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.     

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.     

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.     

A practical approach for predicting fatigue reliability under random cyclic loading

The purpose of this paper is to provide a simple approach for reliability analysis based on fatigue or overstress failure modes of mechanical components, and explain how this integrated method carries out spectral fatigue damage and failure reliability analysis. In exploring the ability to predict spectral fatigue life and assess the reliability under a specified dynamics environment, a methodology for reliability assessment and its corresponding fatigue life prediction of mechanical components using a supply-demand interference approach is developed in this paper. Since the methodology couples dynamics analysis and stochastic analysis for fatigue damage and reliability prediction, the conversion of the duty cycle history for the reliability study of an individual component is also presented. Using the proposed methodology, mechanical component reliability can be predicted according to different mission requirements. For an explanation of this methodology, a probabilistic method of deciding the relationship between the allowable stress or fatigue endurance limit and reliability is also presented.     

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.     

Reliability Allocation for Series-Parallel Systems subject to Potential Propagated Failures

To analyze the dependent failures in the early stage of system development, this paper considers the potential propagated failures in the reliability allocation process. Factors which can be used to not only measure the component importance but also to reflect the influence brought by propagated failures are proposed. Specifically, cooperative game theory is introduced to explore how the propagated failures affect the failure severity level. Failure rates are obtained by using the Alpha Factor Model with the consideration of dependence among components. Reliability improvement rate is also developed to proportionally assign the target improvement of system reliability to the corresponding components. Furthermore, reliability allocation frameworks for series, parallel and series-parallel systems are designed respectively to make the proposed model meet a wide range of applications. An illustrative example of a hydraulic cooling system is presented to show how the proposed approach is applied. The allocation results demonstrate that the proposed method can achieve a valid reliability improvement with the minimum error.     

基于Copula函数的并联结构系统可靠度分析

不完备概率信息条件下变量联合分布函数的确定及其对结构系统可靠度的影响还缺少系统地研究,该文目的在于研究表征变量间相关性的Copula函数对结构系统可靠度的影响规律。首先,简要介绍了变量联合分布函数构造的Copula函数方法。其次,提出了并联系统失效概率计算方法,并推导了相应的计算公式。最后以几种典型Copula函数为例研究了Copula函数类型对结构并联系统可靠度的影响规律。结果表明:表征变量间相关性的Copula函数类型对结构系统可靠度具有明显的影响,不同Copula函数计算的系统失效概率存在明显的差别,这种差别随构件失效概率的减小而增大。当并联系统的失效区域位于Copula函数尾部时,Copula函数的尾部相关性对系统可靠度有明显的影响,计算的失效概率比没有尾部相关性的Copula函数的失效概率大。当组成并联系统的两构件功能函数间正相关时,系统失效概率随相关系数的增大而增加;当构件功能函数间负相关时,系统失效概率随相关系数的增大而减小。此外,无论构件失效概率和变量间相关系数如何变化,Copula函数计算的失效概率都位于系统失效概率的上下限内。     

Reliability estimations of components from masked system life data

This paper introduces estimations of reliability values for the individual components in a series system using masked system life data. In particular, we compute the maximum likelihood and Bayes estimates of component reliabilities when the system components have constant failure rates. In obtaining Bayes estimates, it is assumed that the component reliabilities are independent random variables having piecewise linear prior distributions. The model is illustrated for a two-component series. A numerical simulation study is presented to show how one can utilize the present approach to compute estimations of component reliabilities for a practical problem. Further, we investigate the comparison between the maximum likelihood and Bayes estimates, based on the respective percentage errors.     

Accelerated Degradation Tests: Modeling and Analysis

High reliability systems generally require individual system components having extremely high reliability over long periods of time. Short product development times require reliability tests to be conducted with severe time constraints. Frequently few or no failures occur during such tests, even with acceleration. Thus, it is difficult to assess reliability with traditional life tests that record only failure times. For some components, degradation measures can be taken over time. A relationship between component failure and amount of degradation makes it possible to use degradation models and data to make inferences and predictions about a failure-time distribution. This article describes degradation reliability models that correspond to physical-failure mechanisms. We explain the connection between degradation reliability models and failure-time reliability models. Acceleration is modeled by having an acceleration model that describes the effect that temperature (or another accelerating variable) has on the rate of a failure-causing chemical reaction. Approximate maximum likelihood estimation is used to estimate model parameters from the underlying mixed-effects nonlinear regression model. Simulation-based methods are used to compute confidence intervals for quantities of interest (e.g., failure probabilities). Finally we use a numerical example to compare the results of accelerated degradation analysis and traditional accelerated life-test failure-time analysis.     

Testing for reliability improvement or deterioration in repairable systems

This paper reviews the derivation and application of the reverse arrangement test which is used to assess whether a system has improved or deteriorated in a reliability sense. Because the well-known and published table of statistics for this test is erroneous, the prime objective of this paper is to provide the correct statistical table. A secondary aim, however, is to demonstrate how this table can be applied when there is a paucity of failure data for each individual system and to show how a more meaningful reliability assessment can be obtained by pooling results, from the reverse arrangement test, for several systems.     

Availability, reliability and downtime of systems with repairable components

Closed-form expressions are derived for the steady-state availability, mean rate of failure, mean duration of downtime and lower bound reliability of a general system with randomly and independently failing repairable components. Component failures are assumed to be homogeneous Poisson events in time and repair durations are assumed to be exponentially distributed. The results are expressed in terms of the mean rates of failure and mean durations of repair of the individual components. Closed-form expressions are also derived for the rates of change of the various probabilistic system performance measures with respect to the mean rate of failure and the mean duration of repair of each component. These expressions provide a convenient framework for identifying important components within the system and for decision-making aimed at upgrading the system availability or reliability, or reducing the mean duration of system downtime. Example applications to an electrical substation system demonstrate the use of the formulas developed in the paper.     

An iterative approach for estimating component reliability from masked system life data

Life data from systems of components are often analysed to estimate the reliability of the individual components. These estimates are useful since they reflect the reliability of the components under actual operating conditions. However, owing to the cost or time involved with failure analysis, the exact component causing system failure may be unknown or ‘masked’. That is, the cause may only be isolated to some subset of the system's components. We present an iterative approach for obtaining component reliability estimates from such data for series systems. The approach is analogous to traditional probability plotting. That is, it involves the fitting of a parametric reliability function to a set of nonparametric reliability estimates (plotting points). We present a numerical example assuming Weibull component life distributions and a two-component series system. In this example we find estimates with only 4 per cent of the computation time required to find comparable MLEs.     

System Reliability and Component Importance Under Dependence: A Copula Approach

System reliability and component importance are of great interest in reliability modeling, especially when the components within the system are dependent. We characterize the influence of dependence structures on system reliability and component importance in coherent systems with discrete marginal distributions. The effects of dependence are captured through copula theory. We extend our framework to coherent multi-state system. Applications of the derived results are demonstrated using a Gaussian copula, which yields simple interpretations. Simulations and two examples are presented to demonstrate the importance of modeling dependence when estimating system reliability and ranking of component importance. Proofs, algorithms, code, and data are provided in supplementary materials available online.     

Quantifying reliability uncertainty from catastrophic and margin defects: A proof of concept

We aim to analyze the effects of component level reliability data, including both catastrophic failures and margin failures, on system level reliability. While much work has been done to analyze margins and uncertainties at the component level, a gap exists in relating this component level analysis to the system level. We apply methodologies for aggregating uncertainty from component level data to quantify overall system uncertainty. We explore three approaches towards this goal, the classical Method of Moments (MOM), Bayesian, and Bootstrap methods. These three approaches are used to quantify the uncertainty in reliability for a system of mixed series and parallel components for which both pass/fail and continuous margin data are available. This paper provides proof of concept that uncertainty quantification methods can be constructed and applied to system reliability problems. In addition, application of these methods demonstrates that the results from the three fundamentally different approaches can be quite comparable.     

A fuzzy knowledge based method for maintenance planning in a power system

The inspection planning in electric power industry is used to assess the safety and reliability of system components and to increase the ability of failure situation identification before it actually occurs. It reflects the implications of the available information on the operational and maintenance history of the system. The output is a ranked list of components, with the most critical ones at the top, which indicates the selection of the components to be inspected.In this paper, we demonstrate the use of a fuzzy relational database model for manipulating the data required for the criticality component ranking in thermal power systems inspection planning, incorporating criteria concerning aspects of safety and reliability, economy, variable operational conditions and environmental impacts. Often, qualitative thresholds and linguistic terms are used for the component criticality analysis. Fuzzy linguistic terms for criteria definitions along with fuzzy inference mechanisms allow the exploitation of the operators' expertise.The proposed database model ensures the representation and handling of the aforementioned fuzzy information and additionally offers to the user the functionality for specifying the precision degree by which the conditions involved in a query are satisfied.In order to illustrate the behavior of the model, a case study is given using real inspection data.     

Competing failure analysis considering cascading functional dependence and random failure propagation time

Functional dependence (FDEP) exists in many real‐world systems, where the failure of one component (trigger) causes other components (dependent components) within the same system to become isolated (inaccessible or unusable). The FDEP behavior complicates the system reliability analysis because it can cause competing failure effects in the time domain. Existing works have assumed noncascading FDEP, where each system component can be a trigger or a dependent component, but not both. However, in practical systems with hierarchical configurations, cascading FDEP takes place where a system component can play a dual role as both a trigger and a dependent component simultaneously. Such a component causes correlations among different FDEP groups, further complicating the system reliability analysis. Moreover, the existing works mostly assume that any failure propagation originating from a system component instantaneously takes effect, which is often not true in practical scenarios. In this work, we propose a new combinatorial method for the reliability analysis of competing systems subject to cascading FDEP and random failure propagation time. The method is hierarchical and flexible without limitations on the type of time‐to‐failure distributions for system components. A detailed case study is performed on a sensor system used in smart home applications to illustrate the proposed methodology.     

Resource allocation for reliability of a complex system with aging components

To assess the reliability of a complex system, many different types of data may be available. Full‐system tests are the most direct measure of reliability, but may be prohibitively expensive or difficult to obtain. Other less direct measures, such as component or section level tests, may be cheaper to obtain and more readily available. Using a single Bayesian analysis, multiple sources of data can be combined to give component and system reliability estimates. Resource allocation looks to develop methods to predict which new data would most improve the precision of the estimate of system reliability, in order to maximally improve understanding. In this paper, we consider a relatively simple system with different types of data from the components and system. We present a methodology for assessing the relative improvement in system reliability estimation for additional data from the various types. Various metrics for comparing improvement and a response surface approach to modeling the relationship between improvement and the additional data are presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Extended reliability model of a unified power flow controller

One of the most important aspects in evaluating system reliability is to have a complete understanding of the engineering implications of the system and its associated components. The next step involved in reliability assessment is to appropriately model the system components to represent their characteristics and functions in the overall system. The unified power flow controller (UPFC) is an important flexible AC transmission system controller that can be used to enhance power system reliability. A complete reliability model of a UPFC is developed. A UPFC consists of three subsystems, and a reliability model associated with each subsystem is developed. The individual equivalent models are then combined to form a complete state-space model that represents the UPFC. A sensitivity analysis is conducted to illustrate the impacts on UPFC availability of variations in the key component failure rates.     

Kepler's Physical Framework for Planetary Motion

Summary
Ten years after formulating the two laws that govern the motion of an individual planet, Kepler confirmed, in Epitome , that these laws could be generated independently, each by one of the two components of planetary velocity perpendicular to, and along, the Sun-planet line in turn. Then, constrained by his Aristotelian principles, Kepler quantified the two separate physical causes of these component velocities: the single rotating solar force, and an individual planetary magnetism, respectively. Thus Kepler's achievement was to create a mathematically-complete two-cause explanation by which planetary motion is exactly resolved in accordance with modern standards.     

Schwingungsverschleiß – Erscheinungsformen,Prüfmethoden und Abhilfemaßnahmen

Fretting Wear The characteristic feature of fretting wear compared with other types of wear lies in the intensive interactions between transfer of debris, mode of vibration and wear. In particular, the forms of wear are heavily dependent on the continued presence or removal of the resulting wear particles and on the accessibility to lubricants. The systematic treatment of the individual forms of wear facilitates the analysis in cases of damage. Despite the system dependence of wear, the methods of the test chain and of parameter variation makes it possible to achieve practical test results also with component and model tests. An example shows how the quality of tribologically stressed components can be systematically improved in this way.