System Reliability Indices Research Articles

Estimating the Reliability and Sensitivity of a Public Address System Through the Markov Decision Process

This research aims to evaluate the reliability indices of a public address system (PAS) through the Markovian approach. Many organizations and businesses use this system to address or broadcast a message or pass on important information to the huge gatherings assembled at big premises. This system is the nerve of these organizations and businesses. The major components of a PAS are a microphone, mixer, amplifier, and speaker. These components should work in harmony with one another to execute the intended task. Any failure in these components leads to big issues for the public, and they may miss very important information. Therefore, the reliability assessment of this system is of utmost importance. The authors used the Markovian decision process to model the PAS by analyzing the various failure rates and repairs of the components. The explicit expressions for reliability, availability, and MTTF have been obtained for clear understanding about the PAS behavior with time as well as different failures. The sensitivity analysis of reliability is performed as well to determine the critical components of the system. The obtained results show that the reliability of the PAS at 2000 operated hours is 0.8. Also, the finding reflects that the PAS reliability is much sensitive with the failure rate of microphone, mixer, and amplifier.

The impact of high‐voltage circuit breaker condition on power system reliability indices

AbstractCondition monitoring data can be used to assess the health of a power system component but is rarely used to assess the reliability of the power system they are part of. For high‐voltage circuit breakers (HVCBs), the susceptibility to various failures can be assessed by examining trip coil current (TCC) measurements. HVCBs have two failure modes, failure to trip on command and tripping without a command, which are triggered by various failure mechanisms that in turn may depend on the technical condition of the HVCBs. The aim of this article is to demonstrate a methodology for quantifying the impact that the technical condition of HVCBs has on the power system reliability indices. An equivalent transmission line failure rate considering protection system failures, including failures related to HVCBs, can be calculated by computing contributions from various fault types (FTs). This article proposes a framework that can quantify the frequency of the FTs that are affected by HVCB condition. The system‐level effects are then evaluated using approximate methods for power system reliability evaluation. To demonstrate the principles and benefits of this methodology, a case study is presented that incorporates HVCB condition data from the Icelandic transmission grid into an illustrative 4‐bus test system; a dataset of 83 TCC measurements from 38 HVCBs from the Icelandic Transmission System Operator is used, together with an outage database of life histories of 464 HVCBs from the Icelandic transmission grid. Results indicate that the condition deterioration associated with the probability of an HVCB failing to trip on command can significantly degrade the reliability indices.

Enhancing safety and reliability in multistory construction: A multi-state system assessment of shoring/reshoring operations using interval-valued belief functions

Ensuring safety and reliability in multistory concrete construction necessitates rigorous assessment methodologies capable of addressing the inherent uncertainties of the construction process. This paper introduces a novel reliability assessment methodology for shoring/reshoring (S/R) operations, framed within a multi-state parallel-series system (MSS). Our approach innovatively combines concrete slab capacities, forming system strengths, and construction quality, integrating cost and time efficiencies. Central to our method is the use of Interval Universal Generating Functions (IUGF), which leverage Dempster-Shafer (D-S) theory and interval analysis to robustly estimate system reliability under uncertainty. For instance, the model considers concrete strength ranging from 0.72 × 2.1D to 0.96 × 2.1D at different curing stages, producing a system reliability index between 0.63 and 0.76, against a desired threshold of 0.8. This methodology produces interval-valued belief functions that capture a comprehensive range of potential system states and their likelihoods, offering a refined perspective on system safety. An illustrative case study demonstrates the practical application of this methodology in optimizing formwork removal and S/R schedules, significantly enhancing decision-making in construction operations. This paper aligns with the core themes of reliability engineering and system safety by addressing critical safety and reliability issues in complex technological systems through advanced probabilistic safety assessment methods. It significantly enriches the professional discourse by presenting a robust method that can be adapted across various engineering fields facing similar reliability challenges.

Bayesian inference for reliability of K-out-of-N: G repairable retrial systems with mixed standbys, switching failure and reboot delay

Existing reliability studies on K-out-of-N: G repairable retrial systems with mixed standbys mainly consider the case where the standby switching is completely reliable and the repair time follows an exponential distribution, and most of them directly analyze the system reliability indices based on probability theory. Given the existence of such phenomenon as standby switching failure in engineering, this paper proposes a novel reliability model of K-out-of-N: G repairable retrial system with switching failure, and performs statistical inference on the reliability to realize the modeling and evaluation of the system. The considered system consists of mixed standbys and a repairer with vacation. When an operating component fails, the warm standby one is switched to the operating one immediately, and the probability of switching failure during the switchover process is p. In the case where the repair time of failed components follows a general distribution, based on the supplementary variable method and recursive algorithm, the steps for calculating the system steady-state availability are presented. In the case of unknown parameters for repair time and retrial time, the Bayesian estimator of the steady-state availability under the squared error loss function and highest posterior density (HPD) confidence interval are obtained. In numerical simulation, the system reliability inference is realized by using the Monte Carlo (MC) method, and the validity of the inference method is analyzed.

Unreliability tracing of power systems with reservoir hydropower based on a temporal recursive model

AbstractPower system unreliability tracing model allocates the system's reliability index to individual components, identifying potential weaknesses. This study expands its scope by considering the impact of storage resources. Unreliable factors leading to load shedding are categorized into two groups: objective factors inherent to the component and insufficient storage resources. The latter requires a retrospective analysis of other components that caused unreliability previously. When allocating responsibility for load shedding at a certain time, it begins by allocating it among components based on differences between fixed expected output and actual supply. Expected output insufficiency is considered as the unreliable factor. This insufficiency due to insufficient storage resources is then decomposed into segments, each caused by excessive output in earlier instances of the same component. The expected output excess is attributed to the expected output insufficiency of other components in previous times, for which responsibility has been allocated to each component. Consequently, the expected output insufficiency at a particular time can be traced back based on a temporal recursive model, with the load shedding further allocated to components before that time. Case studies based on several systems demonstrate that the proposed model's allocation results are reasonable and more accurate than the traditional model.

System reliability analysis of geogrid reinforced retaining wall using random finite element method

Stabilizing earthwalls is extremely important in geotechnical engineering projects and has become an integral part of transportation infrastructures. Meanwhile, geogrid reinforced retaining walls have been the attention of designers due to their advantages. On the other hand, the soil heterogeneity and the requirement of investigating the internal (geogrid rupture and geogrid pullout) and external (global and lateral displacement) stability modes of these structures have necessitated performing system reliability analysis. In this study, finite element in conjunction with random fields is used to evaluate the reliability of these walls. For this purpose, a finite element program is coded in MATLAB to obtain internal and external safety factors considering staged construction. The deterministic program is extended to a stochastic framework to account for spatial variability of soil parameters in retained backfill, foundation soil, and reinforced fill. In the last part of this study, reliability indices of stability modes are calculated to obtain the series system reliability index, utilizing the Sequential Compounding Method (SCM). The results indicated that the effect of soil heterogeneity is more significant on internal stability modes compared to external stability modes especially geogrid pullout. The results of the system reliability analysis demonstrated more critical conditions thus the reliability index of the system was less than the reliability index of individual components.

Stochastic modeling and optimization of discrete-time cold standby repairable systems with unreliable repair facility and retrial mechanism

This study develops novel reliability models for discrete-time cold standby repairable systems with unreliable repair facility and retrial mechanism. In view of the situation that the state of some engineering systems cannot be continuously monitored, discrete distribution is used to describe the distribution of random variables involved in this paper. For the case that multiple events can occur simultaneously in the discrete-time system model, the priority order of multiple events occurring simultaneously is defined. Two different models are proposed based on two types of priority rules. The retrial mechanism of the components is considered in the case that the failure information of the system components cannot be successfully transmitted to the repair facility. The preventive maintenance (PM) and repair after the breakdown of the repair facility are considered. The key reliability indices are derived by using the iterative algorithm of the difference equation and the generative function method. The algorithms for calculating system state probability, key reliability indices and cost–benefit ratio (CBR) are designed. To demonstrate the impact of each parameter on the system reliability indices, numerical results are provided. The optimal repair rate configuration scheme is chosen using the Particle Swarm Optimization (PSO) algorithm to achieve the lowest possible CBR. The impact of the system model with or without PM on stationary availability and CBR is shown. In addition, the impact of the number of system components on a series of system performance indices is analyzed, and the optimal number of components of the system corresponding to the minimum value of CBR is obtained.

A System-Level Reliability Growth Model for Efficient Inspection Planning of Offshore Wind Farms

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.

Unsaturated soil nailing wall system reliability analysis using random finite element

This study focuses on the evaluation of stability for a typical unsaturated Soil Nailing Wall System (SNWS), considering variations in soil shear strength, suction, and elasticity modulus. The Random Finite Element Method (RFEM) is employed to derive the reliability indices for stability modes, including Global Stability (GS), Lateral Displacement Stability (LDS), Tensile Strength Stability (TSS), and Pullout Resistance Stability (PRS), which serve as essential components of the SNWS. Finally, the Sequential Compounding Method (SCM) is utilized to combine these modes of stability and their direct influence on the system reliability index. The results show although the maximum Coefficient of Variation (COV) of the soil parameters was 11%, the COV of lateral displacements at the top of the wall was obtained as 19%, which shows the significant influence of considering the soil heterogeneity. Furthermore, uncertainties of elasticity modulus and matric suction lead to an increase in GS, LDS, and PRS. The calculated system reliability index was found to be lower than the lowest reliability index of the individual components. The findings indicate that while the inclusion of matric suction and elasticity modulus may enhance the mean values of stability modes, there is a possibility that the system reliability index could decrease.

Determining target levels of power distribution system reliability indices using machine learning

Electrical distribution system (EDS) reliability has always been a critical subject due to the considerable share of distribution systems in power interruptions to end-users. Meeting regulatory service quality standards requires distribution companies to achieve defined reliability levels for performance improvement. Conventionally, specialists determine target reliability based on experience, experimental knowledge, and rules of thumb. However, these methods are error-prone and may result in suboptimal investments, economic inefficiency, and inadequate resource allocation in EDS operation and planning. Accordingly, this paper presents a machine learning-based method to determine the target level for EDS's reliability indices based on its historical performance. The approach involves comprehensive analysis of historical EDS reliability data, followed by a data envelopment analysis (DEA) to assess performance across subdivisions like substations or feeders, identifying the most effective units. Subsequently, machine learning models—Random Forest (RF), Support Vector Machine (SVM), and Radial Basis Function (RBF) network—are trained on optimal subdivisions from the DEA stage. These models accurately estimate target reliability for all subdivisions, contributing to the overall determination of the EDS target reliability level. A three-scenario case study validates the proposed method, suggesting its potential applicability as a valuable tool for regulatory agencies in setting EDS reliability targets. While admitting the potential challenges, notably the method's reliance on the quality and completeness of the historical data collected by distribution companies, the paper emphasizes the importance of collaborative efforts to ensure data accuracy and sufficiency. The proposed method leads to a fair mechanism to determine the target level for a real EDS's reliability indices in comparison with a business-as-usual scenario. Moreover, it provides a reliability performance ranking for the EDS's subdivisions.

A Fast Reliability Evaluation Strategy for Power Systems under High Proportional Renewable Energy—A Hybrid Data-Driven Method

With the increasing scale of the power system, the increasing penetration of renewable energy, and the increasing uncertainty factors, traditional reliability evaluation methods based on Monte Carlo simulation have greatly reduced computational efficiency in complex power systems and cannot meet the requirements of real-time and rapid evaluation. This article proposes a hybrid data-driven strategy to achieve a rapid assessment of power grid reliability on two levels: offline training and online evaluation. Firstly, this article derives explicit analytical expressions for reliability indicators and component parameters, avoiding the computational burden of repetitive Monte Carlo simulation. Next, a large number of samples are quickly generated by parsing expressions to train convolutional neural networks (CNNs), and the system reliability index is quickly calculated under changing operating conditions through CNNs. Finally, the effectiveness and feasibility of the proposed method are verified through an improved RTS-79 testing system. The calculation results show that the method proposed in this article can achieve an online solution of second-level reliability indicators while ensuring calculation accuracy.

A novel computational approach for assessing system reliability and damage detection delay: Application to fatigue deterioration in offshore structures

Fatigue cracks in welded components can cause loss of structural integrity and failures of structural systems. To ensure the safety and reliability of deteriorating structural systems, system damage should be detected as early as possible through inspection, and timely maintenance or repair is required. Delays in damage detection lead to maintenance or repair delays, which adversely affect structural integrity and functionality. In this study, a probabilistic approach to quantify the reliability of deteriorating structural systems with explicit damage detection delay computations was developed for the first time and applied to an offshore structural system. To obtain the system damage detection delay, the system damage occurrence and detection times were rationally defined. Subsequently, the effects of different inspection strategies on system damage detection delay were studied. Finally, the relationship between system reliability and system damage detection delay was investigated. The results show that the system damage detection delay decreases as the inspection quality, number of inspections, or number of components inspected simultaneously increases. It is interesting to determine the law of diminishing marginal system damage detection delay. In addition, there is an approximately negative linear relationship between the system reliability index and system damage detection delay.

A Novel Dynamic Pricing Time‐Based Demand Response Program for Net‐Load Flexibility of Microgrids

In recent years, concerns about electrical energy supply have led to the extensive use of renewable energy sources (RESs). In addition to all the benefits and reasons that justify the unlimited use of RESs, the unplanned exploitation of these sources can challenge the reliability indices of the power system. Demand‐side management (DSM) by demand response programs (DRPs) is one of the most effective and powerful measurements to provide flexibility for the system. DRPs can change the pattern of customer consumption as well as the shape of the load curve. In this study, a novel time‐based demand response model is proposed to control the slope of demand changes. Consequently, dynamic/fixed pricing models with a controllable time step are extracted. These models are implemented on experimental networks, and the results are analyzed and presented for three cases. According to the desired model, the electricity price management at particular hours of the day affects the behavior of the consumers, and it reduces the steep slope in the net‐load ramping curves (62.5% and 50% reduction in peak to valley (P2V) distance for hourly curve and daily curve, respectively).

Application of Power System Reliability and Outage Cost Indices on 33/11 kV Distribution Injection Substation: A Case Study of Asaba Business District

The energy satisfaction that consumers can obtain from a power service provider solely depends on how reliable the feeder to which such customers are connected guarantees adequate and secure energy delivery. This research work is, therefore, to assess the reliability indices and the cost of expected electricity not supplied to the Asaba metropolis through the Benin Electricity Distribution Company (BEDC) Asaba 33/11 kV distribution injection substation. The method used consists of computing the System Average Interruption Duration Index (SAIDI), System Average Interruption Frequency Index (SAIFI), Customer Average Interruption Duration Index (CAIDI), Average Service Availability Index (ASAI), and Expected Energy Not Supplied Index (EENS) of the four feeders emanating from the substation and radiating into the metropolis. This is achieved by first collecting the outage hour, frequency of outage, and expected energy at the point of outage from the station's hourly logbook. The input data is fed into a program written in a MATLAB/OCTAVE environment. The values of the most important reliability index, ASAI, or availability, computed on the SPC, Anwai, Express, and Asaba Commercial feeders are 0.24, 0.23, 0.23, and 0.76 p.u., respectively, in 2020, while in 2021, these values are 0.32, 0.31, 0.33, and 0.83 p.u., respectively. Using the ASAI standard value from IEEE Standard 1366-2003, which is 0.999 as a benchmark, shows that all the feeders can be categorized as less reliable in the years under study. The annual cost of expected energy not supplied during power interruptions to Asaba electricity consumers in 2020 is $2,426,187.046 and $2,214,669.91 in 2021, respectively.

Quantifying Reliability Indices of Garbage Data Collection IOT-based Sensor Systems using Markov Birth-death Process

The aim of this paper is to analyze the performance of a Garbage data collecting sensor network system (GDCSNS) through mathematical modelling and a reliability approach. The reliability assessment of such a system is essential to ensuring that it can collect data related to garbage at different locations consistently and accurately. After the determination of the reliability measures of the system, the next aim is to identify the weakest sensors of the system so that a timely maintenance strategy for the weakest sensor can be planned to avoid disruption in the collection of data from the sensor systems. In the considered system, three sensors have been installed at various location in the city that send the information to the center office (hub point) and then from the center office to the person who is responsible for collecting the garbage from the location and dumping it at some predefined places. These sensors collect data related to garbage level, weight, and other information and send it to computers at the city's central office. Markov modelling has been used to model the system. Based on the mathematical model, a state transition diagram and a set of Kolmogorov time-dependent differential equations have been obtained. The various state probabilities (explicit expressions) related to the performance of the system, namely, Reliability, Mean time to failure, have been obtained to understand the different maintenance policies that can be used. A sensitivity analysis has also been performed to determine the weakest sensor among the sensors.

Optimization of distribution network operating parameters in grid tied microgrid with electric vehicle charging station placement and sizing in the presence of uncertainties

ABSTRACT The power generated by renewable sources is prone to uncertainties which encourages to perform effective modelling to ensure the reliable operation of the grid-connected microgrid (MG) system. This work focuses on the uncertainty modelling of primary sources of solar power, wind power and electric vehicle (EV) load considering three factors battery capacity, state of charge (SoC) and type of EVs charged by employing Monte-Carlo Simulation (MCS) to minimize the distribution system's voltage stability, reliability and power loss (VRP) index. The objective function is tested on the modified IEEE-33 bus distribution system under three diverse scenarios with optimum sizing and placement of RESs and EVCS. To obtain optimal solutions for the proposed problem in a reasonable computation time, modified version of teaching and learning-based optimization (TLBO) and the JAYA algorithm are applied as the rate of convergence is superior to other existing methods in the literature and does not require any precise control parameters. For all the scenarios, it can be seen that the modified JAYA algorithm outperforms TLBO and other existing approaches. The findings of the results reveal the efficacy of uncertainty modelling in a proposed grid-connected DC MG to curtail the VRP index.

Reliability analysis of a two-dimensional linear consecutive-(r,s)-out-of-(m,n): F repairable system

Most of the existing studies on the two-dimensional consecutive system have focused on the non-repairable case. Nevertheless, considering the repairable case of components in engineering, it is necessary to study the reliability of the two-dimensional consecutive repairable system. Owing to the more complex spatial structure of the two-dimensional consecutive system, the analysis methods of the one-dimensional consecutive repairable system are not applicable to the two-dimensional case. In this work, we give a general method to analyze the reliability of a two-dimensional linear consecutive-(r,s)-out-of-(m,n): F repairable system. Firstly, to calculate the number of different cases of the system in a certain state, a key issue in the analysis of the consecutive repairable system, we propose the sliding window search method and inverse search method, whose computational complexities are compared and correctness is verified. Next, under the assumption that the repair time follows a general distribution, we analyze the reliability of the two-dimensional linear consecutive-(r,s)-out-of-(m,n): F repairable system using the supplementary variable method. Finally, we use an example of a wireless sensor network to analyze the effects of system parameters on system reliability indices, such as steady-state availability, steady-state failure frequency, and MTTFF.

Reliability modeling of wave energy converters based on pelamis technology

Wave generators, as renewable sources, are increasingly applied for power generation in developed electric networks. With the development of wave generator technologies, large-scale devices such as oscillating water columns, pelamis, wave-dragon, oyster, buoy, sea wave slot cone converter, and tapchan have been invented to extract electrical power from wave energies. The output of wave generators relies on the height and period of waves, and because of the wide variation in these quantities, the produced power from them changes widely. Therefore, in electric networks incorporating large wave generators, reliability is influenced and should be analyzed. In this paper, for the first time, the reliability modeling of pelamis, as a kind of commercial-scale wave generator, is executed. In the proposed multi-state reliability model of pelamis, failures of composed components and changes in the production of power are addressed. To obtain the optimal number of power states in the model, the XB factor is computed. Then, to reduce the number of power states in the model, the fuzzy c-means clustering methodology is applied. The obtained model is used to examine the adequacy assessment of an electric network containing a pelamis farm. Numerical results show that wave converters can improve the reliability performance of electric systems. However, wave period and height affect the reliability indices of the power system. The effectiveness of the proposed method is validated by comparing the outcomes obtained by the analytical and Sequential Monte Carlo Simulation methods.

Is the safety index of modern safety integrity level(SIL) truly appropriate for the railway?

Safety is paramount in rail transportation. The International Safety Standard IEC 61508, issued by the International Electrotechnical Commission (IEC) in 2000, describes the modern concept of safety and the specifications for safety evaluation in a systematic manner. On this basis, the EN 50129 railway transportation safety standard and safety integrity level(SIL) are established. Through the above analysis, the relationship between safety-related system reliability, acceptable risk, and safety index is summarized. It is clear that the safety index is based on acceptable risks. Nonetheless, as the economy and society advance, the safety index mandated by the SIL falls behind. Consequently, the principles and methodologies for calculating the safety index are presented. The paper proposes a reference for the Chinese railway safety index based on actual data from the Chinese railways over the past few years.

Offshore Electrical-Oil Production Coupling System Reliability Analysis

The role played by offshore oil resources in energy supply is becoming more and more important, and the normal operation of oil production system on offshore oil platforms requires the reliable operation of the electric power system as a prerequisite; the failure of the components in the oil production system may lead to a large-scale production shutdown, and cause the related electrical components to shut down, making the power system ineffective in a certain range. In this paper, a coupled system model of the electric power system and production system of an offshore oil platform based on massively parallel computing is proposed. By analysing the connection between the oil production system and the electric power system, the coupled system model is established and the load data are calculated. Meanwhile, the reliability model of the coupling components is established based on the fault data, and the electric-related reliability index and the production-related reliability index of the coupling system are proposed. The broad-first search (BFS) algorithm was used to determine whether the coupling nodes were powered, and the depth-first search (DFS) algorithm was used to determine the connectivity of the coupling system. In addition, a minimum load-shedding model based on the integrated fault degree is proposed to reduce the load shedding of the coupled system.