A Decomposition Method for Computing System Reliability by a Boolean Expression

In general, a system is understood as a technical arrangement of clearly identifiable (system—) components whose functioning depends on the proper functioning of all or a subset of its components. For a reliability analysis, a number of idealizations are convenient if not necessary. It is assumed that the components can attain only two states, i.e. one functioning (safe, working, active,...) and one failure (unsafe, defect, inactive,...) state. This is a simplification which is not always appropriate but we will maintain it throughout the text. If there is a natural multi—state description of a component or a system we shall assume that this is reduced to a two-state description in a suitable manner. In practice, this step of modeling might be not an easy task. It is, nevertheless, mandatory in practical system reliability analyses. Several attempts have been made to establish concepts for analyzing systems with multi—state components (see, for example, Caldarola, 1980; Fardis and Cornell, 1981). It should be clear that systems then have also multiple states and the definition of safe or failure states requires great care. Such relatively recent extensions of the classical concepts cannot be dealt with herein.

In this paper, structural systems reliability analysis was used to estimate the system reliability of a typical semi-submersible based on the characteristic structure failure mechanisms under extreme wave loads. First, a three-dimensional simulation model was created for the chosen semi-submersible platform using an elastic-perfectly plastic material model, neglecting the effect of the strain hardening assumption. Then, under design wave conditions, and characteristic structural failure mechanisms of a semi-submersible platform were examined, and a system reliability model was developed based on the failure mechanism of the chosen platform. Finally, system reliability methods were used to determine the platform’s system reliability. It was discovered that the main node’s system reliability makes a significant contribution to the overall structure reliability, so it is strongly advised that the reliability of the main nodes be taken into account when determining the overall structure’s reliability. This research aims to apply reliability theory in offshore engineering and, ideally, to encourage the reliability-based design of semi-submersible platforms and other similar structures.

When a natural or man-made hazard occurs, it is essential to detect damaged components in lifeline networks to enable rapid recovery of the utility service in the impacted areas. However, inspections of individual network components such as buried pipes are often impractical due to exceedingly large costs and time. This paper presents a new system reliability method using a Bayesian method developed for identifying network components with higher conditional probabilities of damage given post-disaster network flow monitoring data. This method achieves an optimal matrix-based representation of the problem for efficient damage detection. The developed method is demonstrated by a water pipeline network consisting of 15 pipelines. The conditional probabilities of damage in 15 pipelines given post-disaster network flow observations are obtained by a Bayesian method for damage detection purpose. The results of the post-disaster damage detection by the proposed system reliability method are compared to those by Monte Carlo simulations and by the matrix-based system reliability method without selective expansion scheme in order to demonstrate the accuracy and efficiency.

According to the deficiency of traditional Markov chain approach in dynamic fault tree analysis, a new modular method for system reliability analysis is proposed. This paper focuses on dividing the fault tree of system into independent subtrees using a linear-time algorithm, and the processing method for different subtrees: Binary decision diagram solution for static subtrees and Bayesian Network solution for dynamic subtrees, respectively. In addition, an approach is also provided for mapping some dynamic logic gates into discrete-time Bayesian network. At last, the modular method has been applied to assess the reliability of a satellite key device and the results have shown that the proposed method can overcome the state explosion problem, and is useful for assessing the reliability of large and complex systems.

System reliability analysis of transmission line towers

In rural regions with limited access to the power grid, self-reliance for electricity generation is paramount. This study focuses on enhancing the design of stand-alone photovoltaic installations (SAPV) to replace conventional fuel generators thanks to the decreasing costs of PV modules and batteries. This study presents a particle swarm optimization (PSO) method for the reliable and cost-effective sizing of SAPV systems. The proposed method considers the variability of PV generation and domestic demand and optimizes the system design to minimize the total cost of ownership while ensuring a high level of reliability. The results show that for the PSO method with 500 iterations, the error is around 2%, and the simulation time is approximately 2.25 s. Moreover, the PSO method allows a much lower number of iterations to be used in the Monte Carlo simulation, with a total of 100 iterations used to obtain the averaged results. The optimization results, encompassing installed power, battery capacity, reliability, and annual costs, reveal the effectiveness of our approach. Notably, our discretized PSO algorithm converges, yielding specific parameters like 9900 W of installed power and a battery configuration of five 3550 Wh units for the case study under consideration. In summary, our work presents an efficient SAPV system design methodology supported by concrete numerical outcomes, considering supply reliability and installation and operational costs.

Purpose of research. Methodology and analysis of system reliability models, including monitoring the condition of individual components and failure assessment based on the failure rate and the probability of failure-free operation of modules. The work is aimed at creating effective methods for predicting failures and estimating system recovery time, taking into account the failure parameters of individual modules and their interaction. The work also involves modeling the monitoring of the state and functioning of the system.Methods. Research methods include analyzing system reliability using failure rates, modeling the probability of uptime of system components, calculating the average time to failure, using probability distributions to determine system status, monitoring system status in real time, estimating system recovery time, as well as developing algorithms for detecting failures and managing system recovery, modeling methods.Results. The results of the study show that as the system's operating time increases, the probability of uptime for each component decreases due to the accumulation of failures. The simulation showed that the reliability of the system depends on the failure rate of each module and their relationship in the system. For three different systems with different failure rates, the change in the probability of uptime (R(t)) was calculated as a function of time. The analysis showed that as the operating time increases, the probability of system failure increases, which is confirmed by a decrease in the value of R(t) as the time t increases. When modeling system recovery, it was found that the recovery time depends on the number of failed modules and the intensity of their failures. The monitoring system successfully reacts to changes in real time, identifying significant events such as module failure, and estimating system recovery time based on current component status data.Conclusion. In the course of the research, a method for modeling system reliability based on an analysis of the failure rates of its components and the probability of uptime (R(t)) was developed and implemented. The methods considered made it possible to calculate the average time to system failure, as well as to estimate the system recovery time after failure, which is a key factor in ensuring the smooth operation of critical systems. The effectiveness of the monitoring system has been demonstrated, which, based on data on the state of components (M(t)), can quickly identify failure events and predict recovery time, which allows for prompt measures to restore system operability.

This paper describes a cross-layer design method for digital circuit fault-tolerant design. This cross-layer hierarchical scheme mainly contains selective duplication in logic level and spare cache design in micro-architecture level, working together seamlessly. When compared to traditional fault tolerance techniques, this method takes advantage of information from different circuit design levels to generate an effective solution. It also has great potential to work with other circuit design levels (e.g., core level) to meet the high demand in system reliability and robustness. Experimental results obtained using an ARM core instruction decoder demonstrate that, on average, the number of fault-free circuits is increased 250% by selectively duplicating 25% of the decoder. On top of selective duplication in logic level, adding a spare cache with 5 to 20 cache lines in micro-architecture level can further increase the number of fault-free circuits by 0.66 to 49.83 times depending on different number of defects injected.

These are the proceedings of the twenty-first working conference of the International Federation of Information Processing (IFIP) Working Group 7.5 on Reliability and Optimization of Structural Systems, which took place at the University of California, Berkeley, USA, on August 19–21, 2024. This volume contains 15 selected papers from the 20 presentations delivered at the conference. The conference was supported by Pacific Earthquake Engineering Research (PEER) Center, and by the University of California, Berkeley, which provided outstanding facilities in the conference venue and remarkable logistic support throughout the event. The purpose of the WG7.5 Working Group is to promote modern theories and methods of structural and system reliability and optimization, to stimulate research, development, and applications in these areas, to foster the dissemination and exchange of information, and to encourage education on those subjects. The main themes of the conference included structural reliability methods, engineering risk and resilience analysis, Bayesian methods, reliability-based design optimization, and sensitivity analysis, along with their applications in civil engineering, dynamics, and natural hazards. The conference facilitated engaging discussions among participants, both during and after the technical sessions. Notably, a significant number of presentations were delivered by promising young researchers, who contributed fresh perspectives and innovative ideas to the field.

Following several recent failures and catastrophic collapses due to man-made and natural hazards, there has been increased interest in upgrading the bridge design philosophy from a member-oriented to a system-oriented approach in order to ensure that bridge structures possess adequate levels of structural redundancy and robustness. To account for uncertainties associated with the quantification of the levels of redundancy of complex structures and be consistent with the reliability basis of recent bridge design code developments, system reliability methods must be applied. In this paper, the authors review the applicability of Markov-based advanced simulation techniques to study the reliability of bridge structural systems. To evaluate the probability of structural collapse due to different damage scenarios, a simulation approach referred to as DRSCAM-SS is used. The method combines the benefits of the Subset Simulation (SS) and those of the Delayed Rejection (DR) and Single Component Adaptive Metropolis Samplers (SCAM). The proposed approach is efficient and robust and can be used to obtain approximate expressions for the limit state equations for the pertinent failure modes. Examples are provided to illustrate the applicability of the procedure for evaluating the reliability of bridge systems and quantifying their levels of redundancy and robustness.

Sensitivity analysis measures how changes in system inputs affect outputs. Previously, a large amount of sensitivity analysis research was relevant to the precise probability that is regarded as an ideal condition of engineering. Due to insufficient test samples and the low accuracy of test data, system reliability with hybrid uncertainty is difficult to be described as a precise value. As a profusion of highly integrated electromechanical equipment is applied in modern life, it is impossible to apply sufficient resources to eliminate the stochastic property of every component, which necessitates the identification of highly sensitive components to efficiently reduce imprecision. Hence, based on the theory of imprecise probability, imprecise sensitivity analysis has become a popular research topic in the last decade. In this paper, a method for uncertain system reliability and imprecise sensitivity analysis is proposed based on a Bayesian network, a probability box and the pinching method. The feasibility and accuracy of the combined method are fully verified through the evaluation and analysis of a numerical example and a case study of an electromechanical system, and the highly sensitive components that heavily influence the imprecision of system outputs are accurately identified.

In the last twenty years, the methods for structural system reliability evaluation have evolved considerably. Since these methods are based on different assumptions, it is necessary to evaluate their capabilities. For this reason, a research study was initiated at the University of Colorado at Boulder in order to investigate the accuracy and reliability of various methods for structural system reliability evaluation. This paper emphasizes certain important parametric studies on system reliability methods under uncertainty. The sensitivity of the accuracy of the methods to changes in both strength and load correlations is demonstrated by means of numerical examples.

Finding the reliability expression of different substation configurations can help design a distribution system with the best overall reliability. This paper presents a computerized a nd implemented algorithm, based on Disjoint Sum of Product (DSOP) algorithm. The algorithm was synthesized and applied for the first time to the determination of reliability expression of a substation to determine reliability indices and costs of different substation arrangements. It deals with the implementation and synthesis of a new designed algorithm for DSOP implemented using C/C++, incorporating parallel problem solving capability and overcoming the disadvantage of Monte Carlo simulation which is the lengthy computational time to achieve satisfactory statistical convergence of reliability index values. The major highlight of this research being that the time consuming procedures of the DSOP solution generated for different substation arrangements using the proposed method is found to be significantly lower in comparison with the time consuming procedures of Monte Carlo-simulation solution or any other method used for the reliability evaluation of substations in the existing literature such as meta-heuristic and soft computing algorithms. This implementation gives the possibility of RBD simulation for different substation configurations in C/C++ using their path-set Boolean expressions mapped to probabilistic domain and result in simplest Sum of Disjoint Product which is on a one-to-one correspondence with reliability expression. This software tool is capable of handling and modeling a large, repairable system. Additionally, through its intuitive interface it can be easily used for industrial and commercial power systems. With simple Boolean expression for a configuration’s RBD inputted, users can define a power system utilizing a RBD and, through a fast and efficient built-in simulation engine, the required reliability expressions and indices can be obtained. Two case studies will be analyzed in this paper. The effects of different substation configurations on the reliability are analyzed and compared. Then, the reliability of a radial distribution system will be evaluated using DSOP solution. The failure results will be combined with a load flow scenario, and indices such as SAIDI, SAIFI will be determined.

Statistical Tolerance Analysis of a Mechanism with Gaps based on System Reliability Methods

Fuzzy repairable reliability based on fuzzy gert