Exact System Reliability Research Articles

System Reliability of a Modern Distributed Network with Node Failure and Budget Consideration Using Analytical Algorithm and Deep Learning Model

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

Dynamic reliability modeling for general standby systems

General standby systems with component lifetimes following independent and nonidentical phase-type (PH) distributions are presented in a state-space model using state transition block matrices. The model is constructed by identifying a block matrix representing each system state and a block matrix that causes a transition from one system state to another. This general model is applicable to hot, warm, or cold standby and any combination of them in K-out-of-N general standby structures. The resulting model becomes a PH representation of the system lifetime distribution and is thus useful for exact dynamic system reliability analysis. The advantage is that many functional system reliability measures, such as the reliability, hazard, and mean residual life functions, can be obtained by simple matrix algebra. These functions are shown to be useful for determining optimal component ordering. Comparisons with other methods from previous publications are presented.

Reliability optimization for non-repairable series-parallel systems with a choice of redundancy strategies and heterogeneous components: Erlang time-to-failure distribution

The redundancy allocation problem (RAP) of non-repairable series-parallel systems considering cold standby components and imperfect switching mechanism has been traditionally formulated with the objective of maximizing a lower bound on system reliability instead of exact system reliability. This objective function has been considered due to the difficulty of determining a closed-form expression for the system reliability equation. But, the solution that maximizes the lower bound for system reliability does not necessarily maximize exact system reliability and thus, the obtained system reliability may be far from the optimal reliability. This article attempts to overcome the mentioned drawback. Under the assumption that component time-to-failure is distributed according to an Erlang distribution and switch time-to-failure is exponentially distributed, a closed-form expression for the subsystem cold standby reliability equation is derived by solving an integrodifference equation. A semi-analytical expression is also derived for the reliability equation of a subsystem with mixed redundancy strategy. The accuracy and the correctness of the derived equations are validated analytically. Using these equations, the RAP of non-repairable series-parallel systems with a choice of redundancy strategies is formulated. The proposed mathematical model maximizes exact system reliability at mission time given system design constraints. Unlike most of the previous formulations, the possibility of using heterogeneous components in each subsystem is provided so that the active components can be of one type and the standby ones of the other. The results of an illustrative example demonstrate the high performance of the proposed model in determining optimal design configuration and increasing system reliability.

System reliability analysis of small-cell deployment in heterogeneous cellular networks

This paper exhibits a primer on the use of modern system reliability techniques on several important topologies of small-cell deployment in multi-tier dense cellular networks. We synthesize a network into several subnetworks and use outage probability as a performance metric to formulate the small-cell deployment problem in the Boolean domain by means of an indicator function. The methodology employed herein includes disjointness for logically added expressions, arriving at a probability ready expression, and a transformation to the probability domain on a one-to-one basis by replacing indicator Boolean variables by their expectations and replacing logical operations by their arithmetical counterparts. This work also presents a systematic procedure of computing several reliability metrics such as the useful redundancy region, mean-time-to-failure, importance measures of the links, and quantification of uncertainty in system reliability as a function of uncertainties in link reliabilities by considering both identical and non-identical link failures. Non-linear algorithms are also tested on the optimization problem that minimizes system unreliability. We contribute to the important issue of analyzing small-cell deployment by providing exact system reliability metrics and hence open a new frontier for software defined networks controllers.

Approximate Reliability Evaluation of Large-Scale Multistate Series-Parallel Systems

Multistate series-parallel system (MSSPS) is a widely used model for representing engineering systems, whose reliability has been extensively analyzed. Universal generating function (UGF) is an efficient method for evaluating the reliability of MSSPS. However, when facing the large-scale MSSPS, where the number of system components and possible states are enormous, calclating the exact system reliability can be rather time-consuming. To evaluate the reliability of large-scale MSSPS more efficiently, this paper proposes an approximation method, named continuization discretization approximation (CDA) method. The CDA approach consists of continuization and discretization processes. The continuization process applies Gaussian approximation method based on the central limit theory and the UGF technique to evaluate parallel subsystems. While the discretization process discretizes the continuous distribution to a discrete one, and proposes an algorithm to evaluate the series subsystems efficiently. The efficiency and accuracy performance of the CDA method can be adjusted by parameters according to the computational resource and the system scale. The newly proposed method is compared to the existing methods in evaluating the large-scale MSSPS. Numerical examples show that the CDA method has evident advantage in computational efficiency with satisfactory accuracy performance.

System reliability upper bound assessment for health-aware control of complex systems

When a system is composed of a large number of components, the computation of its exact reliability turns computationally costly and depending on the number of components it has such computation could be infeasible. This paper investigates the possibility of using a system reliability approximation. Specifically, an upper bound of the system reliability will be computed in order to overcome the computational problem of determining the exact system reliability and its integration into a health-aware control strategy. A comparison between the exact and the approximated approaches is presented on a drinking water network system.

Narrower System Reliability Bounds With Incomplete Component Information and Stochastic Process Loading

Incomplete component information may lead to wide bounds for system reliability prediction, making decisions difficult in the system design stage. The missing information is often the component dependence, which is a crucial source for the exact system reliability estimation. Component dependence exists due to the shared environment and operating conditions. But it is difficult for system designers to model component dependence because they may have limited information about component design details if outside suppliers designed and manufactured the components. This research intends to produce narrow system reliability bounds with a new way for system designers to consider the component dependence implicitly and automatically without knowing component design details. The proposed method is applicable for a wide range of applications where the time-dependent system stochastic load is shared by components of the system. Simulation is used to obtain the extreme value of the system load for a given period of time, and optimization is employed to estimate the system reliability bounds, which are narrower than those from the traditional method with independent component assumption and completely dependent component assumption. Examples are provided to demonstrate the proposed method.

주기적 검사가 실시되는 원샷 시스템의 신뢰도 분석

This paper considers one-shot systems such as missiles, air bags of automobiles that are stored for a long time and are used at most once. One shot systems are inspected periodically to detect system failures and repair the system because we do not know whether the system will work or not on demand. Thus, we can keep high availability of the system by periodic inspection. Martinez (1984) obtained the system reliability approximately. In this paper, we obtain the exact system reliability under periodic inspection. Finally, we compare the system reliability from our formula with one of Martinez (1984) by numerical examples.

Optimal Allocation of Connecting Elements in Phase Mission Linear Consecutively-Connected Systems

Many continuous transportation systems and communication networks can be modeled as a linear consecutively connected system (LCCS) consisting of n+1 linearly ordered nodes. Some of these nodes contain connection elements (CEs) with different characteristics. Each CE i in its working state provides a connection between the node to which it belongs and L(i) next nodes, the set of nodes that follow the given node. If the system contains any node not connected with any previous node, then it fails. We consider multi-phase LCCS that should perform a sequence of transmission tasks. In each phase, it should provide continuous connection along a specific path of nodes. Different paths can contain the same nodes, which creates statistical dependence across the phases. Different nodes are characterized by specific conditions expressed by different failure acceleration factors affecting the CEs located at these nodes. Thus, an accurate reliability analysis of a multi-phase LCCS must consider the statistical dependencies of CE states across phases, and dynamics in path structures as well as in the failure acceleration factors. In this paper, we propose a method for optimal allocation of CEs in multi-phase LCCS. The method is based on a recursive algorithm for exact system reliability evaluation, and the genetic algorithm for the optimal allocation of CEs to nodes of LCCS. The proposed approach is illustrated using a practical example of wireless sensor networks.

Evaluation of System Reliabilities for a Maintainable Stochastic-Flow Network

This paper proposes a performance indicator to evaluate the capability of a maintainable stochastic-flow network (MSFN). This MSFN is required to preserve a minimal service level so that it can send <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> units of data or commodity from the source to the sink through multiple paths within time T. The proposed system reliability performance indicator quantifies the probability that a MSFN delivers a capacity level above the minimal service level with a budget no greater than B. Two procedures are integrated in the proposed algorithm: a procedure to estimate system reliability, and an adjusting procedure that utilizes the branch-and-bound approach for exact system reliability. The estimated system reliability with lower and upper bounds, and the exact system reliability, are then computed by applying the recursive sum of disjoint products (RSDP) algorithm.

Reliability Analysis of Nonrepairable Cold-Standby Systems Using Sequential Binary Decision Diagrams

Many real-world systems, particularly those with limited power resources, are designed with cold-standby redundancy for achieving fault tolerance and high reliability. Cold-standby units are unpowered and, thus, do not consume any power until needed to replace a faulty online component. Cold-standby redundancy creates sequential dependence between the online component and standby components; in particular, a standby component can start to work and then fail only after the online component has failed. Traditional approaches to handling the cold-standby redundancy are typically state-space-based or simulation-based or inclusion/exclusion-based methods. Those methods, however, have the state-space explosion problem and/or require long computation time particularly when results with a high degree of accuracy are desired. In this paper, we propose an analytical method based on sequential binary decision diagrams (SBDD) for combinatorial reliability analysis of nonrepairable cold-standby systems. Different from the simulation-based methods, the proposed approach can generate exact system reliability results. In addition, the system SBDD model and reliability evaluation expression, once generated, are reusable for the reliability analysis with different component failure parameters. The approach has no limitation on the type of time-to-failure distributions for the system components or on the system structure. Application and advantages of the proposed approach are illustrated through several case studies.

Estimated and exact system reliabilities of a maintainable computer network

This paper presents an algorithm to evaluate estimated and exact system reliabilities for a computer network in the cloud computing environment. From the quality of service (QOS) viewpoint, the computer network should be maintained when falling to a specific state such that it cannot afford enough capacity to satisfy demand. Moreover, the transmission time should be concerned as well. Thus, the data can be sent through several disjoint minimal paths simultaneously to shorten the transmission time. Under the maintenance budget B and time constraint T, we evaluate the system reliability that d units of data can be sent from the cloud to the client through multiple paths. Two procedures are integrated in the proposed algorithm-an estimation procedure for estimated system reliability and an adjusting procedure utilizing the branch-and-bound approach for exact system reliability. Subsequently, the estimated system reliability with lower bound and upper bound, and exact system reliability are computed by applying the recursive sum of disjoint products (RSDP) algorithm.

Reliability evaluation and optimal design in heterogeneous multi-state series-parallel systems

This paper addresses the heterogeneous redundancy allocation problem in multi-state series-parallel reliability structures with the objective to minimize the total cost of system design satisfying the given reliability constraint and the consumer load demand. The demand distribution is presented as a piecewise cumulative load curve and each subsystem is allowed to consist of parallel redundant components of not more than three types. The system uses binary capacitated components chosen from a list of available products to provide redundancy so as to increase system performance and reliability. The components are characterized by their feeding capacity, reliability and cost. A system that consists of elements with different reliability and productivity parameters has the capacity strongly dependent upon the selection of constituent components. A binomial probability based method to compute exact system reliability index is suggested. To analyze the problem and suggest an optimal/near-optimal system structure, an ant colony optimization algorithm has been presented. The solution approach consists of a series of simple steps as used in early ant colony optimization algorithms dealing with other optimization problems and offers straightforward analysis. Four multi-state system design problems have been solved for illustration. Two problems are taken from the literature and solved to compare the algorithm with the other existing methods. The other two problems are based upon randomly generated data. The results show that the method can be appealing to many researchers with regard to the time efficiency and yet without compromising over the solution quality.

Reliability and component importance analysis of substation automation systems

This paper aims to present a comprehensive technique to quantitatively assess the reliability of substation automation systems. The technique is based on the tie-sets methodology. In order to demonstrate the application of the proposed technique, a variety of substation automation architectures is first introduced. The associated reliability block diagrams as well as the exact system reliability are then given. The impacts and the degree of importance of various components on the reliability of substation automation systems are presented. Two suitable measures of importance are selected. The first is the Birnbaum’s measure used to determine the bottleneck of the system reliability. The second measure uses criticality importance to diagnose failures and generating repair or inspection checklists.

Optimal Structure in Heterogeneous Multi-state Series-parallel Reliability Systems

The problem of allocating optimum heterogeneous redundancy in multi-state series-parallel reliability structures is addressed in this paper. The objective is to obtain a configuration that minimizes the total cost of system design satisfying the given reliability constraint and the consumer load demand. The demand distribution is presented as a piecewise cumulative load curve and each subsystem is allowed to consist of parallel redundant components of not more than four types to construct a reliable system. The redundant components are capacitated binary and chosen from a list of products available in the market. The components are characterized by their feeding capacity, reliability and cost. A system that consists of elements with different reliability and productivity parameters has the capacity strongly dependent upon the selection of constituent components. A binomial probability based method to compute exact system reliability index is suggested. To analyze the problem and suggest an optimal system structure an ant colony optimization (ACO) algorithm is presented. The solution approach consists of a series of simple steps as used in basic ACO algorithms and is still capable to yield very good solutions with promising time efficiency. A randomly generated problem of power station coal transportation system with initial structure is solved for illustration.

Development of an algorithm for automated cause-consequence diagram construction

Cause-consequence analysis is one of the best tools available for a comprehensive reliability study. The Cause-Consequence Diagram (CCD) method, like fault tree analysis, represents the failure logic of the system, but in addition the CCD also identifies the complete set of consequences following a given initiating event. Despite the clear appeal of this approach to engineers the CCD method has its drawbacks. If the diagram construction and its analysis could be automated it would increase the usefulness of the method. This paper describes the development of an algorithm for automated CCD construction. The algorithm builds on methods developed previously for fault tree construction, such as topology diagrams, component decision tables, etc. Once constructed, the diagram can be quantified to give exact system reliability. To demonstrate the feasibility of the approach the algorithm is applied to a simple example.

Sensor system reliability modeling and analysis for fault diagnosis in multistage manufacturing processes

This paper investigates the reliability of coordinate sensor systems used for process fault diagnosis in multistage manufacturing processes. When considering catastrophic sensor failure, the reliability of a coordinate sensor system is defined based on its diagnosability performance. A mathematical tool called matroid theory is applied to study the reliability of the coordinate sensor system; properties of the minimal paths and minimal cuts are derived; efficient methods are developed to evaluate the exact system reliability for two special types of systems; and an efficient algorithm to evaluate the min–max lower bound of system reliability is provided that does not require assuming that all minimal paths must be known in advance. The proposed models and the developed methods are illustrated and applied in two case studies for fault diagnosis of a multistage panel assembly process.

Evaluating methods for the reliability of a three‐dimensional k‐within system

PurposeFor the considered system, an enumeration method is applicable to evaluate the exact system reliability only for very small‐sized systems, because, when the size of system is large, it takes huge execution time. Therefore, the paper provides approximate values for the system reliability as useful for calculating the reliability of large systems in a reasonable execution time.Design/methodology/approachThe paper provides upper and lower bounds of the system reliability, and limit theorem for the reliability of our considered system in i.i.d. case.FindingsThe paper experimentally finds that the proposed upper and lower bounds are effective when component reliabilities close to one or the value of k becomes larger. Next, it concludes approximate values for approximate equation derived from the limit theorem are always smaller than lower bound through numerical experiments.Research limitations/implicationsThe upper and lower bounds for the reliability of a system can be calculated by using the reliability of a small system by the same idea as previous study for two‐dimensional system.Practical implicationsUp to now some researchers studied multi‐dimensional consecutive‐k‐out‐of‐n:F systems, and showed promising applications of such multi‐dimensional models, e.g. diagnosis of a disease diagnosed by reading an X‐ray. As another examples, three‐dimensional system can be applied for the mathematical model of a three‐dimensional flash memory cell failure model, and so on.Originality/valueThe paper considers a kind of three‐dimensional k‐within‐consecutive‐r‐out‐of‐n:F system. It proposes upper and lower bounds of the system reliability and limit theorem.

Evaluating methods for the reliability of a large 2‐dimensional rectangular k‐within‐consecutive‐(r, s)‐out‐of‐(m, n):F system

AbstractA 2‐dimensional rectangular k‐within‐consecutive‐(r, s)‐out‐of‐(m, n):F system consists of m × n components, and fails if and only if k or more components fail in an r × s submatrix. This system can be treated as a reliability model for TFT liquid crystal displays, wireless communication networks, etc. Although an effective method has been developed for evaluating the exact system reliability of small or medium‐sized systems, that method needs extremely high computing time and memory capacity when applied to larger systems. Therefore, developing upper and lower bounds and accurate approximations for system reliability is useful for large systems. In this paper, first, we propose new upper and lower bounds for the reliability of a 2‐dimensional rectangular k‐within‐consecutive‐(r, s)‐out‐of‐(m, n):F system. Secondly, we propose two limit theorems for that system. With these theorems we can obtain accurate approximations for system reliabilities when the system is large and component reliabilities are close to one. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005

Waiting time problems for a two-dimensional pattern

We consider waiting time problems for a two-dimensional pattern in a sequence of i.i.d. random vectors each of whose entries is 0 or 1. We deal with a two-dimensional pattern with a general shape in the two-dimensional lattice which is generated by the above sequence of random vectors. A general method for obtaining the exact distribution of the waiting time for the first occurrence of the pattern in the sequence is presented. The method is an extension of the method of conditional probability generating functions and it is very suitable for computations with computer algebra systems as well as usual numerical computations. Computational results applied to computation of exact system reliability are also given.