Approaches for reliability modeling of continuous-state devices

Three approaches for reliability modelling of continuous state devices are presented in this paper. One uses the random process to fit model parameters of a statistical distribution as functions of time. This approach allows the data set to be from any general distribution. The second approach uses the general path model to fit parameters of the model as functions of time. The relationship between the random process model and the general path model is illustrated. The third approach uses multiple linear regression to fit the distribution of lifetime directly. This approach has less restriction on the degradation data to be analyzed. All three approaches are illustrated with examples. Finally a mixture model is proposed which can be used to model both catastrophic failures and degradation failures. This mixture model also shows engineers how to design experiments to collect both hard failure data and soft failure data. Topics for further investigation in continuous device reliability modelling include further investigation of the mixture model, application of these models to practical situations, and using complex statistical distributions to fit degradation data     

Mis-Specification Analysis of Linear Degradation Models

Degradation models are widely used to assess the lifetime information of highly reliable products if there exists quality characteristics whose degradation over time can be related to reliability. The performance of a degradation model depends strongly on the appropriateness of the model describing a product's degradation path. In this paper, motivated by laser data, we propose a general linear degradation path in which the unit-to-unit variation of all test units can be considered simultaneously with the time-dependent structure in degradation paths. Based on the proposed degradation model, we first derive an implicit expression of a product's lifetime distribution, and its corresponding mean-time-to-failure (MTTF). By using the profile likelihood approach, maximum likelihood estimation of parameters, a product's MTTF, and their confidence intervals can be obtained easily. In addition, laser degradation data are used to illustrate the proposed procedure. Furthermore, we also address the effects of model mis-specification on the prediction of the product's MTTF. It shows that the effect of the model mis-specification on the predictions of a product's MTTF is not critical under the case of large samples. However, when the sample size and the termination time are not large enough, a simulation study shows that these effects are not negligible.     

An alternative degradation reliability modeling approach using maximum likelihood estimation

An alternative degradation reliability modeling approach is presented in this paper. This approach extends the graphical approach used by several authors by considering the natural ordering of performance degradation data using a truncated Weibull distribution. Maximum Likelihood Estimation is used to provide a one-step method to estimate the model's parameters. A closed form expression of the likelihood function is derived for a two-parameter truncated Weibull distribution with time-independent shape parameter. A semi-numerical method is presented for the truncated Weibull distribution with a time-dependent shape parameter. Numerical studies of generated data suggest that the proposed approach provides reasonable estimates even for small sample sizes. The analysis of fatigue data shows that the proposed approach yields a good match of the crack length mean value curve obtained using the path curve approach and better results than those obtained using the graphical approach.     

A genetic algorithm based approach for energy efficient routing in two-tiered sensor networks

Higher power relay nodes can be used as cluster heads in two-tiered sensor networks to achieve improved network lifetime. The relay nodes may form a network among themselves to route data towards the base station. In this model, the lifetime of a network is determined mainly by the lifetimes of these relay nodes. An energy-aware communication strategy can greatly extend the lifetime of such networks. However, integer linear program (ILP) formulations for optimal, energy-aware routing quickly become computationally intractable and are not suitable for practical networks. In this paper, we have proposed an efficient solution, based on a genetic algorithm (GA), for scheduling the data gathering of relay nodes, which can significantly extend the lifetime of a relay node network. For smaller networks, where the global optimum can be determined, our GA based approach is always able to find the optimal solution. Furthermore, our algorithm can easily handle large networks, where it leads to significant improvements compared to traditional routing schemes.     

A modified Weibull distribution

A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type 1 extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.     

Reliability modeling of engineered barrier systems for nuclear waste: A conditional approach

The lifetime of the Engineered Barrier System (EBS) used for containment of high-level radioactive waste will play an important role in controlling the cumulative release of radionuclides from a geological repository. Essentially, an EBS has two major components: a metal barrier and the waste form (cladding). Since any suitable site is above the static water table, the decay heat generated from this waste is expected to keep the surface temperature of a canister above the boiling point of water for a T random time period. Assuming the Weibull lifetime distribution on each component, we use the conditional approach to derive the lifetime distribution of the EBS. In our model, the oxidization process of the metal barrier (i.e. the lifetime of the metal barrier) starts after this time T and the lifetime of the cladding starts after the lifetime of the metal barrier     

基于加速因子不变原则的加速退化数据分析方法

加速退化试验技术已经成为评估退化失效型产品可靠性的高效手段,然而,目前对加速退化数据分析时过多依据主观经验,容易造成可靠性评估结果不准.本文提出了基于加速因子不变原则较为客观分析加速退化数据的一种方法.首先,根据加速因子不变原则推导退化模型各参数在加速退化试验中应该满足的变化规律;然后,利用与加速应力无关的参数等式辨识各加应力水平下的加速退化数据是否有效,核心是构建t统计量检验参数估值是否满足等式关系;接下来,确定与加速应力相关的参数从而实现加速退化建模;最后,利用有效的加速退化数据估计出模型参数值,外推出产品在常规应力下的可靠度.以逆高斯退化模型为例对所提方法进行了具体阐述.仿真试验和实例应用表明,本文研究为基于加速退化数据的可靠性评估提供一种更客观、合理的技术途径.     

A termination rule for degradation experiments

Analysis of degradation data can provide information about the lifetime of highly reliable products, if there exists a product characteristic whose degradation over time can be related to reliability. To obtain a precise estimator of a product mean time-to-failure, one practical problem arising from designing a degradation experiment is: how long should the experiment last? This paper proposes a termination rule to determine an appropriate stopping time of a degradation experiment. A case study of an LED product illustrates the method. The proposed procedure is computationally simple and provides reliability analysis for on-line real-time information of the product lifetime when the termination time is determined     

Optimal design for step-stress accelerated degradation tests

Today, many products are designed to function for a long period of time before they fail. For such highly-reliable products, collecting accelerated degradation test (ADT) data can provide useful reliability information. However, it usually requires a moderate sample size to implement an ADT. Hence, ADT is not applicable for assessing the lifetime distribution of a newly developed or very expensive product which only has a few available test units on hand. Recently, a step-stress ADT (SSADT) has been suggested in the literature to overcome the above difficulty. However, in designing an efficient SSADT experiment, the issue about how to choose the optimal settings of variables was not discussed, such as sample size, measurement frequency, and termination time. In this study, we first use a stochastic diffusion process to model a typical SSADT problem. Next, under the constraint that the total experimental cost does not exceed a predetermined budget, the optimal settings of these variables are obtained by minimizing the asymptotic variance of the estimated 100p/sup th/ percentile of the product's lifetime distribution. Finally, an example is used to illustrate the proposed method.     

A Wiener process model for accelerated degradation analysis considering measurement errors

Accelerated degradation analysis plays an important role in assessing reliability and making maintenance schedule for highly reliable products with long lifetime. In practical engineering, degradation data, especially measured under accelerated condition, are often compounded and contaminated by measurement errors, which makes the analysis more challenging. Therefore, a Wiener process model simultaneously incorporating temporal variability, individual variation and measurement errors is proposed to analyze the accelerated degradation test (ADT). The explicit forms of the probability distribution function (PDF) and the cumulative distribution function (CDF) are derived based on the concept of first hitting time (FHT). Then, combining with the acceleration models, the maximum likelihood estimations (MLE) of the model parameters are obtained. Finally, a comprehensive simulation study involving two examples and a practical application are given to demonstrate the necessity and efficiency of the proposed model.     

不确定退化测量数据下的剩余寿命估计

剩余寿命估计是工程系统预测与健康管理的关键.目前,基于观测的系统退化数据进行剩余寿命估计得到了很大的关注.由于系统随机退化过程和测量误差的影响,测量数据中不可避免包含退化随机性和测量不确定性.然而,现有基于观测数据的剩余寿命估计研究中,没有将退化随机性和测量不确定性对估计的剩余寿命分布的影响同时考虑.鉴于此,提出了一种基于Wiener过程且同时考虑随机退化和不确定测量的退化建模方法,利用Kalman滤波技术,实现了潜在退化状态的实时估计.在退化状态估计的基础上,得到了同时考虑退化状态不确定性和测量不确定性的解析剩余寿命分布.此外,提出了一种基于极大似然方法的退化模型参数估计方法.最后,通过陀螺仪的退化测量数据验证了本文提出的方法优于不考虑测量不确定性的方法,可以提高剩余寿命估计的准确性.     

A model for IC yield analysis and process control

A probabilistic model for an analysis of IC wafer yield is proposed. The model tends to separate various causes of yield degradation, in particular the effects of gross wafer variability related to processing conditions, systematic errors and random spatial yield patterns. The results can also be used for estimating parameters of various yield vs chip area models, of which the “Gross Defect Area” model was chosen as an example. The model can be used for comparing data on different lots of the same product, for routine process control, for data reduction and spatial analysis, and for various other research applications.     

A Variance Minimization Method of Reliability Design

This approach to reliability design seeks to minimize the variance on system lifetime within s-expected life and economic constraints. We consider the case where the parameters of the lifetime distribution are constant and discuss the more general case where the parameters of the lifetime distribution are random variables. The design procedure is illustrated by simple numerical examples which show that for a small increase in cost an appreciable decrease in the variance of the lifetime is obtained. We have restricted our attention to active redundancy but the extension to standby redundancy is straightforward.     

Analysis of link lifetime in wireless mobile networks

Link lifetime (LL) analysis is crucially important in designing and evaluating wireless mobile network protocols. Although a considerable amount of research has been conducted on this issue, the current paper studies several aspects of link lifetime for the first time, e.g. a closed form expression for the probability distribution of the residual link lifetime (RLL) for the constant velocity mobility model is obtained, which facilitates marginal studies on the behavior of link lifetime. As a case, using a tail analysis of LL and RLL distributions, we analytically prove that they are heavy-tailed. Using this outcome, a self-similar behavior in the traffic pattern of a sample delay tolerant network is justified analytically. To extend the model, the effect of stationary nodes, the effect of buffer zone, and the effect of link establishment policies between different node categories on the link lifetime are investigated. Extensive simulation experiments are performed to validate the obtained analytical results and derivations precisely. Moreover, simulation results confirm that the analytic results can also be used for two well known mobility models (random waypoint and random direction) with a negligible error.     

Decisions on an Optimal Life Test Sampling Plan With Warranty Considerations

The choice of an appropriate life test sampling plan is a crucial decision problem because a good plan not only can help producers save testing time, and reduce testing cost; but it also can positively affect the image of the product, and thus attract more consumers to buy it. This study developed a decision model in determining the optimal life test sampling plan with an aim of cost minimization by identifying the appropriate number of product failures in a sample that should be used as a threshold in judging the rejection of a batch. A Weibull distribution with two parameters (i.e. scale factor, and shape factor) was assumed to be appropriate for modeling the lifetime of a product, and a Bayesian decision model was thus constructed to perform the prior, preposterior, and posterior analyses. The cost structure thoroughly encompassed the considerations of rejection, acceptance, testing, and warranty costs for the adoption of an optimal sampling plan, which is capable of providing guidelines for making better decisions. Finally, a practical numerical application was employed to demonstrate the effectiveness of the proposed approach.      

A probabilistic approach to evaluate the reliability of piezoelectric micro-actuators

In this paper, a probabilistic design approach is presented to evaluate the reliability of piezoelectric micro actuators. Based on the relationship between the lifetime, and degradation mechanism of piezoelectric actuators, and the electric field strength, the concept of "electric strength" is proposed to indicate the electric field strength of the piezoelectric actuators at a specified lifetime. The lifetime (number of cycles to failure) of the piezoelectric actuator, electric strength, and electric load are considered as the random variables; and their probability distributions are discussed. The interference model of electric load, and electric strength is introduced to the reliability design of piezoelectric micro actuators. By this approach, the relationship between the reliability, and the lifetime of the piezoelectric actuator can be given. A case study of the disk drive head positioning system demonstrates the application of the approach.     

Coverage and Lifetime Optimization of Wireless Sensor Networks with Gaussian Distribution

A wireless sensor network (WSN) has to maintain a desirable sensing coverage and periodically report sensed data to the administrative center (i.e., base station) and the reporting period may range from months to years. Coverage and lifetime are two paramount problems in a WSN due to constraint of associated battery power. All previous theoretical analysis on the coverage and lifetime is primarily focused on the random uniform distribution of sensors or some specific network scenarios (e.g., a controllable WSN). In this paper, we provide an analytical framework for the coverage and lifetime of a WSN that follows a two-dimensional Gaussian distribution. We also study the coverage and lifetime when the dimensions of Gaussian dispersion (i.e., x, y) admit different Gaussian parameters (i.e., standard deviation, $sigma_x neqsigma_y$). We identify intrinsic properties of coverage/lifetime in terms of Gaussian distribution parameters, which is a fundamental issue in designing a WSN. Following the results obtained, we further determine the sensor deployment strategies for a WSN that could satisfy a predefined coverage and lifetime. Two deployment algorithms are developed based on using our analytical models and are shown to effectively increase the WSN lifetime.     

基于退化量分布的高量程MEMS加速度计的可靠性评估

高量程MEMS微加速度计主要应用于航空、航天及军工等高可靠性要求的惯导领域。为了更好进行微加速度计的可靠性寿命预测,提出一种基于退化量分布,以实验数据拟合推导出分布模型参数的变化关系从而更加准确的评估微加速度计的可靠性寿命。实验研究结论表明采用新的评估方法能够获得更准确的微加速度计可靠性预测。     

基于加速退化试验的模拟IC寿命评估研究

为解决高可靠性、长寿命模拟集成电路的寿命评估问题,结合半导体器件退化失效的特点,提出了基于加速退化试验的模拟集成电路寿命评估方法。在此基础上,以某型电压基准模拟IC为研究对象,通过对退化数据的分析研究,获得了其在正常工作应力下的寿命数据。     

考虑不完全维护影响的随机退化设备剩余寿命预测

针对寿命周期中存在不完全维护影响的随机退化设备剩余寿命难以预测的问题,提出了一种考虑不完全维护影响的退化建模和剩余寿命预测方法.首先,在Wiener过程理论架下,建立了能够表征不完全维护影响的分阶段退化过程模型,然后从阶段时间服从的逆高斯分布出发,利用逆高斯分布的卷积特性,从理论上推导出存在不完全维护下寿命分布的解析解,并将维护效果的随机性和维护次数的影响传递到寿命分布中.进一步通过时间尺度变换,得到了考虑未来存在不完全维护影响下的剩余寿命分布解析解.通过极大似然估计和最小二乘法对模型未知参数进行了估计.最后将本文方法应用到陀螺仪的实际退化过程中,验证了所提方法的有效性.