The impact of the operating environment on the design of redundant configurations

Safety systems are often characterized by substantial redundancy and diversification in safety critical components. In principle, such redundancy and diversification can bring benefits when compared to single-component systems. However, it has also been recognized that the evaluation of these benefits should take into account that redundancies cannot be founded, in practice, on the assumption of complete independence, so that the resulting risk profile is strongly dominated by dependent failures. It is therefore mandatory that the effects of common cause failures be estimated in any probabilistic safety assessment (PSA). Recently, in the Hughes model for hardware failures and in the Eckhardt and Lee models for software failures, it was proposed that the stressfulness of the operating environment affects the probability that a particular type of component will fail. Thus, dependence of component failure behaviors can arise indirectly through the variability of the environment which can directly affect the success of a redundant configuration. In this paper we investigate the impact of indirect component dependence by means of the introduction of a probability distribution which describes the variability of the environment. We show that the variance of the distribution of the number, or times, of system failures can give an indication of the presence of the environment. Further, the impact of the environment is shown to affect the reliability and the design of redundant configurations.     

Cold-standby redundancy optimization for nonrepairable systems

A solution methodology is described and demonstrated to determine optimal design configurations for nonrepairable series-parallel systems with cold-standby redundancy. This problem formulation considers non-constant component hazard functions and imperfect switching. The objective of the redundancy allocation problem is to select from available components and to determine an optimal design configuration to maximize system reliability. For cold-standby redundancy, other formulations have generally required exponential component time-to-failure and perfect switching assumptions. For this paper, there are multiple component choices available for each subsystem and component time-to-failure is distributed according to an Erlang distribution. Optimal solutions are determined based on an equivalent problem formulation and integer programming. Compared to other available algorithms, the methodology presented here more accurately models many engineering design problems with cold-standby redundancy. Previously, it has been difficult to determine optimal solutions for this class of problems or even lo efficiently calculate system reliability. The methodology is successfully demonstrated on a large problem with 14 subsystems.     

Maximization of System Reliability with a Choice of Redundancy Strategies

Optimal solutions to the redundancy allocation problem are determined when either active or cold-standby redundancy can be selectively chosen for individual subsystems. This problem involves the selection of components and redundancy levels to maximize system reliability. Previously, solutions to the problem could only be found if analysts were restricted to a predetermined redundancy strategy for the complete system. Generally, it had been assumed that active redundancy was to be used. However, in practice both active and cold-standby redundancy may be used within a particular system design and the choice of redundancy strategy becomes an additional decision variable. Available optimization algorithms are inadequate for these design problems and better alternatives are required. The methodology presented here is specifically developed to accommodate the case where there is a choice of redundancy strategy. The problem is formulated with imperfect sensing and switching of cold-standby redundant components and k -Erlang distributed time-to-failure. Optimal solutions to the problem are found by an equivalent problem formulation and integer programming. The methodology is demonstrated on a well-known test problem with interesting results. The optimal system design is distinctly different from the corresponding design obtained with only active redundancy. The availability of this tool can result in more reliable and cost-effective engineering designs.     

New insights on multi-state component criticality and importance

In this paper, new importance measures for multi-state systems with multi-state components are introduced and evaluated. These new measures complement and enhance current work done in the area of multi-state reliability. In general, importance measures are used to evaluate and rank the criticality of component or component states with respect to system reliability. The focus of the study is to provide intuitive and clear importance measures that can be used to enhance system reliability from two perspectives: (1) how a specific component affects multi-state system reliability and (2) how a particular component state or set of states affects multi-state system reliability. The first measure unsatisfied demand index, provides insight regarding a component or component state contribution to unsatisfied demand. The second measure multi-state failure frequency index, elaborates on an approach that quantifies the contribution of a particular component or component state to system failure. Finally, the multi-state redundancy importance identifies where to allocate component redundancy as to improve system reliability. The findings of this study indicate that both perspectives can be used to complement each other and as an effective tool to assess component criticality. Examples illustrate and compare the proposed measures with previous multi-state importance measures.     

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.     

Multi-state reliability assessment for shipboard hybrid turbine-diesel generation system with redundancy and aging effects

Complex system structures, dynamic energy demands, and tough operating environment pose a huge challenge to reliability assessment and risk control. Taking multi-state, redundant structure and aging impact into account, reliability assessment for shipboard hybrid turbine-diesel generation system is studied. This work adopts a comprehensive method combining the Markov method and universal generating function (UGF): the Markov method is used for reliability modeling at the unit level, and then synthesized and calculated through UGFs to obtain system-level reliability. Based on the above methodology, this work presents a multi-state system (MSS) model with different configuration structures and failure rate types, then compares the availability evaluation results of the single power generation system, the hybrid power system with redundancy and aging effects. The results show that (1) redundant design effectively improves system availability to meet power supply requirements; (2) in the case of system aging and imperfect repair, redundant configuration and power distribution can significantly improve the availability of power supply to be almost unaffected by aging, and effectively reduce the risk of performance failure; and (3) when the redundancy is applied, the system power supply availability is not sensitive in the high-value range of the redundant installed capacity ratio, but sensitive in the high-value range of effective coefficient about power compensation control.     

Soft computing approach for reliability optimization: State-of-the-art survey

In the broadest sense, reliability is a measure of performance of systems. As systems have grown more complex, the consequences of their unreliable behavior have become severe in terms of cost, effort, lives, etc., and the interest in assessing system reliability and the need for improving the reliability of products and systems have become very important. Most solution methods for reliability optimization assume that systems have redundancy components in series and/or parallel systems and alternative designs are available. Reliability optimization problems concentrate on optimal allocation of redundancy components and optimal selection of alternative designs to meet system requirement. In the past two decades, numerous reliability optimization techniques have been proposed. Generally, these techniques can be classified as linear programming, dynamic programming, integer programming, geometric programming, heuristic method, Lagrangean multiplier method and so on. A Genetic Algorithm (GA), as a soft computing approach, is a powerful tool for solving various reliability optimization problems. In this paper, we briefly survey GA-based approach for various reliability optimization problems, such as reliability optimization of redundant system, reliability optimization with alternative design, reliability optimization with time-dependent reliability, reliability optimization with interval coefficients, bicriteria reliability optimization, and reliability optimization with fuzzy goals. We also introduce the hybrid approaches for combining GA with fuzzy logic, neural network and other conventional search techniques. Finally, we have some experiments with an example of various reliability optimization problems using hybrid GA approach.     

The impact of diversity upon common mode failures

Recent models for the failure behaviour of systems involving redundancy and diversity have shown that common mode failures can be accounted for in terms of the variability of the failure probability of components over operational environments. Whenever such variability is present, we can expect that the overall system reliability will be less than we could have expected if the components could have been assumed to fail independently. We generalise a model of hardware redundancy due to Hughes, [Hughes, R. P., A new approach to common cause failure. Reliab. Engng, 17 (1987) 211–236] and show that with forced diversity, this unwelcome result no longer applies: in fact it becomes theoretically possible to do better than would be the case under independence of failures. An example shows how the new model can be used to estimate redundant system reliability from component data.     

On the Effect of Redundancy for Systems with Dependent Components

Parallel redundancy is a common approach to increase system reliability and mean time to failure. When studying systems with redundant components, it is usually assumed that the components are independent; however, this assumption is seldom valid in practice. In the case of dependent components, the effectiveness of adding a component may be quite different from the case of independent components. In this paper we investigate how the degree of correlation affects the increase in the mean lifetime for parallel redundancy when the two components are positively quadrant dependent. A number of bivariate distributions that can be used in the modeling of dependent components are compared. Various bounds are also derived. The results are useful in reliability analysis as well as for designers who are required to take into account the possible dependence among the components.     

Load sharing in series configuration

In reliability engineering, load sharing is typically associated with a system in parallel configuration. Examples include bridge support structures, electric power supply systems, and multiprocessor computing systems. We consider a reliability maximization problem for a high‐voltage commutation device, wherein the total voltage across the device is shared by the components in series configuration. Here, the increase of the number of load‐sharing components increases component–level reliability (as the voltage load per component reduces) but may decrease system–level reliability (because of the increased number of components in series). We provide the solution for the 2 popular life‐load models: the proportional hazard and the accelerated failure time models with the underlying exponential and Weibull distributions for both a single and dual failure modes.     

Reliability measurement of mass storage system for onboard instrumentation

Advances in spaceborne vehicular technology have made possible the long-life duration of the mission in harsh cosmic environments. Reliability and data integrity are the commonly emphasized requirements of spaceborne solid-state mass storage systems, because faults due to the harsh cosmic environments, such as extreme radiation, can be experienced throughout the mission. Acceptable dependability for these instruments has been achieved by using redundancy and repair. Reconfiguration (repair) of memory arrays using spare memory lines is the most common technique for reliability enhancement of memories with faults. Faulty cells in memory arrays are known to show spatial locality. This physical phenomenon is referred to as fault clustering . This paper initially investigates a quadrat-based fault model for memory arrays under clustered faults to establish a reliable foundation of measurement. Then, lifelong dependability of a fault-tolerant spaceborne memory system with hierarchical active redundancy, which consists of spare columns in each memory module and redundant memory modules, is measured in terms of the reliability (i.e., the conditional probability that the system performs correctly throughout the mission) and mean-time-to-failure (i.e., the expected time that a system will operate before it fails). Finally, minimal column redundancy search technique for the fault-tolerant memory system is proposed and verified through a series of parametric simulations. Thereby, design and fabrication of cost-effective and highly reliable fault-tolerant onboard mass storage system can be realized for dependable instrumentation.     

Fast approximate methods for the reliability analysis of computer networks

The complexity of computer communication networks has taken a dramatic upswing, following significant developments in electronic technology such as medium and large scale integrated circuits and microprocessors. Although components of a computer communication network are broadly classified into software, hardware and communications, the most important problem is that of ensuring the reliable flow of information from source to destination. An important parameter in the analysis of these networks is to find the probability of obtaining a situation in which each node in the network communicates with all other remaining communication centres (nodes). This probability, termed as overall reliability, can be determined using the concept of spanning trees. As the exact reliability evaluation becomes unmanageable even for a reasonable sized system, we present an approximate technique using clustering methods. It has been shown that when component reliability ⩾ 0.9, the suggested technique gives results quite close to those obtained by exact methods with an enormous saving in computation time and memory usage. For still quicker reliability analysis while designing the topological configuration of real-time computer systems, an empirical form of the reliability index is proposed which serves as a fairly good indicator of overall reliability and can be easily incorporated in a design procedure, such as local search, to design maximally reliable computer communication network.     

A new efficient algorithm for computing the imprecise reliability of monotone systems

Reliability analysis of complex systems by partial information about reliability of components and by different conditions of independence of components may be carried out by means of the imprecise probability theory which provides a unified framework (natural extension, lower and upper previsions) for computing the system reliability. However, the application of imprecise probabilities to reliability analysis meets with a complexity of optimization problems which have to be solved for obtaining the system reliability measures. Therefore, an efficient simplified algorithm to solve and decompose the optimization problems is proposed in the paper. This algorithm allows us to practically implement reliability analysis of monotone systems under partial and heterogeneous information about reliability of components and under conditions of the component independence or the lack of information about independence. A numerical example illustrates the algorithm.     

Fault-tolerant embedded system design and optimization considering reliability estimation uncertainty

In this paper, we model embedded system design and optimization, considering component redundancy and uncertainty in the component reliability estimates. The systems being studied consist of software embedded in associated hardware components. Very often, component reliability values are not known exactly. Therefore, for reliability analysis studies and system optimization, it is meaningful to consider component reliability estimates as random variables with associated estimation uncertainty. In this new research, the system design process is formulated as a multiple-objective optimization problem to maximize an estimate of system reliability, and also, to minimize the variance of the reliability estimate. The two objectives are combined by penalizing the variance for prospective solutions. The two most common fault-tolerant embedded system architectures, N-Version Programming and Recovery Block, are considered as strategies to improve system reliability by providing system redundancy. Four distinct models are presented to demonstrate the proposed optimization techniques with or without redundancy. For many design problems, multiple functionally equivalent software versions have failure correlation even if they have been independently developed. The failure correlation may result from faults in the software specification, faults from a voting algorithm, and/or related faults from any two software versions. Our approach considers this correlation in formulating practical optimization models. Genetic algorithms with a dynamic penalty function are applied in solving this optimization problem, and reasonable and interesting results are obtained and discussed.     

Reliability optimization of a redundant system with failure dependencies

In a multi-component system, the failure of one component can reduce the system reliability in two aspects: loss of the reliability contribution of this failed component, and the reconfiguration of the system, e.g., the redistribution of the system loading. The system reconfiguration can be triggered by the component failures as well as by adding redundancies. Hence, dependency is essential for the design of a multi-component system.In this paper, we study the design of a redundant system with the consideration of a specific kind of failure dependency, i.e., the redundant dependency. The dependence function is introduced to quantify the redundant dependency. With the dependence function, the redundant dependencies are further classified as independence, weak, linear, and strong dependencies. In addition, this classification is useful in that it facilitates the optimization resolution of the system design. Finally, an example is presented to illustrate the concept of redundant dependency and its application in system design. This paper thus conveys the significance of failure dependencies in the reliability optimization of systems.     

A heuristic for solving the redundancy allocation problem for multi-state series-parallel systems

The redundancy allocation problem is formulated with the objective of minimizing design cost, when the system exhibits a multi-state reliability behavior, given system-level performance constraints. When the multi-state nature of the system is considered, traditional solution methodologies are no longer valid. This study considers a multi-state series-parallel system (MSPS) with capacitated binary components that can provide different multi-state system performance levels. The different demand levels, which must be supplied during the system-operating period, result in the multi-state nature of the system. The new solution methodology offers several distinct benefits compared to traditional formulations of the MSPS redundancy allocation problem. For some systems, recognizing that different component versions yield different system performance is critical so that the overall system reliability estimation and associated design models the true system reliability behavior more realistically. The MSPS design problem, solved in this study, has been previously analyzed using genetic algorithms (GAs) and the universal generating function. The specific problem being addressed is one where there are multiple component choices, but once a component selection is made, only the same component type can be used to provide redundancy. This is the first time that the MSPS design problem has been addressed without using GAs. The heuristic offers more efficient and straightforward analyses. Solutions to three different problem types are obtained illustrating the simplicity and ease of application of the heuristic without compromising the intended optimization needs.     

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.     

Redundancy and robustness of systems of events

The article aims to add a new impetus to rational and objective probabilistic evaluation of redundancy and robustness, based on uncertainties of systems and subsystems of events. An attempt is made to demonstrate the relevance of intuitive comprehension of redundancy and robustness of engineering systems of events. An event-oriented system analysis of a number of random observable operational and failure modes, with adverse probability distributions in a lifetime, may provide a deeper understanding of systems operational abundance and endurance. The system uncertainty analysis is based on the concept of entropy as defined in information theory and applied to probability theory. The article relates reliability, uncertainty, redundancy and robustness of systems of events and their application is illustrated in numerical examples.     

Multi-state component criticality analysis for reliability improvement in multi-state systems

This paper evaluates and implements composite importance measures (CIM) for multi-state systems with multi-state components (MSMC). Importance measures are frequently used as a means to evaluate and rank the impact and criticality of individual components within a system yet they are less often used as a guide to prioritize system reliability improvements. For multi-state systems, previously developed measures sometimes are not appropriate and they do not meet all user needs. This study has two inter-related goals: first, to distinguish between two types of importance measures that can be used for evaluating the criticality of components in MSMC with respect to multi-state system reliability, and second, based on the CIM, to develop a component allocation heuristic to maximize system reliability improvements. The heuristic uses Monte-Carlo simulation together with the max-flow min-cut algorithm as a means to compute component CIM. These measures are then transformed into a cost-based composite metric that guides the allocation of redundant elements into the existing system. Experimental results for different system complexities show that these new CIM can effectively estimate the criticality of components with respect to multi-state system reliability. Similarly, these results show that the CIM-based heuristic can be used as a fast and effective technique to guide system reliability improvements.