Bayesian optimal design of step stress accelerated degradation testing

This study presents a Bayesian methodology for de- signing step stress accelerated degradation testing （SSADT） and its application to batteries. First, the simulation-based Bayesian de- sign framework for SSADT is presented. Then, by considering his- torical data, specific optimal objectives oriented Kullback-Leibler （KL） divergence is established. A numerical example is discussed to illustrate the design approach. It is assumed that the degrada- tion model （or process） follows a drift Brownian motion; the accele- ration model follows Arrhenius equation; and the corresponding parameters follow normal and Gamma prior distributions. Using the Markov Chain Monte Carlo （MCMC） method and WinBUGS software, the comparison shows that KL divergence is better than quadratic loss for optimal criteria. Further, the effect of simulation outiiers on the optimization plan is analyzed and the preferred sur- face fitting algorithm is chosen. At the end of the paper, a NASA lithium-ion battery dataset is used as historical information and the KL divergence oriented Bayesian design is compared with maxi- mum likelihood theory oriented locally optimal design. The results show that the proposed method can provide a much better testing plan for this engineering application.

Accelerated Degradation Reliability Modeling and Test Data Statistical Analysis of Aerospace Electrical Connector

As few or no failures occur during accelerated life test,it is difficult to assess reliability for long-life products with traditional life tests.Reliability assessment using degradation data of product performance over time becomes a significant approach.Aerospace electrical connector is researched in this paper.Through the analysis of failure mechanism,the performance degradation law is obtained and the statistical model for degradation failure is set up; according to the research on statistical analysis methods for degradation data,accelerated life test theory and method for aerospace electrical connector based on performance degradation is proposed by improving time series analysis method,and the storage reliability is assessed for Y11X series of aerospace electrical connector with degradation data from accelerated degradation test.The result obtained is basically consistent with that obtained from accelerated life test based on failure data,and the two estimates of product＇s characteristic life only have a difference of 8.7%,but the test time shortens about a half.As a result,a systemic approach is proposed for reliability assessment of highly reliable and long-life aerospace product.

Step-stress Accelerated Degradation Test Modeling and Statistical Analysis Methods

In order to get a rapid assessment on the storage reliability of high-reliable and long-life products within the storage period, accelerated degradation test data with a large amount of reliability information of product is adopted. Conducting a constant-stress accelerated degradation test（CSADT） is generally very costly as it requires a large sample size and long time for test. To overcome this problem, it is necessary to carry out research on modeling and statistical analysis methods of step-stress accelerated degradation test （SSADT）. Taking electrical connectors as the object, a research is conducted on statistical model and assessment method for SSADT. On the basis of mixed-effect degradation path model, the statistical model of SSADT for electrical connectors is presented, the maximum likelihood method for SSADT data based on mixed-effect degradation model is proposed. SSADT accelerated by temperature stress is conducted to Y11X-1419 type of electrical connectors, and the storage reliability is assessed with the SSADT data. Compared with the result obtained from accelerated life test, the reliability estimation of 32-year storage period for electrical connectors obtained from S SADT data only have a difference of 0.869%, which validates the accuracy of the degradation model and the feasibility of the test data statistic analysis method put forward.

Priori information analysis of optocoupler accelerated degradation experiment based on failure mechanism verification test

The optocoupler is a weak link in the inertial navigation platform of a kind of guided munitions.It is necessary to use accelerated storage test to verify the storage life of long storage products.Especially for small sample products,it is very important to obtain prior information for the design and implementation of accelerated degradation test.In this paper,the optocoupler failure mechanism verification test is designed and the experimental results are analyzed and the prior information is obtained.The results show that optocouplers have two failure modes,one is sudden failure and the other is degradation failure;the maximum temperature stress of optocoupler can’t exceed 140℃;the increase of leakage current of optocoupler is caused by movable ions contaminating the LED chip.The surface leakage current is proportional to the adsorption amount.The increase of leakage current makes p-n junction tunneling effect occur which LEDs the failure of the optocoupler.The lifetime distribution model of the optocoupler is determined by the failure physics.The lifetime of the optocoupler is subject to the lognormal distribution.The degeneracy orbit of the optocoupler leakage current is described by a power law model.The estimated values of the orbital parameters are initially calculated and the parameters of its life distribution function are deduced.The above information lays a good foundation for the optimization design and data processing of the accelerated degradation experiment.

Multiple Objective Test Design for Accelerated Destructive Degradation Tests

Accelerated destructive degradation tests(ADDTs)are powerful to provide reliability information in the degradation processes with destructive measurements.In order to carry out an ADDT efficiently,both the estimation precision of parameters and the test cost should be considered.On the basis of the given degradation model and failure criterion,a multiple-objective optimization model for the design of ADDTs is proposed.Under constrains of the maximum measurement time,the total sample size and the number of stress levels,a comprehensive target function is suggested to reflect both the precision of lifetime estimation and total cost,and the optimal test plan is obtained,which is composed by optimal choices for samples size,measurement frequency,and the number of measurements at each stress level.A real example is illustrated to demonstrate the implementation of the proposed approach.

An Optimal Design of Accelerated Degradation Tests Based on Degradation Performance

This paper mainly talks about the relationship between an optimal design of accelerated degradation tests and the degradation performance. When there is a linear relationship between the parameter of distribution and the critical values, a special pattern of accelerated degradation tests is presented by taking the critical values as accelerated variable. And the optimal test plan is obtained by minimizing the asymptotic variance of the MLE of the parameter of distribution. Finally, a numerical example is presented to illustrate the procedures of the test plan.

Constant-Stress Accelerated Degradation Life Test of an Organic Light-Emitting Diode Display under Violet Light

The lifetime of commercial OLED display devices increases, so does the need for an accelerated lifetime testing method. The present work proposes a simple and accurate blackbox testing approach for commercial PMOLED display lifetime assessment using violet light-induced accelerated aging. Maximum likelihood estimations using lognormal distributions are performed based on datasets acquired from samples exposed to six different degrees of violet irradiance and accelerated life model is shown to accurately fit experimental data using an inverse power law. Based on these results, weighted average of the logarithmic standard deviation, the average life and median life can then be obtained for specific conditions of operation of the devices. As this method relies exclusively on violet light-induced degradation at room-temperature, this minimally-invasive testing procedure requires no significant modification to the display hardware architecture.

Residual lifetime prediction model of nonlinear accelerated degradation data with measurement error

For the product degradation process with random effect (RE), measurement error (ME) and nonlinearity in step-stress accelerated degradation test (SSADT), the nonlinear Wiener based degradation model with RE and ME is built. An analytical approximation to the probability density function (PDF) of the product's lifetime is derived in a closed form. The process and data of SSADT are analyzed to obtain the relation model of the observed data under each accelerated stress. The likelihood function for the population-based observed data is constructed. The population-based model parameters and its random coefficient prior values are estimated. According to the newly observed data of the target product in SSADT, an analytical approximation to the PDF of its residual lifetime (RL) is derived in accordance with its individual degradation characteristics. The parameter updating method based on Bayesian inference is applied to obtain the posterior value of random coefficient of the RL model. A numerical example by simulation is analyzed to verify the accuracy and advantage of the proposed model.

Strength Degradation of Wood Members Based on the Correlation of Natural and Accelerated Decay Experiments

An accelerated decay test and a natural decay test were conducted synchronically to explore the strength degradation of decaying wood members under long-term exposure to natural environment.A natural decay test was carried out to measure the bending strength,compressive strength parallel to grain and modulus of elasticity of the wood members,with 6 groups of specimens decayed in natural environment for 3 to 18 months respectively.To compare with corresponding decay test,in which 6 other groups of specimens were measured under accelerated conditions.The experimental data collected were evaluated by Pearson productmoment for the correlation.The results indicate that the mechanical properties of the accelerated decay were highly correlated with those in natural environment,both of which decreased in the same trend.Under the given test conditions,the mean value of the accelerated decay test data were curve-fitted to achieve the time-dependent degradation model of the bending strength,the compressive strength parallel to grain,as well as the modulus of elasticity.Due to the high correlation,the acceleration shift factors(ASF)of the two tests were derived,where the bending strength of 2.934,the compressive strength parallel to grain of 2.519 and the elastic modulus of 2.346 were employed to formulate the strength degradation models in the long-term natural environment.The results verify that the exponential function
σ=σ0e^(-βt)enables to exactly capture the degradation of the mechanical properties of wood members decayed in natural environment.

Consistency check of degradation mechanism between natural storage and enhancement test for missile servo system

Reliability enhancement testing(RET) is an accelerated testing which hastens the performance degradation process to surface its inherent defects of design and manufacture. It is an important hypothesis that the degradation mechanism of the RET is the same as the one of the normal stress condition. In order to check the consistency of two mechanisms, we conduct two enhancement tests with a missile servo system as an object of the study, and preprocess two sets of test data to establish the accelerated degradation models regarding the temperature change rate that is assumed to be the main applied stress of the servo system during the natural storage. Based on the accelerated degradation models and natural storage profile of the servo system, we provide and demonstrate a procedure to check the consistency of two mechanisms by checking the correlation and difference of two sets of degradation data. The results indicate that the two degradation mechanisms are significantly consistent with each other.

Preload relaxation analysis and reliable life prediction of space connection and separation device based on accelerated degradation tests

The safety and reliability of space connection and separation device has become a key issue due to the increasing service span of deep space exploration mission.The long-term preload relaxation(a key failure mode)of connection and separation devices is focused in this paper.A series of tests have been designed and implemented to investigate the preload relaxation regulation and a comprehensive method has been constructed to analyze and predict the reliable lifetime of the device.The two-stage preload relaxation law of the device is found and reasonably considered.Due to the different relaxation mechanism,the first-stage preload relaxation is assessed based on the working-condition test results,and the second-stage preload relaxation is characterized by accelerated test results.Finally,the service reliability and reliable life are evaluated.The experiment and assessment results demonstrate the reasonability and effectiveness of the proposed method which can achieve long-service reliability analysis for space connection and separation device within limited time.

Lifetime prediction for tantalum capacitors with multiple degradation measures and particle swarm optimization based grey model

A lifetime prediction method for high-reliability tantalum （Ta） capacitors was proposed, based on multiple degradation measures and grey model （GM）. For analyzing performance degradation data, a two-parameter model based on GM was developed. In order to improve the prediction accuracy of the two-parameter model, parameter selection based on particle swarm optimization （PSO） was used. Then, the new PSO-GM（1, 2, co） optimization model was constructed, which was validated experimentally by conducting an accelerated testing on the Ta capacitors. The experiments were conducted at three different stress levels of 85, 120, and 145℃. The results of two experiments were used in estimating the parameters. And the reliability of the Ta capacitors was estimated at the same stress conditions of the third experiment. The results indicate that the proposed method is valid and accurate.

Reliability modeling of the bivariate deteriorating product with both monotonic and non-monotonic degradation paths

Fiber optical gyroscope(FOG)is a highly reliable navigation element,and the degradation trajectories of its two accuracy indexes are monotonic and non-monotonic respectively.In this paper,a flexible accelerated degradation testing(ADT)model is used for analyzing the bivariate dependent degradation process of FOG.The time-varying copulas are employed to consider the dynamic dependency structure between two marginal degradation processes as the Wiener process and the inverse Gaussian process.The statistical inference is implemented by utilizing an inference function for the margins(IFM)approach.It is demonstrated that the proposed method is powerful in modeling the joint distribution with various margins.

New Indoor Accelerated Weathering Condition for Approximating Molecular Weight Distribution of Outdoor-Exposed LDPE

LDPE （low-density polyethylene） photo degraded through various accelerated weathering tests has the molecular weight distribution curves unlike that through outdoor exposure. The authors therefore developed new weathering test condition based on the existing accelerated weathering test using a xenon arc lamp. Samples of LDPE were photo degraded using various accelerated weathering test conditions and outdoor exposure. The physical properties and chemical structures of the photo degraded samples were studied through a tensile test, infrared spectroscopy, and gel chromatography. The authors found that the molecular weight distribution curve of a sample photo degraded using a xenon lamp at a higher BPT （black panel temperature） （73 ~C） was more similar to that of an outdoor-exposed sample than that of a sample photo degraded at the standard BPT （63 ~C）. It is considered that higher temperature accelerates radical recombination, consequently recreating molecular enlargement similar to the outdoor-exposed sample. Multiple regression analysis using newly introduced Mp （peak-top molecular weight） and Mw （weight-average molecular weight） as explanatory variables was conducted, which successfully enabled the authors to provide a simple explanation for the decrease in polymer tensile strength.

Research on Decalcification Degradation Process of Cement Stone

An accelerated laboratory method（saturated ammonium nitrate solution immersion method） was used to analyze the degradation of cement decalcification process. By studying the changes of intensity, volume, elastic modulus, quality, p H value, the Ca/Si, and mineral phase, it could be found that the first cement decalcification degradation process was the decalcification of calcium hydroxide, and then CSH gel, AFm, etc. The secondary ettringite deposition happened and the decalcification degradation depth was proportional to the square root of time. Moreover, the corresponding strength of cement would be gradually reduced, cement rock volume shrinkage occurred, p H values decreased, the surface elastic modulus decreased down to a certain level, and slightly changed and the Ca/Si was 3.1 from the beginning and lasted down to 1.3.

基于加速退化试验的漏电信号调理电路性能退化及可靠性研究

在电子电路服役过程中,元器件退化会引起电路输出特性变化,降低电子电路的可靠性。漏电信号调理电路作为一种电子电路,其可靠性直接决定了漏电断路器的可靠性。以漏电信号调理电路为研究对象,首先基于灵敏度分析方法确定影响电路性能退化的关键元器件,并对漏电信号调理电路进行了以温度为加速应力、动作电流值为退化特征量的恒定应力加速退化试验;其次根据不同温度应力下的试验数据建立基于Wiener过程的漏电信号调理电路性能退化模型,并利用极大似然估计法求取退化模型的未知参数,进而得出寿命预测的概率密度函数和可靠度函数;最后利用阿伦尼斯(Arrhenius)方程外推出正常应力下漏电信号调理电路的预测寿命。相关结论可为不同电子电路的寿命预测及可靠度分析提供支撑。

基于温度循环加速退化试验的光纤连接器寿命评估

针对光纤连接器在温度交替变化下寿命评估难的问题,提出一种基于修正Coffin-Manson模型的寿命评估方法。首先,分析了光纤连接器失效模式、机理。接着,开展光纤连接器多个加速应力水平下的温度循环加速退化试验,基于插入损耗加速退化数据建立幂函数退化轨迹模型。然后,结合插入损耗的失效阈值,通过假设检验推导不同加速应力水平下光纤连接器的伪失效寿命。最后,引入修正Coffin-Manson加速模型,进而外推空间环境下光纤连接器寿命。本方法评估的某光纤连接器在实际应力水平下的寿命与实际寿命比较接近,验证了修正Coffin-Manson模型方法对光纤连接器寿命评估的有效性和可行性。

复合材料复杂环境效应加速试验设计及评估方法

目的指导复合材料在复杂湿热环境下环境适应性摸底与评价试验的开展,分析评估复合材料在复杂综合应力下的激活能参数。方法分析装备全寿命周期复杂自然环境剖面及各环境因素影响效应,确定复合材料各工作阶段敏感应力类型及条件,基于应力加速模型及累积损伤等原理,制定复合材料复杂环境效应综合加速试验剖面。构建复合材料复杂环境条件下的动力学模型,并提出相应参数估计方法。开展复合材料加速试验,并基于实测数据开展复合材料性能退化建模与评估。结果分析了复合材料全寿命周期环境影响因素及环境效应,明确了各工作阶段敏感应力主要有温度、湿度、太阳辐照、温度交变、振动以及冲击等。依据实际环境数据,设计并开展了3组不同湿热条件(80℃/75%RH、80℃/85%RH、80℃/95%RH)的综合试验,收集得到复合材料拉伸强度、拉剪强度、径向弯曲强度以及纬向弯曲强度等4种性能指标的试验数据。试验数据表明,拉剪强度(最大相对退化速率为0.1773/循环)、径向弯曲强度(最大相对退化速率为0.1292/循环)以及纬向弯曲强度(最大相对退化速率为0.2610/循环)等性能参数可用于产品退化建模与评估。通过参数估计,进一步确定了退化速率与湿热应力的关系,并针对当前试验提供了改进依据。结论复杂环境效应综合加速试验对装备复合材料产品经历复杂环境条件的模拟效果和加速效果较好,试验可实施性较强。提出的改进广义Eyring模型可涵盖温度应力与湿热应力的加速效应,并综合考虑多种应力的相互作用,通过少量组合试验便可量化评估激活能等参数。所建模型指出当前基于激活能参考值(Ea=0.7eV)试验方案可由不同温度应力的综合试验数据进一步修正与优化,且所提试验与分析方法主要针对大部分树脂基复合材料产品,并可依据需要推广至电子产品、机电产品等试验对象。

基于性能退化的铝电解电容寿命预测方法研究

应用表明铝电解电容是电源系统中故障率最高的元件,是影响电源系统长期运行可靠性的关键器件。为了评估铝电解电容在长期应用条件下的可靠性与寿命,对铝电解电容退化机理与退化模型进行研究分析,在已有模型研究成果的基础上,结合铝电解电容加速退化试验数据,提出了一种基于幂函数的电容量退化轨迹模型。采用该退化轨迹模型,开展了基于退化量分布的铝电解电容退化数据统计分析与寿命预测。根据寿命预测结果,某型铝电解电容在正常工作条件下95%可靠寿命超过18年。

Step-stress accelerated degradation test planning based on Wiener processwith correlation

To assess the lifetime distribution of highly reliable or expensive product,one of the most commonly used strategies is to construct step-stress accelerated degradation test(SSADT)which can curtail the test duration and reduce the test cost.In reality,it is not unusual for a unit with a higher degradation rate which exhibits a more volatile degradation path.Recently,Ye,Chen,and Shen[(2015).A new class of Wiener process models for degradation analysis.Reliability Engineering and System Safety,139,58–67]proposed a Wiener process to capture the positive correlation between the drift rate and the volatility.In this paper,an optimal SSADT plan is developed under the assumption that the underlying degradation path follows the Wiener process with correlation.Firstly,the stochastic diffusion process is introduced to model a typical SSADT problem.Then the design variables,including the sample size,the measurement frequency and the numbers of measurements under each stress level,are optimised by minimising the asymptotic variance of the estimated p-percentile of the product’s lifetime distribution subject to the total experimental cost not exceeding a pre-specified budget.Finally,a numerical example is presented to illustrate the proposed method.