Incorporating common-cause failures into nonrepairable multistateseries-parallel system analysis

This paper adapts the universal generating function method of multistate system reliability analysis to incorporate common-cause failures (CCF). An implicit 2-stage approach is used. In stage #1, a polynomial representation of system-output performance distribution is obtained without considering system elements which are subject to CCF. In stage #2, the contribution of CCF is correctly included based on information stored in vector-indicators that describe states of system elements belonging to various common-cause groups. A straightforward procedure is suggested for evaluating reliability functions of nonrepairable series-parallel multistate systems with CCF. This procedure allows the reliability functions to be obtained numerically. Examples are given     

A continuous-time Bayesian network reliability modeling, and analysis framework

We present a continuous-time Bayesian network (CTBN) framework for dynamic systems reliability modeling and analysis. Dynamic systems exhibit complex behaviors and interactions between their components; where not only the combination of failure events matters, but so does the sequence ordering of the failures. Similar to dynamic fault trees, the CTBN framework defines a set of 'basic' BN constructs that capture well-defined system components' behaviors and interactions. Combining, in a structured way, the various 'basic' Bayesian network constructs enables the user to construct, in a modular and hierarchical fashion, the system model. Within the CTBN framework, one can perform various analyses, including reliability, sensitivity, and uncertainty analyses. All the analyses allow the user to obtain closed-form solutions.     

Reliability Evaluation of Phased-Mission Systems With Imperfect Fault Coverage and Common-Cause Failures

This paper proposes efficient methods to assess the reliability of phased-mission systems (PMS) considering both imperfect fault coverage (IPC), and common-cause failures (CCF). The IPC introduces multimode failures that must be considered in the accurate reliability analysis of PMS. Another difficulty in analysis is to allow for multiple CCF that can affect different subsets of system components, and which can occur s-dependently. Our methodology for resolving the above difficulties is to separate the consideration of both IPC and CCF from the combinatorics of the binary decision diagram-based solution, and adjust the input and output of the program to generate the reliability of PMS with IPC and CCF. According to the separation order, two equivalent approaches are developed. The applications and advantages of the approaches are illustrated through examples. PMS without IPC and/or CCF appear as special cases of the approaches     

On the construction of hierarchical fuzzy systems models

A review of the basic ideas of fuzzy systems modeling is provided. We introduce a hierarchical-type fuzzy systems model called a hierarchical prioritized structure (HPS) and review its structure, operation, and the interlevel aggregation algorithm. We then turn to the issue of constructing the HPS. Consideration is first given to the case in which rules are provided by an expert. Detailed consideration is given to the problem of completing incomplete priorities by use of the principle of maximal buoyancy. A mathematical programming method is introduced for the implementation of this approach. The issue of tuning hierarchical models is addressed. We next introduce a dynamic approach to the formulation of an HPS directly from data that enables us to continually update our model as more observations become available. This approach allows a system's builder to start with a default model and include exceptions     

Reliability Analysis of Computer Systems Using Dataflow Graph Models

We use dataflow graphs to represent the computational structure, analogous to Petri nets and Turing machines, and have developed a method for analyzing the reliability of computer systems modeled as dataflow graphs. Because of the hierarchical nature of dataflow graphs, systems can be analyzed at several levels of abstraction. Reliabilities of subgraphs can be calculated using either traditional techniques or dataflow approach presented here (recursively). The reliabilities of subgraphs can then be combined leading to decomposition-aggregation approach. The time needed for an actor to complete its operation is not included in our analysis of dataflow graphs. Incorporation of the time element compounds the problem and we have not studied it yet.     

A new dynamic programming method for reliability & redundancy allocation in a parallel-series system

Reliability & redundancy allocation is one of the most frequently encountered problems in system design. This problem is subject to constraints related to the design, such as required structural, physical, and technical characteristics; and the components available in the market. This last constraint implies that system components, and their reliability, must belong to a finite set. For a parallel-series system, we show that the problem can be modeled as an integer linear program, and solved by a decomposition approach. The problem is decomposed into as many sub-problems as subsystems, one sub-problem for each subsystem. The sub-problem for a given subsystem consists of determining the number of components of each type in order to reach a given reliability target with a minimum cost. The global problem consists of determining the reliability target of subsystems. We show that the sub-problems are equivalent to one-dimensional knapsack problems which can be solved in pseudopolynomial time with a dynamic programming approach. We show that the global problem can also be solved by a dynamic programming technique. We also show that the obtained method YCC converges toward an optimal solution.     

部件相依复杂系统可靠性模型及其寿命界限分析

文章应用Copula函数,研究了部件相依的复杂系统可靠性问题,给出了F-G-M Copula函数下一般系统的可靠度、平均寿命、平均寿命误差韵表达式,讨论了部件正象限相依下复杂系统的平均寿命与部件独立时系统的平均寿命的关系,并研究了串联与并联系统的界限,通过算例分析了部件相依下对平均寿命的影响程度。     

Evaluation of system reliability with common-cause failures, by apseudo-environments model

An efficient method for calculating system reliability with CCFs (common-cause failures) is presented by applying the factoring (total probability) theorem when the system and its associated class of CCFs are both arbitrary. Existing methods apply this theorem recursively until no CCF remains to be considered, and so can be time-consuming in computation. The method applies such a theorem only once and can be carried out in two steps: (1) determine each state in terms of the occurrence (or not) of every CCF in the associated class, to regard it as a pseudo-environment and to calculate its probability or weight; (2) determine each resulting subsystem of the system under the environment, calculate its reliability as in the no CCF case and take the weighted sum of such reliabilities, viz, the system reliability. This method is in terms of a Markov process and requires only the occurrence rate of each CCF to obtain the probability of each environment and only the failure rate of each component to obtain the system reliability under each environment; hence, it is practical, efficient, and useful     

Reliability Modeling Using SHARPE

Combinatorial models such as fault trees and reliability block diagrams are efficient for model specification and often efficient in their evaluation. But it is difficult, if not impossible, to allow for dependencies (such as repair dependency and near-coincident-fault type dependency), transient and intermittent faults, standby systems with warm spares, and so on. Markov models can capture such important system behavior, but the size of a Markov model can grow exponentially with the number of components in this system. This paper presents an approach for avoiding the large state space problem. The approach uses a hierarchical modeling technique for analyzing complex reliability models. It allows the flexibility of Markov models where necessary and retains the efficiency of combinatorial solution where possible. Based on this approach a computer program called SHARPE (Symbolic Hierarchical Automated Reliability and Performance Evaluator) has been written. The hierarchical modeling technique provides a very flexible mechanism for using decomposition and aggregation to model large systems; it allows for both combinatorial and Markov or semi-Markov submodels, and can analyze each model to produce a distribution function. The choice of the number of levels of models and the model types at each level is left up to the modeler. Component distribution functions can be any exponential polynomial whose range is between zero and one. Examples show how combinations of models can be used to evaluate the reliability and availability of large systems using SHARPE.     

Hierarchical Variance Decomposition of System Reliability Estimates With Duplicated Components

A hierarchical decomposition procedure is proposed to determine the variance of the reliability estimate for complex systems with duplicated components. For these systems, multiple copies of the same component type are used within the system, but only a single reliability estimate is available for each distinct component type. The variance of the reliability estimate is magnified at the system-level due to the covariance of component reliability estimates. Estimating the covariance becomes a formidable task if the system structure is complicated. A hierarchical model is proposed to decompose the system reliability estimate into component levels through intermediate layers. The decomposition procedure causes reliability estimates of duplicated components to remain $s$-independent when computing the associated variance on the adjacent upper layer. The first order Taylor series expansion is used to propagate the variance from the component level to the system level via intermediate layers. The hierarchical decomposition is preferable for designing robust, reliable systems by reducing or minimizing the system reliability variance at the component level.      

Multilevel Redundancy Allocation Optimization Using Hierarchical Genetic Algorithm

This paper proposes a generalized formulation for multilevel redundancy allocation problems that can handle redundancies for each unit in a hierarchical reliability system, with structures containing multiple layers of subsystems and components. Multilevel redundancy allocation is an especially powerful approach for improving the system reliability of such hierarchical configurations, and system optimization problems that take advantage of this approach are termed multilevel redundancy allocation optimization problems (MRAOP). Despite the growing interest in MRAOP, a survey of the literature indicates that most redundancy allocation schemes are mainly confined to a single level, and few problem-specific MRAOP have been proposed or solved. The design variables in MRAOP are hierarchically structured. This paper proposes a new variable coding method in which these hierarchical design variables are represented by two types of hierarchical genotype, termed ordinal node, and terminal node. These genotypes preserve the logical linkage among the hierarchical variables, and allow every possible combination of redundancy during the optimization process. Furthermore, this paper developed a hierarchical genetic algorithm (HGA) that uses special genetic operators to handle the hierarchical genotype representation of hierarchical design variables. For comparison, the customized HGA, and a conventional genetic algorithm (GA) in which design variables are coded in vector forms, are applied to solve MRAOP for series systems having two different configurations. The solutions obtained when using HGA are shown to be superior to the conventional GA solutions, indicating that the HGA here is especially suitable for solving MRAOP for series systems.      

Design Guidelines for Training-Based MIMO Systems With Feedback

In this paper, we study the optimal training and data transmission strategies for block fading multiple-input multiple-output (MIMO) systems with feedback. We consider both the channel gain feedback (CGF) system and the channel covariance feedback (CCF) system. Using an accurate capacity lower bound as a figure of merit that takes channel estimation errors into account, we investigate the optimization problems on the temporal power allocation to training and data transmission as well as the training length. For CGF systems without feedback delay, we prove that the optimal solutions coincide with those for nonfeedback systems. Moreover, we show that these solutions stay nearly optimal even in the presence of feedback delay. This finding is important for practical MIMO training design. For CCF systems, the optimal training length can be less than the number of transmit antennas, which is verified through numerical analysis. Taking this fact into account, we propose a simple yet near optimal transmission strategy for CCF systems, and derive the optimal temporal power allocation over pilot and data transmission.     

System Stress-Strength Reliability: The Multivariate Case

Present day complex systems with dependence between their components require more advanced models to evaluate their reliability. We compute the reliability of a system consisting of two subsystems S ₁, and S₂ connected in series, where the reliability of each subsystem is of general stress-strength type, defined by R₁ = P(A ^TX > B^TY). A & B are column-constant vectors, and strength X & stress Y are multigamma random vectors, i.e. (X, Y) ~ MG (alpha, beta), where alpha and beta are k-dimensional constant vectors. A Bayesian approach is adopted for R₂ = P(B ^TW > 0), where W is multinormal, i.e. W ~ MN(mu, T), with the mean vector mu, and the precision matrix T having a joint s-normal-Wishart prior distribution. Final computations are carried out by simulation, an approach which plays a major role in this article. The results obtained show that the approach adopted can deal effectively with the dependence between components of X & Y     

A hierarchical model for estimating the early reliability of complex systems

We describe a hierarchical Bayesian model for assessing the early reliability of complex systems, for which sparse or no system level failure data are available, except that which exists for comparable systems developed by different categories of manufacturers. Novel features of the model are the inclusion of a "quality" index to allow separate treatment for systems produced by "experienced" & "inexperienced" manufacturers. We show how this index can be employed to distinguish the behavior of systems produced by each category of manufacturer for the first few applications, with later pooling of outcomes from both categories of manufacturers after the first few uses (i.e., after inexperienced manufacturers gain experience). We demonstrate how this model, together with suitable informative priors, can reproduce the reliability growth in the modeled systems. Estimation of failure probabilities (and associated uncertainties) for early launches of new space vehicles is used to illustrate the methodology. Disclaimer-This paper is provided solely to illustrate how hierarchical Bayesian methods can be applied to estimate systems reliability (including uncertainties) for newly introduced complex systems with sparse or nonexistent system level test data. The example problem considered (i.e. estimating failure probabilities of new launch vehicles) is employed solely for illustrative purposes. The authors have made numerous assumptions & approximations throughout the document in order to demonstrate the central techniques. The specific methodologies, results, and conclusions presented in this paper are neither approved nor endorsed by the United States Air Force or the Federal Aviation Administration.     

Minimal-cost system reliability with discrete-choice sets for components

We focus on systems whose components come from discrete choice sets. In a choice set, the alternatives have increasing cost with increasing reliability. The objective is to ensure minimal cost for achieving a specified reliability for the systems under consideration. Earlier work restricted itself to series-parallel/parallel-series (S/P) systems and provided formulations and algorithms. However, these are not amenable for dealing with more general systems. In this paper, we develop alternative formulations and algorithms based on a dynamic programming approach, and these are generalized for S/P-reducible systems. The algorithms we obtain are pseudo-polynomial and possess fully polynomial approximation schemes. Moreover, the formulations & algorithms are amenable for further generalizations to k-out-of-n : G and k-out-of-n : G-reducible systems, though we cannot claim pseudo-polynomiality in these cases. The results of this paper are useful for developing reliable systems at minimum cost. As such, the formulation & algorithms are of vital interest for systems & reliability professionals & researchers.     

Approximate sensitivity analysis for acyclic Markov reliability models

Acyclic Markov chains are frequently used for reliability analysis of nonmaintained mission-critical computer-based systems. Since traditional sensitivity (or importance) analysis using Markov chains can be computationally expensive, an approximate approach is presented which is easy to compute and which performs quite well in test cases. This approach is presented in terms of a Markov chain which is used for solving a dynamic fault-tree, but the approach applies to any acyclic Markov reliability model.     

Some notes on wear-dependent systems

A system is subject to random failure through use. The key parameter of degradation, w, is measured continuously. A w-parametrization of the main reliability factors is introduced, simplifying the usual analyses. The limits of this approach are discussed.     

Reliability optimization of communication networks using simulated annealing

Two concepts of communication network reliability are considered. The first one, the ‘s-t’ reliability, is relevant for communication between a source station and a terminal station as in the case of a two way telephone communication. The second one, the overall reliability, is a measure of simultaneous connectedness among all stations in the network. An algorthm is presented which selects the optimal set of links that maximizes the overall reliability of the network subject to a cost restriction, given the allowable node-link incidences, the link costs and the link reliabilities. The algorithm employs a variaton of the simulated annealing approach coupled with a hierarchical strategy to achieve the gobal optimum. For complex networks, the present algorithm is advantageous over the traditional heuristic procedures. The solutions of two representative example network optimization problems are presented to illustrate the present algorithm. The potential utilization of parallel computing strategies in the present algorithm is also identified.     

Approximated reliability of r-out-of-n(F) system with common cause failure and maintenance

In modern industries very high reliability system are needed. To improve the reliability of system, the component redundancy and maintenance of component or system play an impotant role and must be studied. This paper presents a reliability model of a r-out-of-n(F) redundant system with maintenance and Common Cause Failure. Failed component repair times are arbitrarily distributed. The system is in a failed state when r units failed because of the combination of single element failure or CCF(Common Cause Failure). Laplace transformation of reliability is derived by using analysis of Markov state transition graph. By using the analyzed MTBF, we compute MTBF of r-out-of-n(F) system. The MTBF with CCF is saturable even if repair rate is large.Approximated reliability of the r-out-of-n(F) system with maintenance and Common Cause Failure O.SummaryThe paper presents a reliability model of a r-out-of-n(F) redundant system with maintenance and Common Cause Failure. Failed component repair times are arbitrarily distributed. The system is in a failed state when r units failed because of the combination of single element failure or Common Cause Failure. Laplace transformation of reliability is derived by using analysis of Markov state transition graph. By analyzing this mean visiting time equations, we compute MTBF and shows computational example. The MTBF with CCF is saturable even if repair rate is large. In general the maintenance overcomes MTBF bounds, But the repair method not overcome the MTBF saturation when the system has Common Cause Failure.