样本受限下产品广义退化路径建模及分类优化

For the life estimation of highly reliable products, the product's failure data cannot be gotten by even doing the accelerated stress test in the limited test time. If quality characteristics do exist whose degradation over time can be related to the life of the product, the degradation model can then be constructed based on the degradation data of quality characteristics. Based on the existing modeling studies and due to the restriction of the samples, this research establishes the degradation path model of multiple quality characteristics, which take into consideration both random effects between different products and stochastic effects about time correlation and can describe both the linear degradation and nonlinear degradation path. This model also consider the impact of the measurement error. There are four main tasks in this research: (1) The generalized degradation model of multiple quality characteristics; (2)The optimization of the samples test allocation based on the generalized degradation model; (3)The analysis of model mis-specification and its impact on life estimation; (4)The three-stage classification policy based on the linear discriminant analysis. This research will lead to a new scientific basis and practical tools for life estimation of product. This will also expand the product degradation path model theory, enrich the methodology of product's classification. The theoretical method will bring benefit to the reliability optimization design and optimization of screening test. Meanwhile, it is conducive to reduce the test costs and shorten the test cycle time.

对高可靠产品的寿命预计，有时即使采用加速应力试验方法，也无法在有限时间内获得失效数据。此时，若存在与寿命相关的性能参数且随时间逐渐退化，可借助性能参数的退化量，建立退化路径模型来预计产品寿命。本项目将考虑样本受限条件，基于多性能参数，建立一种既能描述产品间变异的随机效应又能描述退化路径时间相关性,既能描述线性又能描述非线性的广义退化路径模型，同时考虑测量误差的影响。研究内容主要包括：（1）多性能参数的广义退化路径建模；（2）基于广义退化路径模型的试验配置优化；（3）模型误判研究及对寿命和试验方案的影响；（4）基于线性区别分析的三阶段产品分类决策。本研究将为高可靠性产品寿命预计奠定一种新的科学基础和实践工具，扩展产品退化路径建模理论，丰富产品分类优化方法。该理论方法一方面有益于产品可靠性优化设计，另一方面也有益于产品的分类筛选。同时，对于减少试验成本，缩短研制周期等也都有着重要的作用。

本项目的研究基于性能退化参数，针对高可靠性产品，建立了一种既能描述产品间变异的随机效应又能描述退化路径时间相关性,既能描述线性又能描述非线性的广义退化路径模型，同时考虑测量误差的影响。项目的研究成果主要包含以下几个方面。首先基于Wiener过程，考虑非线性特征、产品之间的异质性和测量的误差影响，构建了基于性能退化参数的广义退化路径模型。针对加速退化试验配置优化的研究，基于广义退化路径模型，建立了加速退化模型，通过决策试验中的样本数量、测量时间和测量次数，实现在约束条件下得到较高的产品寿命评估精度的目标，从而获得最佳的试验方案。在退化模型的误判方面，考虑了随机效应模型、随机过程模型以及两者混合模型相互误判所造成的影响程度大小，并对比了三种退化模型间相互误判对产品分类和预防维护的影响程度。最后，采用广义退化路径模型来描述批产品的退化过程，以线性区别分析方法构造了分类判别准则，确定了产品分类的最佳区分点和最佳预烧时间，建立了批产品最优分类决策。本研究为高可靠性产品寿命预计奠定了一种新的科学基础和实践工具，扩展了产品退化路径建模理论，丰富了产品分类优化方法。

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