Reliability of redundant ductile structures with uncertain system failure criteria

Current reliability based approaches to structural design are typically element based: they commonly include uncertainties in the structural resistance, applied loads and geometric parameters, and in some cases in the idealized structural model. Nevertheless, the true measure of safety is the structural systems reliability which must consider multiple failure paths, load sharing and load redistribution after member failures, and is beyond the domain of element reliability analysis. Identification of system failure is often subjective, and a crisp definition of system failure arises naturally only in a few idealized instances equally important. We analyse the multi-girder steel highway bridge as a k out of n active parallel system. System failure is defined as gross inelastic deformation of the bridge deck; the subjectivity in the failure criterion is accounted for by generalizing k as a random variable. Randomness in k arises from a non-unique relation between number of failed girders and maximum deflection and from randomness in the definition of the failure deflection. We show how uncertain failure criteria and structural systems analyses can be decoupled. Randomness in the transverse location of trucks is considered and elastic perfectly plastic material response is assumed. The role of the system factor modifying the element-reliability based design equation to achieve a target system reliability is also demonstrated.     

Reliability optimization using multiobjective ant colony system approaches

The multiobjective ant colony system (ACS) meta-heuristic has been developed to provide solutions for the reliability optimization problem of series-parallel systems. This type of problems involves selection of components with multiple choices and redundancy levels that produce maximum benefits, and is subject to the cost and weight constraints at the system level. These are very common and realistic problems encountered in conceptual design of many engineering systems. It is becoming increasingly important to develop efficient solutions to these problems because many mechanical and electrical systems are becoming more complex, even as development schedules get shorter and reliability requirements become very stringent. The multiobjective ACS algorithm offers distinct advantages to these problems compared with alternative optimization methods, and can be applied to a more diverse problem domain with respect to the type or size of the problems. Through the combination of probabilistic search, multiobjective formulation of local moves and the dynamic penalty method, the multiobjective ACSRAP, allows us to obtain an optimal design solution very frequently and more quickly than with some other heuristic approaches. The proposed algorithm was successfully applied to an engineering design problem of gearbox with multiple stages.     

Reliability assessment of embedded digital system using multi-state function

This work describes a combinatorial model for estimating the reliability of the embedded digital system by means of multi-state function. This model includes a coverage model for fault-handling techniques implemented in digital systems. The fault-handling techniques make it difficult for many types of components in digital system to be treated as binary state, good or bad. The multi-state function provides a complete analysis of multi-state systems as which the digital systems can be regarded. Through adaptation of software operational profile flow to multi-state function, the HW/SW interaction is also considered for estimation of the reliability of digital system. Using this model, we evaluate the reliability of one board controller in a digital system, Interposing Logic System (ILS), which is installed in YGN nuclear power units 3 and 4. Since the proposed model is a generalized combinatorial model, the simplification of this model becomes the conventional model that treats the system as binary state. This modeling method is particularly attractive for embedded systems in which small sized application software is implemented since it will require very laborious work for this method to be applied to systems with large software.     

Structure optimization of multi-state system with time redundancy

In this article, a multi-state system with time redundancy where each system element has its own operation time is considered. In addition, the system total task must be performed during the restricted time. The reliability optimization problem is treated as finding the minimal cost system structure subject to the reliability constraint. A method for reliability optimization for systems with time redundancy is proposed. This method is based on the universal generating function technique for the reliability index computation and on genetic algorithm for the optimization. It provides a solution for the optimization problem for the complex series–parallel system and for the system with bridge topology. Two types of systems will illustrate the approach: systems with ordinary hot reserve and systems with work sharing between elements connected in parallel. Numerical examples are also given.     

Ant system for reliability optimization of a series system with multiple-choice and budget constraints

Many researchers have shown that insect colonies behavior can be seen as a natural model of collective problem solving. The analogy between the way ants look for food and combinatorial optimization problems has given rise to a new computational paradigm, which is called ant system. This paper presents an application of ant system in a reliability optimization problem for a series system with multiple-choice constraints incorporated at each subsystem, to maximize the system reliability subject to the system budget. The problem is formulated as a nonlinear binary integer programming problem and characterized as an NP-hard problem. This problem is solved by developing and demonstrating a problem-specific ant system algorithm. In this algorithm, solutions of the reliability optimization problem are repeatedly constructed by considering the trace factor and the desirability factor. A local search is used to improve the quality of the solutions obtained by each ant. A penalty factor is introduced to deal with the budget constraint. Simulations have shown that the proposed ant system is efficient with respect to the quality of solutions and the computing time.     

Structure optimization of multi-state system with two failure modes

When systems with two failure modes (STFM) are considered, introducing redundant elements may either increase or decrease system reliability. Therefore the problem of system structure optimization arises. In this paper we consider systems consisting of elements characterized by different reliability and nominal performance rates. Such systems are multi-state because they can have different levels of output performance depending on the combination of elements available at the moment. The algorithm that determines the structure of multi-state STFM, which maximizes system reliability and/or expected performance is presented. In this algorithm, system elements are chosen from a list of available equipment. Reliability is defined as the probability of satisfaction of given constraints imposed on system performance in both modes.The procedure developed to solve this problem is based on the use of a universal moment generating function (UMGF) for the fast evaluation of multi-state system reliability and a genetic algorithm for optimization. Basic UMGF technique operators are developed for two different types of systems, based, respectively, on transmitting capacity and on processing time. Examples of the optimization of series–parallel structures of both types are presented.     

Reliability modeling and optimization of K/N phased mission system with backup missions and global redundancy strategy

The mission success probability (MSP) is a critical indicator for phased mission systems (PMSs). In the modern aerospace industry, redundancy techniques, including component/phase redundancy, are commonly seen to increase the MSP of the whole system. These component/phase redundancies make the reliability analysis more complex. Meanwhile, one or more components are required for normal working for different subsystems, called the K/N structure. In this article, a Markov-process method is proposed for PMS with K/N subsystems and different redundancy strategies. Then, a universal system optimization model is proposed to optimize system structure and redundancy strategies for all subsystems at the same time. Then, an improved genetic algorithm (GA) is used to resolve the optimization problem. At last, a propulsion system is used as an engineering case, showing the proposed binary decision diagram-based method.     

Common cause failure probabilities in standby safety system fault tree analysis with testing—scheme and timing dependencies

Modelling and quantification of common cause failures (CCFs) in redundant standby safety systems can be implemented by implicit or explicit fault tree techniques. Common cause event probabilities are derived for both methods for systems with time-related CCFs modelled by general multiple failure rates. The probabilities are determined so that the correct time-average risk can be obtained by a single computation. The impacts of test intervals and test staggering are included. Staggered testing is best with a certain extra-testing rule, although extra testing is not important for 1-out-of-n:G systems. An economic model provides insights into the impacts of various parameters: the optimal test interval increases with increasing redundancy and testing cost, and it decreases with increasing accident cost and initiating event rate. Staggered testing with extra tests allows for the longest optimal test intervals. A practical technique is outlined for incorporating assessment uncertainties in the estimation of multiple failure rates based on data from many plants or systems.     

Reliability optimization for weighted voting system

The voting system studied consists of n units, each of which provides a binary decision (0 or 1), or abstains from voting. The system output is 1 if the cumulative weight of all 1-opting units is at least a pre-specified fraction τ of the cumulative weight of all non-abstaining units. Otherwise the system output is 0.The existing method for evaluating the reliability of a weighted voting system can not be applied to real systems without imposing some restrictions because of its combinatorial complexity. In this paper a method is suggested which allows the reliability of weighted voting system to be exactly evaluated without imposing constraints on unit weights or threshold value. The approach is based on using a universal generating function technique. Using the suggested method an optimization procedure is developed for system reliability maximization by choosing proper unit weights and threshold values. A genetic algorithm is used as the optimization tool. Examples are presented.     

Redundancy analysis for repairable multi-state system by using combined stochastic processes methods and universal generating function technique

This paper discusses a type of redundancy that is typical in a multi-state system. It considers two interconnected multi-state systems where one multi-state system can satisfy its own stochastic demand and also can provide abundant resource (performance) to another system in order to improve the assisted system reliability. Traditional methods are usually not effective enough for reliability analysis for such multi-state systems because of the “dimensional curse” problem. This paper presents a new method for reliability evaluation for the repairable multi-state system considering such kind of redundancy. The proposed method is based on the combination of the universal generating function technique and random processes methods. The numerical example is presented to illustrate the proposed method.     

Reliability optimization of series-parallel systems with a choice of redundancy strategies using a genetic algorithm

This paper proposes a genetic algorithm (GA) for a redundancy allocation problem for the series-parallel system when the redundancy strategy can be chosen for individual subsystems. Majority of the solution methods for the general redundancy allocation problems assume that the redundancy strategy for each subsystem is predetermined and fixed. In general, active redundancy has received more attention in the past. However, in practice both active and cold-standby redundancies may be used within a particular system design and the choice of the redundancy strategy becomes an additional decision variable. Thus, the problem is to select the best redundancy strategy, component, and redundancy level for each subsystem in order to maximize the system reliability under system-level constraints. This belongs to the NP-hard class of problems. Due to its complexity, it is so difficult to optimally solve such a problem by using traditional optimization tools. It is demonstrated in this paper that GA is an efficient method for solving this type of problems. Finally, computational results for a typical scenario are presented and the robustness of the proposed algorithm is discussed.     

Reliability allocation problem in a series–parallel system

In order to improve system reliability, designers may introduce in a system different technologies in parallel. When each technology is composed of components in series, the configuration belongs to the series–parallel systems. This type of system has not been studied as much as the parallel–series architecture. There exist no methods dedicated to the reliability allocation in series–parallel systems with different technologies. We propose in this paper theoretical and practical results for the allocation problem in a series–parallel system. Two resolution approaches are developed. Firstly, a one stage problem is studied and the results are exploited for the multi-stages problem. A theoretical condition for obtaining the optimal allocation is developed. Since this condition is too restrictive, we secondly propose an alternative approach based on an approximated function and the results of the one-stage study. This second approach is applied to numerical examples.     

马尔可夫链模型在软件可靠性测试中的应用

现行的软件可靠性分析方法禁锢了人们从更简单层次对软件系统的可靠性进行研究。基于上述认识,为了缩短软件测试周期,文中提出了一种新的软件可靠性测试分析方法。该方法把马尔可夫链模型运用于软件可靠性测试中,在测试过程中使用了新的评判准则分析测试结果,通过实例证明了该评判准则的实用性和有效性。从而为更快速地评估软件的可靠性提供了可能。     

潜艇自航模试验系统可靠性冗余优化

可靠性设计水平直接影响潜艇自航模系统设计的成败.在某潜艇自航模任务与系统构成分析的基础上,开展了某潜艇自航模系统的可靠性分析,应用多阶段任务系统可靠性模型理论建立了该系统的任务可靠性分析和计算模型,综合潜艇自航模的设计约束条件,并结合满意度的概念,建立了系统可靠性冗余优化模型且利用微粒群算法求解.示例证明了模型的可用性及可信性.     

Reliability graph with general gates: an intuitive and practical method for system reliability analysis

In this paper, we propose an intuitive and practical method for system reliability analysis. Among the existing methods for system reliability analysis, reliability graph is particularly attractive due to its intuitiveness, even though it is not widely used for system reliability analysis. We provide an explanation for why it is not widely used, and propose a new method, named reliability graph with general gates, which is an extension of the conventional reliability graph. An evaluation method utilizing existing commercial or free software tools are also provided. We conclude that the proposed method is intuitive, easy-to-use, and practical while as powerful as fault tree analysis, which is currently the most widely used method for system reliability analysis.     

Reliability and failure analysis of GaAs mesfets on GaAs and Si substrates

Reliability of GaAs MESFET's on GaAs and Si was studied using high-temperature storage tests. Tested MESFETs were back etched and analysed by SEM, EDX and TEM. The major failure modes have been identified as gate sinking and an increase of ohmic contact resistance through Au particle formation.     

Reward optimization of a repairable system

This paper analyzes a system subject to repairable and non-repairable failures. Non-repairable failures lead to replacement of the system. Repairable failures, first lead to repair but they lead to replacement after a fixed number of repairs. Operating and repair times follow phase type distributions (PH-distributions) and the pattern of the operating times is modelled by a geometric process. In this context, the problem is to find the optimal number of repairs, which maximizes the long-run average reward per unit time. To this end, the optimal number is determined and it is obtained by efficient numerical procedures.     

Quantitative reliability analysis of different design alternatives for steer-by-wire system

For a fault-tolerant SBW (Steer-By-Wire) system, two structural designs with and without a backup mechanical coupling are proposed and assessed by a unified approach from a reliability point of view. An operation procedure to cope with partial system degradations prior to a complete loss of steering is presented for each design. The procedure can be represented by a transition diagram that, in turn, is converted into a layered Markov state transition diagram by introduction of augmented states. Reliabilities of the two designs are quantitatively compared by numerical integration of the Markov diagrams based on realistic failure rate data; system degradation probabilities are obtained as well as the complete steering loss probability. A power source is identified as a key component for the SBW to function without a mechanical backup.     

Bracketing of failure path probability in a system with ageing repair times

In practical terms, the distributions of repair times are not known; we have only mean values. We show here that by assuming these distributions to be ageing, it is possible in many cases to bracket availability and reliability using only Mean Times to Repair. Furthermore, this computation can be carried out using Markov models.     

Reliability of structures in high dimensions. Part II. Theoretical validation

This paper provides proofs to the claims made [Probab. Eng. Mech. (submitted)] concerning the convergence rates of the estimators used.