Reliability Of Redundant Systems Research Articles

Reliability Evaluation of Complex Nuclear Energy Redundancy Systems with Atypical Time-Distribution Events

In complex nuclear energy redundancy systems, there are many failure events that do not follow specific time distribution. For these atypical time-distribution events, traditional dynamic fault tree (DFT) methods cannot be applied directly, which has posed great challenges to reliability modeling and evaluating. In this contribution, we summarize atypical time-distribution events in nuclear energy redundancy systems and propose new modeling and evaluating methods based on DFT. To demonstrate the reasonability of the proposed methods, two case studies about make-up water pumps and emergency diesel generators are analyzed in comparison with traditional DFT. The results indicate that the proposed methods can effectively model and analyze the reliability of redundant systems with atypical time-distribution events. The proposed methods can provide useful information for optimization design of nuclear energy redundancy systems and has potential to improve the economy of nuclear power plants by relaxing overestimated unreliability.

On the Feasibility of Wireless Communications for Safety Applications in Industry

This article presents a methodology to characterize the reliability and safety capabilities of redundant wireless systems planned for an industrial application. The equations that describe the residual error are presented and studied in situations that model an industrial wireless scenario. We propose different voting systems and their performance is evaluated analytically and by simulations. Likewise, a voting system based on a combination of filtering and cross-checking techniques is proposed. This solution significantly reduces the probability of undetected dangerous events while maintaining availability under control. Moreover, an improved version with triple redundancy is also presented. The results demonstrate that it is possible to fulfill the requirements of standard IEC 61508 without compromising system availability statistics. The solutions have been implemented on hardware wireless prototypes to illustrate the effectiveness of the proposed voting systems.

A Consistent Analytical Method to Assess Reliability of Redundant Safety Instrumented Systems

The significance of determining Safety Integrity Level (SIL) has grown substantially in numerous industry sectors since the publication of international standard for functional safety (IEC61508). To detect SIL using IEC61508, the demand mode must first be recognised. However, there is not any 100% accurate method to identify the demand mode. Design engineers must assume the demand mode based on their assessment of the likely number of failures each year in the system under consideration, referred to as demand rate. This signifies that a defective demand mode assumption leads to an incorrect SIL determination. In addition, the formulas provided by the IEC standards for the SIL determination did not include the demand duration. The majority of prior publications in the literature relied on SIL determination using IEC61508. As a result, the literature suffers from the constraints of the IEC61508 standard, which include ignoring demand duration and uncertainty in assuming the system’s demand mode for determining SIL. This paper addresses the aforementioned issues in literature through proposing a scenario based-formula to calculate Hazardous Event Frequency (HEF) using Markov process for safety system with dual redundancy. The HEF calculated can then be utilized to select SIL while considering the demand duration and obviating the requirement to use the SIS demand mode. The results demonstrated that the proposed method provides higher accuracy in calculating the HEF value compared to the existing traditional formulas.

Modelling Diversity in Redundant Systems: Case Study of Satellite Systems

Diversity plays an essential role in increasing reliability of redundant systems, however in safety and mission critical applications. The onboard computer of satellites and the flight computer of aircrafts, which are ultra-reliable system, utilizes various hardware platforms for their redundant architecture to resolve the common cause failure problem. Furthermore, the software is also developed by separate teams based on different software platforms to mitigate the specification and design flaws, and implementation mistakes. This paper focuses on modelling diversity of redundant systems using Markov reliability analyzing method. The proposed scheme is explored in two types of applications: mission critical applications (with long mission time) and safety critical applications (with short mission time). Analytical and simulation results show the effectiveness of diversity in increasing the reliability of these systems. Since about ten percent of all failures appear as common cause failures, which restrict reliability improvement through similar redundant modules, achieving ultra-reliable necessitate to consider diversity in these systems

On A Methods Of Using Weighted Simulation Improving Reliability To Redundant Fiber Optic Communication Systems

The article describes the methodology of weighted modelling to increase the reliability of redundant fibre-optic communication systems. In a specific example, a network graph of a many-node fibre-optic communication system is considered. Applying general ideas to determine the reliability characteristics of systems consisting of a large number of different types of elements with different functional relationships between them is quite a difficult task. The materials presented in this article are intended to solve this problem. Along with their relative simplicity, they are highly accurate. The numerical examples in this chapter show that the use of these methods for highly reliable systems can reduce the variance of the estimate by several orders of magnitude compared to the direct modelling method, and thus reduce the time required for calculations on electronic computers by several orders of magnitude. The purpose of the study is to increase the reliability of fibre-optic communication systems. The research methodology is based on models with a limited number of monotonous failure chains, which is available for visual enumeration of the reliability of highly reliable systems. As a result, it is proposed to obtain an approximate formula for assessing the reliability of a highly reliable system, both by modelling and analytically, and calculations using it can be performed using the quadrature method or moment methods. This allows you to build a model according to the block principle, including full-scale blocks or records of the results of their tests, simplifies the interpretation of the results, and creates convenience in software implementation.

Assurance of complex pressure control system operability in high-temperature media

For the purpose of control and overpressure protection in pipeline systems of power industry and pressure vessels, indirect-action valves consisting of a main valve and a pilot valve are often used. Such devices are characterized by smaller reliability due to complication of their structure depending on operability of these two valves. A pilot valve controlling the whole safety system is the weakest element of the system. It is especially typical of machines operated in severe conditions, since life of sensing elements quickly decreases during work with high-temperature and polluted media. The authors considered the ways for improving reliability of pressure control systems operated in severe conditions by redundancy of the sensing element of the valve with a system equipped with a metal bellows. The authors analyzed reliability of initial systems and redundant systems at various operating temperatures.

OPTIMAL STRUCTURAL RESERVATION OF TECHNICAL SYSTEMS

Purpose. The purpose of the article is to give designers of highly reliable technical systems that do not have special knowledge in the field of optimization and programming skills, a simple and accessible mathematical tool for choosing the optimal solution for structural redundancy of systems. Methodology. The article poses the problem of optimal structural redundancy of technical systems. Two typical redundancy schemes are considered: a) a separate "hot" backup scheme; b) a separate "cold" backup scheme. The computational models for estimating the reliability of redundant systems are formulated. We offer optimization models that allow us to find a rational option for reserving a system that is being designed, taking into account conflicting requirements for its reliability and cost. These models are numerically implemented in the operating environment of the Excel spreadsheet as applied to the main object, consisting of 7 elements. The optimal variants of reserving this object according to the "hot" and "cold" separate reservation schemes are given. Findings. Calculated models for estimating reliability, as well as models for optimizing the systems reserved for the "hot" and "cold" separate backup schemes, have been developed. With the use of the Excel spreadsheet, the optimal options for reserving 7 element objects are found for separate "hot" and "cold" backups. Originality. New computational models for estimating the reliability of redundant systems are proposed, as well as optimization models developed on the basis of these, which are formulated using the decomposition of unknown initial problem of structural redundancy into binary components. In this case, the obtained optimization models belong to the class of problems of non-linear mathematical programming with binary variables, for the numerical solution of which (even for a sufficiently large dimension) well-known packages of applied computer programs, in particular, the MS Excel spreadsheet, are well adapted. Thus, the process of solving the initially very complicated problem of optimal structural redundancy is much simpler and reduced to performing elementary actions in the corresponding software interfaces. Practical value. The proposed calculation models for estimating the reliability of redundant systems, models for optimal structural redundancy, and the methodology for their formation, in order to simplify further numerical implementation, can be useful in solving problems of ensuring the reliability of technical systems in the early stages of their design.

Reliability Modeling of Redundant Systems Considering CCF Based on DBN

Common cause failure (CCF) has become a hot topic in reliability and availability analysis of redundant systems. Aiming at the shortage of $$\beta $$ -factor model in distinguishing three or more failures, multiple error shock theory is put forward. Having the problem in determining minimal cut sets and structure functions for dynamic fault tree (DFT), dynamic Bayesian network (DBN) is applied to transit DFT events to corresponding nodes and express causal relations between the nodes. On the base of explicit modeling for CCF, DBN models for hot spare (HSP) gate, cold spare (CSP) gate and warm spare (WSP) gate are established considering CCF processes. For a HSP gate, all failure processes are listed in the stress event layer for each component. For a CSP gate and a WSP gate, CCF node and intermediate nodes are introduced to express causal relations. At last, a control unit and its improved type are taken as examples. The DBN models are built by referring to corresponding DFT structures when taking CCFs into consideration. From the results, it is obvious that the modern unit has a relative higher reliability and availability. And it is less easily influenced by uncertainty such as failure rates and coverage factor through sensitivity analysis.

Evaluating MTTF of 2-out-of-3 redundant systems with common cause failure and load share based on alpha factor and capacity flow models

K-out-of-n redundant systems are used to increase reliability in various industries. The failure of a component in such systems is dependent upon the failure of other components. Therefore, if an appropriate model is not developed to take dependent failures into consideration, reliability and MTTF of redundant systems are evaluated wrongly. One of the most crucial varieties of dependent failures is common cause failure. Common cause failure refers to the failure of two or more components of a k-out-of-n system which occurs simultaneously or within a short time interval and thus components are direct failures resulting from a shared cause. Another type of dependent failure in k-out-of-n redundant systems is load share, where the failure of one component leads to increased load in surviving components, hence changing their failure rate. In this paper, using Markov chain, three models are used to evaluate the MTTF of a 2-out-of-3 redundant system by taking dependent failures into account. Model I addresses the MTTF of a 2-out-of-3 redundant system by considering common cause failure based on alpha factor model. In Model II, both dependent failures (common cause failure and load share) are examined based on capacity flow and alpha factor model. In Model III, in addition to common cause failure and load share, component repair is studied, too. In order to examine the validity of the models introduced and conduct sensitivity analysis, some diagrams are drawn for each model. Considering the dependent failures in the 2-out-of-3 redundant systems, all the three proposed models can be practical and be used to evaluate MTTF.

Modeling of Complex Redundancy in Technical Systems with Bayesian Networks

Redundancy is a common approach to improve system reliability, availability and safety in technical systems. It is achieved by adding functionally equivalent elements that enable the system to remain operational even though one or more of those elements fail. This paper begins with an overview on the various terminologies and methods for redundancy concepts that can be modeled sufficiently using established reliability analysis methods. However, these approaches yield very complex system models, which limits their applicability. In current research, Bayesian Networks(BNs), especially Dynamic Bayesian Networks (DBNs) have been successfully used for reliability analysis because of their benefits in modeling complex systems and in representing multi-state variables. However, these approaches lack appropriate methods to model all commonly used redundancy concepts. To overcome this limitation, three different modeling approaches based on BNs and DBNs are described in this paper. Addressing those approaches, the benefits and limitations of BNs and DBNs for modeling reliability of redundant technical systems are discussed and evaluated.

Simulation model to calculate the indices of reliability of redundant radio electronic systems

Purpose . To define quantitative estimates of reliability indices of redundant radio electronic systems, the methods of reliability theory, analytical methods or simulation modeling are applied. This paper describes the application of these methods for systems of diverse complexity, as well as the complex of programs “Dialogue” developed for the calculation of reliability indices. Methods. The main obstacle for wide application of the simulation modeling method to obtain the reliability indices is high labor intensity of the creation of these models. The current software tools are not very useful. This problem can be solved using the developed complex of programs “Dialogue”. This is achieved by creating the simulation models programs automatically on the basis of input initial data. The time of creation of a model is determined by the time of the input. Generating of the simulation models is based on the principle that if the system’s behavior in case of failures is determined only by its scope structure, connections between components, failure criteria and redundancy switches, i.e. when the system’s response to a failure of its component is uniquely defined in advance, then it will be possible to create models with equal structures for the systems with any configurations. It helps to create the basis for the initial text of the model, common for all simulation models of this type. Such basis forms a permanent part of the model, and the data which define the specifics of failure behavior of the concrete system, are set in form of insertions to the main text. Results . The complex of programs that is being described is intended to calculate the reliability indices of different technical systems using simulation models, and its consists of the program for the description of system to be simulated “Dialogue-OS”, the program for the model synthesis “Dialogue-Synthesis” and special sub-programs combined to a separate library. The complex helps to create specialized simulation models of redundant systems which undergo statistical tests, and based on the obtained results the reliability indices are defined. Using the complex “Dialogue” we can obtain the following reliability indices: 1) probability of reliable operation for a predetermined period of time, 2) failure rate at the end of a predetermined period of time, 3) mean time to failure, 4) data to build a graph of dependence of the probability of reliable operation on time, 5) data to build a graph of dependence of the failure rate on time. Conclusion. This article provides the results of calculations carried out by theoretical methods, and by the method of simulation modeling that show a good coincidence (relative error is not more than 1%). The complex “Dialogue” makes it possible to calculate the reliability indices of redundant radio-electronic systems of any complexity with accuracy sufficient for practice. It should be noted that the complex “Dialogue” allows for creating the simulation model of reliability for redundant radio-electronic systems, whose reliability characteristics can not be calculated by theoretical methods due to their complexity.

Optimal structure of multi-state systems with multi-fault coverage

Due to imperfect fault coverage, the reliability of redundant systems cannot be enhanced unlimitedly with the increase of redundancy. Thus it is essential to study the optimal structure of redundant systems. This paper considers a multi-state series-parallel system with two types of parallelization: redundancy and work sharing. Different from existing works which consider single-fault coverage, multi-fault coverage is considered in order to adapt to a wider range of fault tolerant mechanisms. For multi-fault coverage, the coverage factor of an element failure in a work sharing group depends on the status of other elements. It is assumed that the uncovered failures in the elements belonging to the group of elements sharing the same task can cause failure of the entire group. The optimal trade-off between the two kinds of parallelization has been studied based on various settings of fault coverage factor. Examples of data transmission systems and task processing systems are presented to illustrate the applications of results.

다중구조관리자 특성이 반영된 확률모델 기반의 몬테카를로 신뢰도 해석 기법 연구

Critical systems with high reliability feature fault tolerant redundancy. Conventional analytical reliability analysis methods that use the Reliability Block Diagram do not adequately reflect characteristics of the redundancy management system and are not suitable for this applications. This paper uses Monte-Carlo method to calculate the reliability of complicated redundant systems. The method was first validated for cases with analytical solutions. Then, the tool was successfully applied to analyze reliability of the flight control systems with a voter as redundancy management system.

Reliability Acceptance Criteria for Deteriorating Elements of Structural Systems

A systematic approach to determining reliability-based acceptance criteria for deteriorating elements in structural systems is proposed as a basis for calibration of safety factors in codes and standards and for verifying acceptability of inspection and maintenance strategies for specific structures. The goal is to establish deterioration acceptance criteria for the elements of a structural system in compliance with criteria formulated for the system. Existing methods significantly overestimate the deterioration reliability of redundant structural systems because they neglect the joint effect of deterioration failures of different elements. To more realistically capture the load-sharing behavior of deteriorating redundant structural systems, it is proposed to establish deterioration acceptance criteria on the basis of easily computable, idealized structural systems, which are calibrated to the characteristics of the real structure. The approach is validated on an example structural system and is found to represent a significant improvement over current methods. The paper concludes with a study of the main factors influencing acceptance criteria of deterioration reliability.

Systems reliability in case of regenerative flow of elements failures

Reliability of large redundant systems is studied in asymptotics of time compression. We consider two possibilities, namely, the failed elements are either repaired or not repaired. At first it is supposed that the number of repair devices is infinite (or large enough) then a case of one device is considered. A flow of elements failures is assumed to be regenerative. A particular case of semi-Markov flow is considered as well.

Estimating system reliability with correlated component failures

Correlated component failures, recognised to be a major impediment in the power of redundancy to improve system reliability, need to be factored into the reliability assessment of fault-tolerant systems. In this paper, we present a methodology to derive an approximate analytical expression for mean reliability of on-demand systems with correlated failures. Applying the methodology, we derive expressions for the mean reliability of common redundant structures, namely, k-out-of-n, series-parallel and bridge systems. We illustrate the potential of these expressions to systematically assess the influence of pairwise component correlations on system reliability. An examination of the error between the system reliability estimates obtained from the analytical expressions to those obtained from simulations indicates that our method accurately captures the trends in system reliability and can hence provide a computationally faster alternative to simulation for system reliability analysis.

Efficient Reliability Assessment of Redundant Systems Subject to Imperfect Fault Coverage Using Binary Decision Diagrams

Systems requiring very high levels of reliability, such as aircraft controls or spacecraft, often use redundancy to achieve their requirements. This paper provides highly efficient techniques for computing the reliability of redundant systems involving simple k-out-of-n arrangements, and those involving complex structures which may include imbedded k-out-of-n structures. Techniques for modeling systems subject to imperfect fault coverage must be appropriate to the redundancy management architecture utilized by the system. Systems for which coverage can be associated with each of the redundant components, perhaps taking advantage of the component's built-in test capability, are modeled with what we term element level coverage (ELC); while systems which utilize majority voting for the selection from among redundant components are modeled with fault level coverage (FLC). In FLC, systems coverage is a function of the fault sequence, i.e., coverage will be greater for the initial faults which can utilize voting for redundant component selection, but will have a lower coverage value when the system must select from among the last two operational components. Occasionally, FLC systems can be adequately modeled using a simplified version of FLC in which it can be assumed that the initial fault coverage values are unity. This model is called one-on-level coverage (OLC). The FLC algorithms provided in this paper are of particular importance for the correct modeling of systems which utilize voting to select from among their redundant elements. While combinatorial, and recursive techniques for modeling ELC, FLC, and OLC have been previously reported, this paper presents new table-based algorithms, and binary decision diagram-based algorithms for these models which have superior computational complexity. The algorithms presented here provide the ability to analyse large, and complex systems very efficiently, in fact with a computational complexity comparable to the best available techniques for systems with perfect fault coverage.

Validity of Markov processes for reliability analysis

ABSTRACTThe use of Markov analysis to calculate the reliability of repairable redundant systems has been deprecated because published examples gave incorrect results. Reasons given for these errors were that the process of repair itself is not a Markov process, specifically it is not Independent of events that occurred prior to the start of the repair, and the time to repair is not exponentially distributed. An alternative explanation for the erroneous results is that they were based upon incorrect Markov models of the system. Given an appropriate model, Markov analysis will provide answers that are entirely consistent with those derived by other methods, and furthermore can provide useful results, In particular for short mission times, that are more difficult to obtain otherwise.

Assessment of redundant systems with imperfect coverage by means of binary decision diagrams

In this article, we study the assessment of the reliability of redundant systems with imperfect fault coverage. We term fault coverage as the ability of a system to isolate and correctly accommodate failures of redundant elements. For highly reliable systems, such as avionic and space systems, fault coverage is in general imperfect and has a significant impact on system reliability. We review here the different models of imperfect fault coverage. We propose efficient algorithms to assess them separately (as k-out-of- n selectors). We show how to implement these algorithms into a binary decision diagrams engine. Finally, we report experimental results on real life test cases that show on the one hand the importance of imperfect coverage and on the other hand the efficiency of the proposed approach.

A design diversity metric and analysis of redundant systems

Redundant systems are designed using multiple copies of the same resource (e.g., a logic network or a software module) in order to increase system dependability. Design diversity has long been used to protect redundant systems from common-mode failures. The conventional notion of diversity relies on independent generation of different implementations. This concept is qualitative and does not provide a basis for comparing the reliabilities of two diverse systems. In this paper, for the first time, we present a metric to quantify diversity among several designs and illustrate its effectiveness using several examples. Applications of this metric in analyzing reliability and availability of diverse redundant systems, and deriving simple relationships between diversity, system failure rate, and mission time are also demonstrated.