【作者】 王欢；

【导师】 王冠军；

【作者基本信息】 东南大学 ， 统计学， 2016， 硕士

【摘要】 步进应力加速退化试验(SSADT)是估计高可靠性产品或者价格昂贵的产品寿命分布的有效工具。在假设产品的退化过程服从维纳过程、伽马过程的基础上,SSADT最优试验设计问题已经得到了广泛的研究。然而,逆高斯过程模型虽在退化数据分析中扮演着重要角色,但基于逆高斯过程的SSADT最优化设计问题仍是一个亟待研究的问题。本文旨在研究在假设产品的退化过程服从逆高斯过程的基础上SSADT的最优试验设计问题。这篇文章首先假设产品的退化过程服从平稳逆高斯过程,并在一系列假设的基础上,推导出产品在SSADT中的退化模型及其似然函数。然后在总试验费用不超过预先给定的阂值的约束下,选择最优的设计变量使得产品在正常工作水平下的寿命分布的p分位点估计的渐近方差最小。设计变量包括样本量、观测频率及每个应力水平上的观测次数。最后,引用碳膜电阻器这个实例来验证该模型的可用性,灵敏度检验结果表明最优设计变量对参数估计偏差具有很好的稳健性,我们也用蒙特卡洛(MC)算法验证了最优设计方案的稳定性。我们进一步探讨基于非平稳逆高斯过程的SSADT最优试验设计问题。这部分建立的SSADT模型是基于累积损伤(CE)模型,即产品的在任何时刻后续的退化路径只依赖于当前退化累积量和当前的应力水平,而与累积方式无关。我们以总试验费用不超过预先给定的阈值为约束条件,以最小化产品在正常工作水平下的寿命分布的p分位点估计的渐近方差为目标,来确定SSADT最优设计方案。我们将该模型应用到一种插座插孔的应力松弛数据的SSADT最优试验设计中,并对最优试验方案进行灵敏度和稳定性检验。此外,本文以随机波动率模型为例研究了产品的退化过程服从含有随机效应的逆高斯过程的SSADT最优试验设计问题。这部分仍用CE模型建立SSADT。然后,我们在总试验费用不超过预先给定的阈值的约束下,选择最优的设计变量使得产品在正常工作水平下的寿命分布的矿分位点的估计的渐近方差最小。最后,用这部分提出的模型构造出插座插孔的SSADT最优试验设计。更多还原

【Abstract】 The step-stress accelerated degradation test (SSADT) is a useful tool for as-sessing the lifetime distribution of highly reliable product or very expensive product. Some efficient SSADT plans have been proposed when the underlying degradation follows the Wiener process or Gamma process. However, how to design an efficient SSADT plan for the inverse Gaussian (IG) process, which also plays an important role in degradation data analysis, is an essential problem to be solved. The aim of this paper is to provide an optimal SSADT test plan for the IG degradation process.Firstly, We assume that the degradation follows a stationary IG process. The SSADT degradation model of the product and its likelihood function are deduced based on a series of assumptions. Under the constraint that the total experimental cost does not exceed a pre-specified budget, the design variables, including sample size, measurement frequency, and the number of measurements for each stress level, are optimized by minimizing the asymptotic variance of the estimated p-quantile of the failure time distribution of the product. Finally, we illustrate the proposed procedure with a numerical example based on the data from the carbon-film-resistor problem. The sensitivity of the SSADT plan is also studied, and we find the optimal test plan is quite robust for a moderate departure from the values of the parameters. We also use Monte Carlo simulations to prove the stability of the optimal test plan.Furthermore, we investigate the planning of SSADT for the non-stationary IG process. A cumulative exposure (CE) model for the SSADT is adopted, in which the future degradation path depends only on the current stress level and the degradation accumulated, and has nothing to do with the way of accumulation. Next, under the constraint that the total experimental cost does not exceed a pre-specified budget, the optimal design variables are obtained by minimizing the asymptotic variance of the estimated the p-quantile of the failure time distribution. Finally, we use the proposed method to deal with the optimal SSADT design for a type of electrical connector. The sensitivity and stability of the optimal test plan are studied.We also use the random volatility model to discuss SSADT planning for a random-effects IG process model. We still use the CE model to establish the S-SADT. Next, under the constraint that the total experimental cost does not exceed a pre-specified budget, the optimal design variables are obtained by minimizing the asymptotic variance of the estimated the p-quantile of the failure time distribution of the product. We then use the proposed methods to deal with the optimal SSADT design for a type of electrical connector based on a set of stress relaxation data.更多还原