turbines.
By using the expectation-maximization technique, this paper tackles the crucial issue of estimating unknown parameters in competing risks models. In a framework with latent failure periods following exponential and Weibull distributions, we develop Bayesian estimates under linear-exponential and squared-error loss functions, in addition to standard maximum likelihood estimates. The accuracy of the suggested estimators is evaluated in a thorough simulation exercise using a range of parameter values. Additionally, two real-world datasets in engineering and survival areas illustrate the methodology's applicability. The outcomes demonstrate that the expectation-maximization method can handle partial cause-of-failure data, making it a flexible tool for reliability and survival research.
This paper presents a novel framework for evaluating the network reliability of stochastic flow networks (SFNs) by integrating fuzzy set theory to address the inherent uncertainty in lead time constraints. Traditional network reliability models typically assume deterministic lead times, which fail to capture the variability and imprecision encountered in real-world operational environments. To overcome this limitation, this research represents lead times as fuzzy numbers using triangular membership functions, thereby enabling a more realistic characterization of temporal uncertainty in network performance analysis. The proposed methodology employs alpha -cut operations at multiple confidence levels to transform fuzzy lead times into crisp intervals, generating both optimistic (best-case) and pessimistic (worst-case) reliability scenarios for each alpha-level. By systematically evaluating the network across different confidence thresholds, the framework produces reliability intervals that reflect the full spectrum of uncertainty. Such SFNs serve as probabilistic models for analyzing system capacity. These fuzzy reliability results are subsequently converted into a single, actionable crisp value through the Center of Area (COA) defuzzification method, facilitating practical decision-making while preserving the richness of uncertainty information. The proposed approach offers significant advantages for network planning and resource allocation in contemporary infrastructure systems, including transportation, energy distribution, and communication networks, where operational parameters are subject to volatility and uncertainty. By acknowledging and quantifying inherent uncertainties while providing risk-aware insights through reliability intervals, this framework supports more robust and informed decision-making in dynamic operational environments.
This study investigates the performance of goodness-of-fit tests for the ARA(infinity)-PLP imperfect maintenance model, with a particular emphasis on entropy-and extropy-based test statistics. Test statistics are constructed using three different approaches: martingale residuals, probability integral transform, and information-based measures. Extensive simulation studies are conducted under several alternative hypotheses, including ARA1, ARA(infinity)-LLP, QR, EGP, and Brown-Proschan models, to evaluate the empirical power of the proposed tests. In addition to numerical power comparisons, graphical analyses are employed to illustrate the behavior of the test statistics and to provide further insight into their sensitivity under different repair scenarios. The simulation results demonstrate that entropy-and extropy-based statistics generally outperform classical goodness-of-fit tests, particularly in detecting deviations from the null model under moderate and severe imperfect repair effects. The consistency observed between graphical patterns and numerical findings further confirms the robustness and interpretability of the proposed procedures. An application to a real dataset related to automobile failure times illustrates the practical effectiveness of the methodology and supports the suitability of the ARA(infinity)-PLP model for real-world repairable systems.
Machine learning (ML) techniques have gained traction in software bug detection. A persistent challenge in ML-based approaches arises from the imbalance between correct and incorrect training data. Specifically, there is a scarcity of incorrect data (containing bugs) compared to the abundance of correct data, degrading model performance. To mitigate this, researchers have proposed artificially injecting bugs into correct code to augment datasets. In addition to balancing data distribution, diversity in training examples significantly affects model performance. Programs written in high-level languages can exhibit a wide range of syntactic variations while maintaining identical functionality. Motivated by this observation, the objective of our research is to generate diverse incorrect examples stemming from a single root cause (i.e., a specific bug). Specifically, we plan to inject bugs into LLVM IR code and translate it into high-level source code using a probabilistic language model. In this paper, we present a preparatory step toward that goal: the generation of correct, bug-free examples using an IR-to-C translator based on a sequence-to-sequence (seq2seq) architecture. We investigate the resulting consistency and diversity of the generated correct examples by training the model on real-world software code.
Surrogate models are widely utilized in performance reliability analysis due to their superior abilities in balancing computational cost and accuracy. However, few of the existing relevant studies effectively integrate multi-fidelity information, leading to inefficiency in estimating small failure probabilities. To address this, a clustering-based surrogate modeling method under multiple failure modes is proposed, systematically incorporating both high-and low-fidelity data. Specifically, an active learning strategy guided by clustering selectively retains high-value sample points to promote surrogate accuracy during iteration. Besides, it integrates mixed-weight importance sampling to evaluate system failure probability while reflecting the contribution of individual failure modes, with optimal model parameters via particle swarm optimization algorithm. The proposed approach enhances the efficiency of small failure probability analysis by innovatively integrating clustering-based multi-fidelity data and quantifying failure mode interactions with mixed weights. Numerical and engineering studies demonstrate that PRA-MFCS achieves superior accuracy and efficiency compared to traditional channels, providing a reliable tool for the refined design of complex mechanical systems.
The present study proposes a multi-criteria approach for prioritizing failure modes in naval systems, with the aim of improving decision-making for sustainable maintenance strategies. It builds upon a previous conference paper that introduced a framework for failure modes prioritization in autonomous ship navigation systems. The analysis is conducted through two parallel paths. The Analytic Hierarchy Process (AHP) was first independently applied to determine the relative importance of criteria and to produce a complete ranking of failure modes. Second, the AHP is combined with the ELimination Et Choix Traduisant la REalite I (ELECTRE I) method with the goal to integrate pairwise weighting with the outranking logic, thus obtaining an alternative prioritization. The criteria set includes both traditional Failure Mode, Effects and Criticality Analysis (FMECA) dimensions, which are Severity, Occurrence and Detection, and some additional ones that characterize the specific scenario, that are Economic Factor (EC), Sustainability Maintenance Strategies (SMS) and Management and Data Security (MDS). The first-ranked failure mode from AHP standalone analysis is compared with the top-ranked result of the integrated AHP+ELECTRE I approach to highlight analogies and discrepancies. Finally, a sensitivity analysis is performed to evaluate the robustness of the findings.
This paper presents an integrated flood prevention framework for substations, combining a fuzzy Bayesian network (FBN) for continuous flood risk assessment with mixed integer linear programming (MILP) for real-time resource allocation. Building on recent studies of substation resilience and flood mitigation, the proposed approach captures both static site data and dynamic meteorological inputs to generate accurate, up-to-the-minute predictions of flood probability. The MILP model then allocates resources, such as pumps, barriers, and drainage systems, based on the FBN's probabilistic estimates. In tests conducted on a 500 kV substation under simulated flood scenarios, the proposed system achieved higher accuracy and lower computational overhead relative to mainstream methods, including decision trees (DT), k-nearest neighbors (KNNs), and support vector machines (SVMs). A sensitivity analysis further revealed the model's robust performance under varying flood severities and resource constraints, highlighting its potential for broader deployment. While the results underscore notable advantages in adaptability and operational resilience, challenges remain in gathering consistent, high-quality data and scaling the model for large or complex networks. Overall, this study offers a proactive, data-driven strategy for enhancing substation flood prevention efforts and reducing outage risks under extreme weather conditions.
Accurate prediction of the remaining useful life (RUL) is crucial for avoiding unscheduled downtime, enhancing safety, and reducing maintenance costs. Traditional methods face challenges with high-dimensional, nonlinear, and uncertain data. This paper presents a framework based on Bayesian additive regression trees (BART), integrating RUL prediction with feature selection. The model is trained and tested on the NASA CMAPSS dataset, identifying key sensor features through SHAP analysis. Results show that BART can achieve accurate predictions, reasonable uncertainty estimates, and effectively identify critical variables.
As a typical external disaster, earthquakes not only can trigger the failure of individual nuclear power equipment but may also lead to common-cause failures, thereby significantly increasing the risk of systemic failure. To assess seismic risk of multi-equipment common-cause failures, this paper constructs an integrated probabilistic analysis framework of "ground motion parameter-equipment response-system failure." Based on a system failure probability modeling approach that considers failure dependencies, probabilistic risk parameters derived from seismic hazard analysis and seismic fragility assessments are integrated to achieve accurate quantification of multi-equipment failures. Quantitative analysis of failure dependencies under varying ground motion intensities is conducted based on the alpha-factor model, revealing a significant nonlinear evolutionary pattern of failure correlation coefficients with respect to ground motion intensity. The rationality of the framework and methodology is validated through practical case studies. This research provides an analytical tool with both theoretical rigor and engineering applicability for seismic risk assessment in the nuclear engineering field, effectively enhancing the precision of probabilistic safety analysis for complex redundant systems.
Optimal single sampling inspection plans with fixed acceptance numbers are developed to provide the appropriate protection to consumers when the lifetime of products follows a type-I half-logistic Nadarajah-Haghighi (TIHLNH) distribution. The best inspection plan using percentile life as a measure of reliability is determined when the conventional consumer risk is specified. Operating characteristic (OC) values for the different quality level options are reported. A minimum ratio between the true median life and the pre-specified life has been supplied for the specific producer's risk. The optimal single sampling plans are then derived using prior knowledge on fraction defective by controlling the expected consumer risk in the Bayesian setting. The results show that the proposed Bayesian sampling plans are more efficient than the current sampling plans in terms of sample size. For illustrative purposes, the proposed methods are applied to a real dataset.
