A general Bayes weibull inference model for accelerated life testing

This article presents the development of a general Bayes inference model for accelerated life testing. The failure times at a constant stress level are assumed to belong to a Weibull distribution, but the specification of strict adherence to a parametric time-transformation function is not required. Rather, prior information is used to indirectly define a multivariate prior distribution for the scale parameters at the various stress levels and the common shape parameter. Using the approach, Bayes point estimates as well as probability statements for use-stress (and accelerated) life parameters may be inferred from a host of testing scenarios. The inference procedure accommodates both the interval data sampling strategy and type I censored sampling strategy for the collection of ALT test data. The inference procedure uses the well-known MCMC (Markov Chain Monte Carlo) methods to derive posterior approximations. The approach is illustrated with an example.     

A sequential constant‐stress accelerated life testing scheme and its Bayesian inference

In the analysis of accelerated life testing (ALT) data, some stress‐life model is typically used to relate results obtained at stressed conditions to those at use condition. For example, the Arrhenius model has been widely used for accelerated testing involving high temperature. Motivated by the fact that some prior knowledge of particular model parameters is usually available, this paper proposes a sequential constant‐stress ALT scheme and its Bayesian inference. Under this scheme, test at the highest stress is firstly conducted to quickly generate failures. Then, using the proposed Bayesian inference method, information obtained at the highest stress is used to construct prior distributions for data analysis at lower stress levels. In this paper, two frameworks of the Bayesian inference method are presented, namely, the all‐at‐one prior distribution construction and the full sequential prior distribution construction. Assuming Weibull failure times, we (1) derive the closed‐form expression for estimating the smallest extreme value location parameter at each stress level, (2) compare the performance of the proposed Bayesian inference with that of MLE by simulations, and (3) assess the risk of including empirical engineering knowledge into ALT data analysis under the proposed framework. Step‐by‐step illustrations of both frameworks are presented using a real‐life ALT data set. Copyright © 2008 John Wiley & Sons, Ltd.     

Integration of computation and testing for reliability estimation

This paper develops a methodology to integrate reliability testing and computational reliability analysis for product development. The presence of information uncertainty such as statistical uncertainty and modeling error is incorporated. The integration of testing and computation leads to a more cost-efficient estimation of failure probability and life distribution than the tests-only approach currently followed by the industry. A Bayesian procedure is proposed to quantify the modeling uncertainty using random parameters, including the uncertainty in mechanical and statistical model selection and the uncertainty in distribution parameters. An adaptive method is developed to determine the number of tests needed to achieve a desired confidence level in the reliability estimates, by combining prior computational prediction and test data. Two kinds of tests — failure probability estimation and life estimation — are considered. The prior distribution and confidence interval of failure probability in both cases are estimated using computational reliability methods, and are updated using the results of tests performed during the product development phase.     

A Bayesian Approach to Multiple Comparisons

This paper presents maximum likelihood theory for large-sample optimum accelerated life test plans. The plans are used to estimate a simple linear relationship between (transformed) stress and product life, which has a Weibull or smallest extreme value distribution. Censored data are to be analyzed before all test units fail. The plans show that all test units need not run to failure and that more units should be tested at low test stresses than at high ones. The plans are illustrated with a voltage-accelerated life test of an electrical insulating fluid.     

Bayesian Analysis in Partially Accelerated Life Tests for Weighted Lomax Distribution

Accelerated life testing has been widely used in product life testing experiments because it can quickly provide information on the lifetime distributions by testing products or materials at higher than basic conditional levels of stress, such as pressure, temperature, vibration, voltage, or load to induce early failures. In this paper, a step stress partially accelerated life test (SS-PALT) is regarded under the progressive type-II censored data with random removals. The removals from the test are considered to have the binomial distribution. The life times of the testing items are assumed to follow length-biased weighted Lomax distribution. The maximum likelihood method is used for estimating the model parameters of length-biased weighted Lomax. The asymptotic confidence interval estimates of the model parameters are evaluated using the Fisher information matrix. The Bayesian estimators cannot be obtained in the explicit form, so the Markov chain Monte Carlo method is employed to address this problem, which ensures both obtaining the Bayesian estimates as well as constructing the credible interval of the involved parameters. The precision of the Bayesian estimates and the maximum likelihood estimates are compared by simulations. In addition, to compare the performance of the considered confidence intervals for different parameter values and sample sizes. The Bootstrap confidence intervals give more accurate results than the approximate confidence intervals since the lengths of the former are less than the lengths of latter, for different sample sizes, observed failures, and censoring schemes, in most cases. Also, the percentile Bootstrap confidence intervals give more accurate results than Bootstrap-t since the lengths of the former are less than the lengths of latter for different sample sizes, observed failures, and censoring schemes, in most cases. Further performance comparison is conducted by the experiments with real data.     

Reliability Estimation for Accelerated Life Tests Based on a Cox Proportional Hazard Model with Error Effect

In this paper, a Cox proportional hazard model with error effect applied on the study of an accelerated life test is investigated. Statistical inference under Bayesian methods by using the Markov chain Monte Carlo techniques is performed in order to estimate the parameters involved in the model and predict reliability in an accelerated life testing. The proposed model is applied to the analysis of the knock sensor failure time data in which some observations in the data are censored. The failure times at a constant stress level are assumed to be from a Weibull distribution. The analysis of the failure time data from an accelerated life test is used for the posterior estimation of parameters and prediction of the reliability function as well as the comparisons with the classical results from the maximum likelihood estimation. Copyright © 2017 John Wiley & Sons, Ltd.     

Bayesian analysis for the results of fatigue test using full-scale models to obtain the accurate failure probabilities of the Shinkansen vehicle axle

Bayesian analysis was performed to estimate an appropriate value of the uncertain propagation rate of cracks that can be initiated at the wheelseat of a Shinkansen vehicle axle. In the analysis, fatigue life distribution obtained by numerical simulation that employed the crack propagation rate obtained from small specimens was used as the prior distribution. Then it was modified by the results of the fatigue test of full-scale models as additional information to obtain the posterior distribution. It was indicated that the variances of fatigue life distribution reduced through the analysis. By using the crack propagation rate obtained from the posterior fatigue life distribution, the failure probabilities of the Shinkansen vehicle axle in operation, that were calculated previously by using the crack propagation rate due to the experiment of small specimens were recalculated. The resulting probabilities of failure were almost the same as those that were not modified, but were slightly lower. Although the difference was not so significant, it was thought that more confident values of the failure probability were obtained.     

Fatigue life prediction of a rubber mount based on test of material properties and finite element analysis

Failure analysis and fatigue life prediction are very important in the design procedure to assure the safety and reliability of rubber components. The fatigue life of a rubber mount was predicted by combining test of material properties and finite element analysis (FEA). The natural rubber material material’s fatigue life equation was acquired based on uniaxial tensile test and fatigue life tests of the natural rubber. The strain distribution contours and the maximum total principal strains of the rubber mount at different loads in the x and y directions were obtained using finite element analysis method. The critical region cracks prone to arise were obtained and analyzed. Then the maximum total principal strain was used as the fatigue parameter, which was substituted into the natural rubber’s fatigue life equation, to predict the fatigue life of the rubber mount. Finally, fatigue lives of the rubber mount at different loads were measured on a fatigue test rig to validate the accuracy of the fatigue life prediction method. The test results imply that the fatigue lives predicted agree well with the test results.     

Austempering retards pitting failure in ductile iron spur gears

In this study, the effect of austempering process on pitting formation in spur gears made of ductile iron is analysed. A series of experiments are carried out to determine the pitting formation life. Gear test specimens were first austenitized in a salt bath at 900 °C for 90 min after which they were tempered in a salt bath at 250, 325, 375 and 425 °C for 60 and 90 min duration. All gear experiments were performed using FZG test machine. Pitting formation is investigated using scanning electron microscopy. It is concluded from the analysis that austempering contributes to the increase of pitting formation life.     

Cyclic oxidation – guidelines for test standardisation,aimed at the assessment of service behaviour†

Abstract

This paper reviews current procedures used for cyclic oxidation testing and their ability to simulate service behaviour for life time prediction modelling. Test complexity varies from a simple laboratory, slow cycle, furnace test to the use of high velocity dynamic combustion rigs. It is shown that the response of an alloy under cyclic oxidation testing varies, depending on the exact test conditions chosen and the length of test exposure, but for many alloy systems this response has common features. It is proposed that all alloys that are protected by a stable, slow growing oxide scale conform to a common, generic behaviour under cyclic oxidation conditions. This life cycle of such alloys involves first the formation of a stable, protective oxide. At a critical thickness this may start to spall, increasing the rate of scale forming element consumption. When the activity of such elements falls below a critical level, in the near surface region, internal oxidation results together with the formation of less protective scales. Ultimately, it is no longer possible for the alloy to self repair following a thermal cycle and then breakaway corrosion ensures, marking the end of the alloys life.

Thus the choice of cyclic test procedure must be tailored to the particular phase of the alloy life cycle under investigation.     

某汽车排气系统振动特性

建立某汽车排气系统的有限元模型,对其进行模态分析仿真,得到排气系统的前若干阶的固有频率及其振型。基于模态分析和排气系统的振动测试结果,对排气系统在发动机不同转速下的激励引起的振动进行分析,研究排气系统的振动特性,提出结构的改进意见,为提高排气系统的工作可靠性和使用寿命提供参考。     

Utilizing Accelerated Degradation and Field Data for Life Prediction of Highly Reliable Products

For newly developed, highly reliable, and long‐lifespan products, it is quite difficult to implement effective remaining useful life (RUL) prediction in the early usage under limited time cost. However, accelerated degradation testing (ADT) is generally used for lifetime evaluation for such products with harsher test conditions and shorter test time in the late research and development phase. Thus, in this paper, we propose a life prediction framework to integrate the information from ADT to conduct field RUL prediction for highly reliable products. Because ADT belongs to reliability testing used for inferring the population information from the selected test samples, we at first present the modified Wiener process (MWP) model. Different from traditional methods that embody both the random variability and unit‐to‐unit variability into the diffusion coefficient, the proposed method describes them separately in ADT analysis. Then, the MWP model from ADT is used as a prior for field RUL prediction of the target product during which the strong tracking filtering algorithm is introduced for updating the hidden state and computing the RUL prediction results when the new monitoring data are available. Because of the complexity of the MWP model, the Markov chain Monte Carlo method is provided to estimate the unknown parameters. Finally, the simulation study and the light‐emitting diode application verify the effectiveness of the proposed framework that can achieve reasonable life prediction results for highly reliable products for both linear and nonlinear scenarios. Copyright © 2015 John Wiley & Sons, Ltd.     

Statistical inference on progressive-stress accelerated life testing for the logistic exponential distribution under progressive type-II censoring

The accelerated life testing (ALT) is an efficient approach and has been used in several fields to obtain failure time data of test units in a much shorter time than testing at normal operating conditions. In this article, a progressive-stress ALT under progressive type-II censoring is considered when the lifetime of test units follows logistic exponential distribution. We assume that the scale parameter of the distribution satisfying the inverse power law. First, the maximum likelihood estimates of the model parameters and their approximate confidence intervals are obtained. Next, we obtain Bayes estimators under squared error loss function with the help of Metropolis-Hasting (MH) algorithm. We also derive highest posterior density (HPD) credible intervals of the model parameters. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation. Finally, one data set has been analyzed for illustrative purposes.     

Bayesian Analysis of Step‐Stress Accelerated Life Test with Exponential Distribution

In this article, we propose a general Bayesian inference approach to the step‐stress accelerated life test with type II censoring. We assume that the failure times at each stress level are exponentially distributed and the test units are tested in an increasing order of stress levels. We formulate the prior distribution of the parameters of life‐stress function and integrate the engineering knowledge of product failure rate and acceleration factor into the prior. The posterior distribution and the point estimates for the parameters of interest are provided. Through the Markov chain Monte Carlo technique, we demonstrate a nonconjugate prior case using an industrial example. It is shown that with the Bayesian approach, the statistical precision of parameter estimation is improved and, consequently, the required number of failures could be reduced. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimal design of partially accelerated life tests for the lognormal distribution under type I censoring

This paper considers optimal designs of partially accelerated life tests in which test items are first run simultaneously at use condition for a specified time, and the surviving items are then run at accelerated condition until a predetermined censoring time. For items having lognormally distributed lives maximum likelihood estimators (MLEs) of the location and scale parameters of the lifetime distribution at use condition, and the acceleration factor which is the ratio of the mean life at use condition to that at accelerated condition are obtained. The change time is determined to minimize either the asymptotic variance of MLE of the acceleration factor or the generalized asymptotic variance of MLEs of the model parameters.     

TNT基炸药储存寿命评估研究?

为解决有效评估炸药储存寿命的难题,提出一套基于炸药加速退化试验失重率阈值的储存寿命评估技术。采用基于伪失效寿命的加速寿命试验数据建模与处理方法,对某TNT基炸药加速退化试验数据,使用正态分布和威布尔分布模型,估计了两种模型参数,评定了其储存寿命。研究表明,该评估技术可行,结论可信。     

Reliability analysis of exponentiated Poisson-exponential constant stress accelerated life test model

Accelerated life testing is an efficient tool frequently adopted for obtaining failure time data of test units in a lesser time period as compared to normal use conditions. We assume that the lifetime data of a product at constant level of stress follows an exponentiated Poisson-exponential distribution and the shape parameter of the model has a log-linear relationship with the stress level. Model parameters, the reliability function (RF), and the mean time to failure (MTTF) function under use conditions are estimated based on eight frequentist methods of estimation, namely, method of maximum likelihood, method of least square and weighted least square, method of maximum product of spacing, method of minimum spacing absolute-log distance, method of Cramér-von-Mises, method of Anderson–Darling, and Right-tail Anderson–Darling. The performance of the different estimation methods is evaluated in terms of their mean relative estimate and mean squared error using small and large sample sizes through a Monte Carlo simulation study. Finally, two accelerated life test data sets are considered and bootstrap confidence intervals for the unknown parameters, predicted shape parameter, predicted RF, and the MTTF at different stress levels, are obtained.     

任意分布参数的涡轮盘裂纹扩展寿命可靠性分析

讨论了某型涡轮盘随机参数服从任意分布时的可靠性问题.在基本随机参数前四阶矩已知的情况下,以Pairs-Erdogan裂纹扩展模型为基础,应用随机摄动理论和Edgeworth 级数技术,采用疲劳寿命模型对某型涡轮盘随机参数服从任意分布时的可靠性进行分析,建立了涡轮盘疲劳寿命可靠性分析模型,并求得了涡轮盘裂纹扩展寿命的可靠度.模型计算结果与Monte-Carlo仿真结果非常接近,文章提出的方法对涡轮盘可靠性设计具有一定的参考价值.     

Bootstrap tests for nonparametric comparison of regression curves with dependent errors

In this paper, the problem of testing the equality of regression curves with dependent data is studied. Several methods based on nonparametric estimators of the regression function are described. In this setting, the distribution of the test statistic is frequently unknown or difficult to compute, so an approximate test based on the asymptotic distribution of the statistic can be considered. Nevertheless, the asymptotic properties of the methods proposed in this work have been obtained under independence of the observations, and just one of these methods was studied in a context of dependence as reported by Vilar-Fernández and González-Manteiga (Statistics 58(2):81–99, 2003). In addition, the distribution of these test statistics converges to the limit distribution with convergence rates usually rather slow, so that the approximations obtained for reasonable sample sizes are not satisfactory. For these reasons, many authors have suggested the use of bootstrap algorithms as an alternative approach. Our main concern is to compare the behavior of three bootstrap procedures that take into account the dependence assumption of the observations when they are used to approximate the distribution of the test statistics considered. A broad simulation study is carried out to observe the finite sample performance of the analyzed bootstrap tests.      

空调测试系统的现场总线应用方案设计

根据空调测试系统测控点的分散性、多样性及多工况的特点,提出一种以快速参数自整定的DS100现场控制器作为底层数据采集和控制单元,与上位工业计算机组成空调测试系统的现场总线应用方案。分析了DS100现场控制器的基本特征及对该测试系统的适用性,讨论了现场总线技术作为空调测试系统的现场测控装置的信息传输可行性,提出了一种基于MODBUS协议的令牌流转技术方案,论述了测试系统实施技术及相关的软件设计方法,最后给出了该空调测试系统的试验结果。