Degradation‐shock‐based Reliability Models for Fault‐tolerant Systems

Reliability modeling of fault‐tolerant systems subject to shocks and natural degradation is important yet difficult for engineers, because the two external stressors are often positively correlated. Motivated by the fact that most radiation‐induced failures are contributed from these two external stressors, a degradation‐shock‐based approach is proposed to model the failure process. The proposed model accommodates two kinds of failure modes: hard failure caused by shocks and soft failure caused by degradation. We consider a generalized m–δ shock model for systems with fault‐tolerant design: failure occurs if the time lag between m sequential shocks is less than δ hours or degradation crosses a critical threshold. An example concerning memory chips used in space is presented to demonstrate the applicability of the proposed model. Copyright © 2015 John Wiley & Sons, Ltd.     

Time-based replacement policies for a fault tolerant system subject to degradation and two types of shocks

A single component nonrepairable system suffering from both an internal stochastic degradation process and external random shocks is investigated in this paper. More specifically, the Wiener process with a positive drift coefficient is introduced to describe the gradual deterioration and the arrival number of external shocks is counted with a nonhomogeneous Poisson process (NHPP). Meanwhile, fault tolerant design is incorporated into the stochastically deterioration system so as to protect it from shock failures to some extent and is consummately addressed via a generalized m − δ shock model. From the actual engineering point of view, external shocks are typically classified into two distinct categories in this current research, that is, a minor shock (Type I shock) increasing the damage load on current degradation level and a traumatic shock (Type II shock) resulting in system catastrophic failure immediately. The closed-form expression of system survival function is derived analytically and is viewed as the generalization of existing reliability function for systems subject to dependent and competing failure processes. Based on which, two time-based maintenance (TBM) policies including an age replacement model and a block replacement model are scheduled, where the expected long-run cost rate (ELRCR) in each model is, respectively, optimized to seek the optimal replacement interval. In the illustrative example part, a subsea blowout preventer (BOP) control system is arranged to validate the theoretical results numerically. To compare which policy is more profitable under different conditions, the relative gain on optimal maintenance cost rate of the two TBM policies is presented.     

Reliability modeling for consecutive k-out-of-n: F systems with local load-sharing components subject to dependent degradation and shock processes

Traditional k-out-of-n models assume that the components are independent, while recent research studies assume that the components are dependent caused by global load-sharing characteristic. In this paper, we investigate the consecutive k-out-of-n systems with dependent components by local load-sharing characteristic. The work load and shock load on failed components will be equally shared by adjacent components, so the components tend to fail consecutively. Consequently, the components degradation processes may be diverse, since their degradation rate (dependent on work load) and abrupt degradation (dependent on shock load) become unequal because of local load-sharing effect. Furthermore, the system failure will be path-dependent on the failure sequences of components, which results in that the same system states may have different system failure probabilities. This new dependence makes the system reliability model more complex. In this work, an analytical model that can be solved numerically is derived to compute the reliability with this complex dependence. The developed model is demonstrated by a cable-strut system in the suspension bridge. The results show that the reliability decreases significantly when the new dependence is considered.     

δ冲击条件下相关性竞争失效过程的系统可靠性建模

研究系统受到δ冲击时,考虑系统自然退化和冲击两个竞争性失效过程间具有相关性时,系统可靠性的建模问题。相关性一方面表现为冲击造成系统退化量的增加,另一方面表现为系统的自然退化程度对冲击结果的影响。假设系统因冲击而失效的过程是δ冲击过程,通过系统自然退化过程和冲击过程的分布函数,导出了系统的可靠度函数,建立了系统可靠度模型的一般形式,并给出一种特例的具体形式,最后利用文献中的具体参数进行仿真,以验证模型的正确性和有效性。     

Reliability modeling for multistage systems subject to competing failure processes

In this paper, a novel multistage reliability model is provided as systems are often divided into many stages according to system degradation characteristics. Multistage hard failure (caused by random shock) process (MHFP) and multistage soft failure (caused by random shock and continuous degradation) process (MSFP) are introduced to describe the competing failure processes, where either the MSFP or MHFP would break down the system. The shock processes impact the system in three ways: (1) fatal load shocks cause hard failure immediately in the hard failure process; (2) time shocks cause a hard failure threshold changing; (3) damage load shocks cause degradation level increasing in the soft failure process. In this paper, a density function dispersion method is carried out to address the multistage reliability model, and the effectiveness of the proposed models is demonstrated by reliability analysis with the one-stage model. Finally, the multistage model is applied to a case study, the degradation process is divided into three stages, and the hard failure threshold can be transmitted twice. The proposed model can be applied in other multistage situations, and the calculation method can satisfy the accuracy requirements.     

Basic studies of ductile failure processes and implications for fracture prediction

Fracture of ductile materials has frequently been observed to result from the nucleation, growth and coalescence of microscopic voids. Experimental and analytical studies have shown that both the stress constraint factor and the effective plastic strain play a significant role in the ductile failure process. Experimental results also suggest that these two parameters are not independent of each other at failure initiation. In this study, a methodology for characterizing the effect of stress constraint A_m (which is defined to be the ratio of the mean stress and the effective stress A_m=σ_m/σ_e ) on ductile failure is proposed. This methodology is based on experimental evidence that shows the effective plastic strain at failure initiation has a one‐to‐one relationship with stress constraint. Numerical analyses based on plane strain and three‐dimensional unit‐cell models have been carried out to investigate failure initiation of the unit cell under different constraint conditions. Results from the numerical studies indicate (a) for each void volume fraction, there exists a local failure locus in terms of mesoscopic quantities, σ_m and σ_e, that adequately predict incipient local micro‐void link‐up, (b) the results are fully consistent with a failure criterion that maximizes mesoscopic effective stress for a constant level of stress constraint A_m, (c) for high to moderate constraint A_m, the link‐up envelope values for σ_m and σ_e are consistent with limit load conditions where the critical principal stress σ_1c corresponds to the maximum principal stress in the loading history and (d) for low constraint, the link‐up envelope values for σ_m and σ_e correspond to link‐up conditions having high levels of plastic strain and a principal stress σ₁ that is lower than the maximum value for this loading history. Thus, the results suggest that a two‐parameter ductile fracture criterion is plausible, such as critical crack opening displacement (COD) and stress constraint A_m, for predicting the process of stable tearing in materials undergoing ductile void growth during the fracture process.     

Research on Au-Al bonding properties based on a thermal shock environment

The thermal shock experiment of Au-Al bonding has been carried out. The mechanical characteristics, structure morphology and electrical characteristics degradation mechanism have also been researched. No cracks were observed in the bonding interface, and the bonding joints also showed good mechanical characteristics with pull stress of 3.0 to 12.0 g. Due to high temperature, the Au-Al intermetallic compound Au₅Al₂ with high resistibility was formed, which ultimately led to electrical failure. For the samples that were fabricated on the basis of the present technique, the bonding reliability has been evaluated. It has been found that the lifespan rule obeys the Weibull distribution, and at a high temperature of 150°C under 95% confidence level, the estimated results are η = 547 h, m = 3.83. In a room temperature environment, the Au-Al bonding samples’ lifespan has also been predicted on the basis of the rule of reliability evaluation. The result shows that the lifespan is about 20 years, while the reliability degree is 90%. Translated from Journal of Functional Materials, 2006, 37(10): 1,539–1,541, 1,544 (in Chinese)     

Reliability of deterministic non‐linear systems subjected to stochastic dynamic excitation

Engineering structures react to exceptionally high forces caused by, for example, extreme winds, sea waves, earthquakes, avalanches, etc. in a non‐linear way, before they finally collapse. Mostly these environmental loadings cause dynamic excitations which are adequately modeled by the so‐called stochastic processes. To identify subsets of the excitation, which may trigger failure, methods based on power inputs of the stochastic excitation will be exploited. This procedure is based on the simple consideration that any excitation that maximizes the energy input into the system has the potential to adversely affect the integrity of the structure. This method considers the velocity of the displacement field of the structure and the energy dissipation induced by viscous damping, friction and hysteresis. For an efficient reliability estimation, the n‐dimensional standard normal space S^[0]∈??ⁿ, in which the stochastic excitation is modeled, is split into two disjunct subspaces S^[1]∈??^m and S^[2]∈??^n?m. The subset S^[1]∈??^m represents the space of important directions, which is identified by a procedure based on an approximation of the gradient of the energy input. Directional sampling in the subspace S^[1] and direct Monte Carlo sampling in the subspace S^[2] are combined to established an efficient estimator for the structural reliability. The proposed methodology is generally applicable to finite element models with strong non‐conservative non‐linearities. Copyright © 2010 John Wiley & Sons, Ltd.     

Reliability and maintenance strategy for systems with aging‐dependent components

An innovative approach is presented for the reliability analysis of aging multistate systems that considers the subsystems and their components' dependency. A reliability function is determined for an aging series system with the component dependency following the local load‐sharing rule, and a reliability function is determined for an aging “m out of n” system with the component dependency following the equal load‐sharing rule. Linking the results of those load‐sharing models, a mixed‐dependency model for multistate “m out of l”‐series systems is constructed by assuming the dependence between subsystems connected in series under the local load‐sharing rule and the dependence between their components under the equal load‐sharing rule. As a special case, the reliability of this system, modeled using piecewise exponential reliability functions, is considered, and the results are applied to characterize shipyard rope elevator reliability. Finally, the maintenance of this elevator as a repairable multistate system is analyzed with the time of renovation ignored.     

Study on Failure Characteristic of Rock‐Like Materials With an Open‐Hole Under Uniaxial Compression

Abstract: The failure strength model of brittle materials with a pre‐existing open‐hole defect is proposed in this paper. A modified Sammis–Ashby model is deduced, in which it can be used to calculate the peak strength of brittle materials. It shows the law between peak strength σ_p and independent variable μ, which is the ratio of open‐hole radius (a) to half‐width of the specimen (t). Moreover, numerical and experimental investigations on failure process of rock‐like materials with an open‐hole imperfection were carried out. In the experiments, 3D‐digital image correlation method, an optical technique which utilises the full‐field and non‐contact measurement, was employed. A progressive elastic damage method realistic failure process analysis (RFPA) was used in the numerical investigation to inspect and verify the modified model and simulate the failure process. The investigation finds that there are good correlations between the experimental, numerical and theoretical results. Moreover, because of the influences of boundary conditions, shear failure type was obtained both experimentally and numerically.     

Reliability Analysis and Condition‐based Maintenance for Failure Processes with Degradation‐dependent Hard Failure Threshold

In this study, we introduce reliability models for a device with two dependent failure processes: soft failure due to degradation and hard failure due to random shocks, by considering the declining hard failure threshold according to changes in degradation. Owing to the nature of degradation for complex devices such as microelectromechanical systems, a degraded system is more vulnerable to force and stress during operation. We address two different scenarios of the changing hard failure threshold due to changes in degradation. In Case 1, the initial hard failure threshold value reduces to a lower level as soon as the overall degradation reaches a critical value. In Case 2, the hard failure threshold decreases gradually and the amount of reduction is proportional to the change in degradation. A condition‐based maintenance model derived from a failure limit policy is presented to ensure that a device is functioning under a certain level of degradation. Finally, numerical examples are illustrated to explain the developed reliability and maintenance models, along with sensitivity analysis. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

A novel pseudo‐maximum likelihood estimation method for accelerated degradation tests under Wiener process

For reliability assessment based on accelerated degradation tests (ADTs), an appropriate parameter estimation method is very important because it affects the extrapolation and prediction accuracy. The well‐adopted maximum likelihood estimation (MLE) method focuses on interpolation fitting and obtains results via maximizing the likelihood of the observations. However, a best interpolation fitting does not necessarily yield a best extrapolation. In this paper, therefore, a pseudo‐MLE (P‐MLE) method is proposed to improve the prediction accuracy of constant‐stress ADTs by considering the degradation mechanism equivalence under Wiener process. In particular, the degradation mechanism equivalence is characterized by a mechanism equivalence factor which presents the proportional relationship between degradation rate and variation. Then, the mechanism equivalence factor is determined via a two‐step method. The other model parameters can be estimated by the general MLE method. The asymptotic variances of acceleration factors and the p‐quantile of product failure time under normal condition are adopted to compare the statistical properties of the proposed method and the general MLE approach. Numerical examples show that the novel P‐MLE method may not achieve a maximum likelihood but can provide more benefits regarding prediction accuracy enhancement especially when the sample size is limited.     

Modeling the bathtub shape hazard rate function in terms of reliability

In this paper, a general form of bathtub shape hazard rate function is proposed in terms of reliability. The degradation of system reliability comes from different failure mechanisms, in particular those related to (1) random failures, (2) cumulative damage, (3) man–machine interference, and (4) adaptation. The first item is referred to the modeling of unpredictable failures in a Poisson process, i.e. it is shown by a constant. Cumulative damage emphasizes the failures owing to strength deterioration and therefore the possibility of system sustaining the normal operation load decreases with time. It depends on the failure probability, 1−R. This representation denotes the memory characteristics of the second failure cause. Man–machine interference may lead to a positive effect in the failure rate due to learning and correction, or negative from the consequence of human inappropriate habit in system operations, etc. It is suggested that this item is correlated to the reliability, R, as well as the failure probability. Adaptation concerns with continuous adjusting between the mating subsystems. When a new system is set on duty, some hidden defects are explored and disappeared eventually. Therefore, the reliability decays combined with decreasing failure rate, which is expressed as a power of reliability. Each of these phenomena brings about the failures independently and is described by an additive term in the hazard rate function h(R), thus the overall failure behavior governed by a number of parameters is found by fitting the evidence data. The proposed model is meaningful in capturing the physical phenomena occurring during the system lifetime and provides for simpler and more effective parameter fitting than the usually adopted ‘bathtub’ procedures. Five examples of different type of failure mechanisms are taken in the validation of the proposed model. Satisfactory results are found from the comparisons.     

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.     

A note on MTTF formulae for redundant systems with Erlangian‐distributed unit and common‐cause times to failure

This communication presents newly developed mean‐time‐to‐failure (MTTF) formulae for systems with Erlangian‐distributed unit and common‐cause times to failure. These systems are parallel, triple modular redundant (TMR), r‐out‐of‐m, bridge, parallel‐series and series‐parallel. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

Set theoretic formulation of performance reliability of multiple response time‐variant systems due to degradations in system components

This paper presents a design stage method for assessing performance reliability of systems with multiple time‐variant responses due to component degradation. Herein the system component degradation profiles over time are assumed to be known and the degradation of the system is related to component degradation using mechanistic models. Selected performance measures (e.g. responses) are related to their critical levels by time‐dependent limit‐state functions. System failure is defined as the non‐conformance of any response and unions of the multiple failure regions are required. For discrete time, set theory establishes the minimum union size needed to identify a true incremental failure region. A cumulative failure distribution function is built by summing incremental failure probabilities. A practical implementation of the theory can be manifest by approximating the probability of the unions by second‐order bounds. Further, for numerical efficiency probabilities are evaluated by first‐order reliability methods (FORM). The presented method is quite different from Monte Carlo sampling methods. The proposed method can be used to assess mean and tolerance design through simultaneous evaluation of quality and performance reliability. The work herein sets the foundation for an optimization method to control both quality and performance reliability and thus, for example, estimate warranty costs and product recall. An example from power engineering shows the details of the proposed method and the potential of the approach. Copyright © 2006 John Wiley & Sons, Ltd.     

Fracture damage prediction in fissured red sandstone under uniaxial compression: acoustic emission b‐value analysis

In this paper, uniaxial compression tests are conducted on fissured red sandstone specimens to predict fracture damage (large‐scale events). The acoustic mission (AE) coupled with digital image correlation (DIC) technologies are used to monitor and record the real‐time cracking process of tested specimens. The AE characteristics are analysed during the cracking process. Moreover, three types of b‐value methods based on the AE parameters are adopted to predict the occurrence of large‐scale events (macro‐cracking). The results show that every macro‐cracking leads to a rapid decrease in three types of b value. When the fissured specimens reach to ultimate failure, all three types of b value reach to the minimum. The b value based on the AE parameters can be used as a predictor of large‐scale events during the cracking process of fissured rocks.     

Application of discrete‐time Bayesian network on reliability analysis of uncertain system with common cause failure

With the increasing complexity of engineering systems, reliability analysis and evaluation of systems with traditional methods can't meet practical engineering requirements. Based on limited experimental conditions, lack of data, complex structure models, insufficient cognitive abilities, and many other issues, people have to consider many uncertain factors in system reliability research. Besides, common cause failure (CCF) has become an important factor of system failure. In this paper, a discrete‐time Bayesian network (DTBN) associated with an eight‐rotor unmanned aerial vehicle (UAV) system is presented to discuss above problems. In this approach, the system is assumed as a two‐state system. After that, interval analysis theory is employed to deal with uncertainty. We consider the four sets of auxiliary propellers in the auxiliary power group as a 3/8 voting system, and β factor model is used to process CCF in the auxiliary power group. The proposed methods prove the validity of proposing interval analysis theory to solve uncertain problems and it is necessary to consider reducing or avoiding CCFs in system.