Inference and optimal design on step-stress partially accelerated life test for hybrid system with masked data

Under Type-Ⅱ progressively hybrid censoring, this paper discusses statistical inference and optimal design on stepstress partially accelerated life test for hybrid system in presence of masked data. It is assumed that the lifetime of the component in hybrid systems follows independent and identical modified Weibull distributions. The maximum likelihood estimations(MLEs)of the unknown parameters, acceleration factor and reliability indexes are derived by using the Newton-Raphson algorithm. The asymptotic variance-covariance matrix and the approximate confidence intervals are obtained based on normal approximation to the asymptotic distribution of MLEs of model parameters. Moreover,two bootstrap confidence intervals are constructed by using the parametric bootstrap method. The optimal time of changing stress levels is determined under D-optimality and A-optimality criteria.Finally, the Monte Carlo simulation study is carried out to illustrate the proposed procedures.

Empirical Approach for Planning and Designing Constant Stress Accelerated Life Tests

Accelerated life testing(ALT)has been widely used to obtain information about the product's life characteristics at normal conditions in a relatively short period of time.Two key issues with ALT are test design and data analysis.The test design of constant stress ALT was studied in this paper.The test design usually combines engineering experiences with optimization models.Such approaches are hard to be implemented by practitioners.A"pure"empirical approach was presented to address this issue.With the proposed approach,some of the decision variables are determined based on the results from the literature,some of the other variables are determined based on engineering analysis and /or judgment,and the remaining variables are determined based on the empirical relations developed in this paper.A real-world example is included to illustrate the appropriateness of the proposed approach.

Constant Stress Accelerated Life Tests for Vacuum Fluorescent Display Based on Least Square Method

To estimate the life of vacuum fluorescent display （VFD） more accurately and reduce test time and cost, four constant stress accelerated life tests （CSALTs） were conducted on an accelerated life test model. In the model, statistical analysis of test data is achieved by applying lognormal function to describe the life distribution, and least square method （LSM） to calculate the mean value and the standard deviation of logarithm. As a result, the accelerated life equation was obtained, and then a self-developed software was developed to predict the VFD life. The data analysis results demonstrate that the VFD life submits to lognormal distribution, that the accelerated model meets the linear Arrhenius equation, and that the precise accelerated parameter makes it possible to acquire the life information of VFD within one month.

Inference for constant-stress accelerated life test with Type-I progressively hybrid censored data from Burr-XII distribution

This paper proposes a simple constant-stress accel- erated life test （ALT） model from Burr type XII distribution when the data are Type-I progressively hybrid censored. The maximum likelihood estimation （MLE） of the parameters is obtained through the numerical method for solving the likelihood equations. Approxi- mate confidence interval （CI）, based on normal approximation to the asymptotic distribution of MLE and percentile bootstrap Cl is derived. Finally, a numerical example is introduced and then a Monte Carlo simulation study is carried out to illustrate the pro- posed method.

Optimum design of equivalent accelerated life testing plans based on proportional hazards-proportional odds model

The optimum design of equivalent accelerated life testing plan based on proportional hazards-proportional odds model using D-optimality is presented. The defined equivalent test plan is the test plan that has the same value of the determinant of Fisher information matrix. The equivalent test plan of step stress accelerated life testing （SSALT） to a baseline optimum constant stress accelerated life testing （CSALT） plan is obtained by adjusting the censoring time of SSALT and solving the optimization problem for each case to achieve the same value of the determinant of Fisher information matrix as in the baseline optimum CSALT plan. Numer- ical examples are given finally which demonstrate the equivalent SSALT plan to the baseline optimum CSALT plan reduces almost half of the test time while achieving approximately the same estimation errors of model parameters.

Novel Accelerating Life Test Method and Its Application by Combining Constan Stress and Progressive Stress

Constant stress accelerated life tests(ALTs) can be applied to obtain a high estimation accuracy of reliability measure?ments, but these are time?consuming tests. Progressive stress ALTs can yield failures more quickly but cannot guaran tee the estimation accuracy of reliability measurements. In this paper, a progressive?constant combination stress ALT is proposed to combine the merits of both tests. The optimal plan, in which the design variables are the initial pro?gressive stress level, the progressive stress ramp rate, the sample allocation proportion of the progressive stress and the constant stress level, is determined using the principle of minimizing the asymptotic variance of the maximum likelihood estimator of the natural log reliable life for the connectors. A comparison between the optimal PCCSALT plan and the CSALT plan with the same sample size and estimation accuracy shows that the test time is reduced by 13.59% by applying the PCCSALT.

Parameter Estimation Based on Censored Data under Partially Accelerated Life Testing for Hybrid Systems due to Unknown Failure Causes

In general,simple subsystems like series or parallel are integrated to produce a complex hybrid system.The reliability of a system is determined by the reliability of its constituent components.It is often extremely difficult or impossible to get specific information about the component that caused the system to fail.Unknown failure causes are instances in which the actual cause of systemfailure is unknown.On the other side,thanks to current advanced technology based on computers,automation,and simulation,products have become incredibly dependable and trustworthy,and as a result,obtaining failure data for testing such exceptionally reliable items have become a very costly and time-consuming procedure.Therefore,because of its capacity to produce rapid and adequate failure data in a short period of time,accelerated life testing(ALT)is the most utilized approach in the field of product reliability and life testing.Based on progressively hybrid censored(PrHC)data froma three-component parallel series hybrid system that failed to owe to unknown causes,this paper investigates a challenging problem of parameter estimation and reliability assessment under a step stress partially accelerated life-test(SSPALT).Failures of components are considered to follow a power linear hazard rate(PLHR),which can be used when the failure rate displays linear,decreasing,increasing or bathtub failure patterns.The Tempered random variable(TRV)model is considered to reflect the effect of the high stress level used to induce early failure data.The maximum likelihood estimation(MLE)approach is used to estimate the parameters of the PLHR distribution and the acceleration factor.A variance covariance matrix(VCM)is then obtained to construct the approximate confidence intervals(ACIs).In addition,studentized bootstrap confidence intervals(ST-B CIs)are also constructed and compared with ACIs in terms of their respective interval lengths(ILs).Moreover,a simulation study is conducted to demonstrate the performance of the estimation procedures and the methodology discussed in this paper.Finally,real failure data from the air conditioning systems of an airplane is used to illustrate further the performance of the suggested estimation technique.

Detonator stepping stress acceleration life test

Through the failure mechanism analysi s and simulation test of a certain kind of detonator,this paper confirms the str ess level of the stepping stress acceleration life test of the detonator,and t hen e stablishes the data processing mathematical model and storage life forecasting m ethod.At last,according to the result of the stepping stress acceleration lif e test of the detonator,this paper forecasts the reliable storage life of the detonator under the normal stress level.

An Experimental Study on Constant Current Load Test of Reinforced Concrete based on 3D Paraffin Isolation

Aiming at the complex corrosion degradation factors of reinforced concrete and clearing the deterioration mechanism in the constant stress state,a new type of constant current accelerated corrosion method in the saline soil environment was developed.The three-dimensional paraffin isolation specimens and the three-dimensional penetration specimens were taken as the research objects,and the Cl−content and AC impedance Bode diagram were measured.The macro morphology and micro analysis were also used to evaluate the corrosion degradation laws of the two groups of specimens.A constant current three-factor system accelerated model was established for the current acceleration factor,chloride ion,and sulfate ion acceleration factor.The experimental results show that,in the constant stress test of the saline soil environmental conditions,the paraffin isolation layer can effectively isolate corrosive chloride ions,which is a brand-new research method of single factor variable control in the constant stress test.According to the basic corrosion data,the law of constant current acceleration test is summarized and divided into five corrosion degradation stages,and each stage has significant changes in the accelerated corrosion efficiency.The corrosion degradation of a constant stress test is the combined effect of constant current,positive and negative penetration of chloride ions and sulfate ions.

基于恒定应力加速寿命试验的SF_(6)气体密度表可靠性研究

SF_(6)气体密度表作为电网体系中一次设备的重要监测设备,其可靠性关乎变电设备的安全运行。为了确保SF_(6)气体密度表的可靠运行,有必要对其可靠性和寿命进行评估,而恒定应力加速寿命试验方法是结构复杂机械产品可靠性评估的有效方法之一。文章分析了SF_(6)气体密度表的加速应力和正常应力水平,确定了多应力加速寿命试验方案,利用Weibull寿命-应力模型综合估计了SF_(6)气体密度表的中位寿命、特征寿命、可靠寿命、平均寿命及相应的失效率,得到了其正常应力下可靠度曲线,为SF_(6)气体密度表生产制造和使用维护提供了理论依据和数据参考。

An accelerated life test model for harmonic drives under a segmental stress history and its parameter optimization

Harmonic drives have various distinctive advantages and are widely used in space drive mechanisms. Accelerated life test （ALT） is commonly conducted to shorten test time and reduce associated costs. An appropriate ALT modet is needed to predict the lifetime of harmonic drives with ALT data. However, harmonic drives which are used in space usually work under a segmental stress history, and traditional ALT models can hardly be used in this situation. This paper proposes a dedicated ALT model for harmonic drives applied in space systems. A comprehensive ALT model is established and genetic algorithm （GA） is adopted to obtain optimal parameters in the model using the Manson fatigue damage rule to describe the fatigue failure process and a cumulative dam- age method to calculate and accumulate the damage caused by each segment in the stress history. An ALT of harmonic drives was carried out and experimental results show that this model is acceptable and effective.

多应力小样本加速寿命试验设计与评估方法

针对目前多应力加速寿命试验需要的组合应力水平多、时间长、费用高的问题,提出一种多应力小样本加速寿命试验设计与评估方法。该方法建立了正常使用应力水平下可靠寿命的单侧置信下限与加速应力水平下的可靠寿命置信限之间的数学关系式,给出了正常使用应力水平下高置信度、高可靠度的可靠寿命单侧置信下限计算公式。文中首先针对工程上最常用的双应力情况,分别建立了无耦合和有耦合的双应力小样本加速寿命试验设计与评估方法,它只需在三个(无耦合)或四个(有耦合)组合应力水平下进行加速寿命试验,即可对产品在正常使用应力水平下高置信度、高可靠度的可靠寿命进行评估。然后针对一般的m种应力情况,建立了基于多应力线性加速模型的小样本加速寿命试验设计与评估方法,它只需在m+1个组合应力水平下进行加速寿命试验,即可求得产品在正常使用应力水平下高置信度、高可靠度的可靠寿命单侧置信下限。该方法计算简单,而且对完全数据、不完全数据以及各种分布均适用。大量工程算例和Monte Carlo模拟验证表明,与传统多应力加速寿命试验方法相比,本文方法不但可以节省大量试样和试验时间,而且理论上更加严谨,精度更高。

STATISTICAL INFERENCE OF WEIBULL DISTRIBUTION FOR TAMPERED FAILURE RATE MODEL IN PROGRESSIVE STRESS ACCELERATED LIFE TESTING

In this note,the tampered failure rate model is generalized from the step-stress accelerated life testing setting to the progressive stress accelerated life testing for the first time.For the parametric setting where the scale parameter satisfying the equation of the inverse power law is Weibull,maximum likelihood estimation is investigated.

Comparison Analysis of Efficiency Between Double-Synchronous Step-Down-Stress and Step-Up-Stress Accelerated Life Tests

Double-crossed-step-stress(DCSS) accelerated life test(ALT) method is widely used for estimating the lifetime of products with high reliability and long lifetime. In order to further reduce the test time and test cost, a double-synchronous-step-stress(DSSS) ALT method which combines a double-synchronous-step-downstress(DSSDS) ALT method and a double-synchronous-step-up-stress(DSSUS) ALT method is proposed. The accelerated stresses decrease and increase in a synchronous way with one step in the DSSDS-ALT and DSSUSALT methods, respectively. Monte Carlo method is adopted to simulate the two methods, and the validity and efficiency of them are demonstrated by the simulation results. In addition, a comparison analysis of efficiency between DSSDS-ALT method and DSSUS-ALT method is carried out. The result shows that the DSSDS-ALT method compared with the DSSUS-ALT method can significantly improve the test efficiency under the same test condition.

可靠性加速试验技术研究

为了更好地理解和运用可靠性加速试验技术,通过文献调研的方式,对加速寿命试验(ALT)、加速退化试验(ADT)、加速可靠性增长试验(ARGT)、高加速寿命试验(HALT)以及高加速应力筛选(HASS)等可靠性加速试验技术进行了研究。阐述了不同类型的可靠性加速试验技术在产品全生命周期内的适用阶段及其应用特点,并将可靠性加速试验与传统可靠性模拟试验技术进行了对比。对比结果表明,可靠性加速试验技术已经发展为产品寿命与可靠性评估的新途径,为高可靠性、小子样、长寿命、零失效产品的可靠性评估提供了有效方法,解决了传统可靠性模拟试验技术难以暴露产品设计缺陷和薄弱环节的问题。指出可靠性加速试验技术的应用前景以及未来方向。该研究有利于加强对可靠性加速试验技术的深入理解,以及推进该技术的长久发展。

Statistical analysis of dependent competing risks model in constant stress accelerated life testing with progressive censoring based on copula function

In this paper, we consider the statistical analysis for the dependent competing risks model in theconstant stress accelerated life testing (CSALT) with Type-II progressive censoring. It is focusedon two competing risks from Lomax distribution. The maximum likelihood estimators of theunknown parameters, the acceleration coefficients and the reliability of unit are obtained by usingthe Bivariate Pareto Copula function and the measure of dependence known as Kendall’s tau.In addition, the 95% confidence intervals as well as the coverage percentages are obtained byusing Bootstrap-p and Bootstrap-t method. Then, a simulation study is carried out by the MonteCarlo method for different measures of Kendall’s tau and different testing schemes. Finally, a realcompeting risks data is analysed for illustrative purposes. The results indicate that using copulafunction to deal with the dependent competing risks problems is effective and feasible.

基于高加速寿命试验的MLCC寿命建模研究

为了解决多层片式陶瓷电容器(MLCC)在高可靠产品应用、研发验证和产品改进等环节对快速可靠性评价技术的需求,提出了一种基于Procopowicz-Vaskas模型(P-V模型)的高加速寿命试验(HALT)评价方法,开展了某10μF 6.3 V MLCC产品在9组不同高温、高电压下的HALT研究。获得了样品在不同温度和电压应力下的失效分布特征,其P-V寿命模型参数的激活能为1.30 eV、电场加速因子为3.79。建立了高容量MLCC产品的HALT寿命模型,为其可靠性快速评价提供了参考。

基于Arrhenius模型和Peck模型的分段非线性加速模型

目的 解决Arrhenius模型无法估计湿度应力敏感产品和Peck模型试验时间较长的问题。方法 考虑温度应力和湿度应力对产品贮存寿命的综合影响,在产品激活能不变的假设下,将Arrhenius模型对产品激活能的估计和Peck模型对湿度应力参数的估计相结合,建立Arrhenius&Peck分段非线性加速寿命估计模型。基于此模型,在双应力恒加试验条件下,得到产品的寿命估计方程。结果 以弹上电子产品的恒定应力加速贮存试验为例,进行仿真分析,得到产品寿命的估计,并对比产品实际寿命。Arrhenius&Peck模型的寿命误差和失效率误差均控制在5%以内,准确度高于Arrhenius模型和Peck模型。结论 构建的Arrhenius&Peck分段非线性加速寿命模型可以充分利用温度和湿度条件下的试验数据,对温湿敏感产品的寿命估计有较好的应用效果,为导弹产品的寿命估计提供一种可选方法。

引信步进应力加速试验贮存寿命预测研究

目的 针对某机电引信加速寿命试验数据,采用传统统计分析方法存在计算量大、寿命预测精度难以保证的问题,开展与智能算法相结合的引信贮存寿命预测研究。方法 针对步进应力加速寿命试验数据,采用贝叶斯理论的环境因子法,对各级应力下的贮存时间进行折合计算。利用进化策略对粒子群算法进行改进,进而对所建立的BP神经网络预测模型的全局参数进行调整和优化,突破传统方法的局限。将折合后的试验时间、样本量、应力水平作为网络输入,失效数作为输出,来预测引信贮存寿命。结果 利用训练好的BP神经网络预测引信在正常应力水平下的失效数,计算其贮存可靠度。在迭代402次后,模型找到最优解,且预测误差在1%以内。结论 步进应力加速寿命试验与智能算法相结合的方法计算过程简单,预测精度较高,可有效提高引信贮存寿命的预测精度。

逐步Ⅰ型混合截尾下复合Rayleigh分布竞争失效产品部分步加寿命试验的统计分析

本文在逐步Ⅰ型混合截尾下,研究复合Rayleigh分布竞争失效产品部分步加寿命试验的统计分析问题。首先,基于复合Rayleigh分布竞争失效产品和损伤失效率(TFR)模型,运用极大似然理论和渐近似然理论,给出未知参数和加速因子的极大似然估计和渐近置信区间;然后,对未知参数和加速因子选取先验,利用MH抽样算法获得参数和加速因子的Bayes估计和最大后验密度置信区间(HPD);最后,通过Monte Carlo模拟对2种估计方法进行比较。结果表明:贝叶斯估计效果整体优于极大似然估计(MLE),在相同置信水平下,基于Bayes估计的HPD置信区间长度略短于MLE的渐近置信区间长度。