Analysis and application of exponential degradation paths with random failure thresholds
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摘要: 目前在退化试验中, 通常是将产品的性能降低或升高到某一固定门限值定义为产品失效, 即单点型退化. 虽然该定义被广泛应用, 但却不够合理, 不能够完全描述产品退化失效问题. 本文对单点型退化标准进行改进, 将固定门限推广为某一区间的随机值, 构建区间型退化模型. 主要研究当退化轨道是指数型函数时, 讨论各种情况下区间型退化寿命分布. 本文利用数值积分和蒙特卡罗法对区间退化模型和单点退化模型的寿命分布进行模拟对比分析, 揭示区间型退化和单点型退化的关系. 最后通过模拟结果说明采用区间型退化更合理有效.Abstract: In a classical degradation experiment, the performance of a product is reduced or raised to a certain threshold value, which is regarded as a product failure; this is often refereed to as single-point degradation. Although this definition is widely used, it is not sufficiently comprehensive and cannot be used alone to describe the full product degradation process. In this study, we improve the single-point degradation model and propose the interval degradation model; in this context, the previously fixed threshold value will be generalized to a random value at a specified interval. We discuss the lifetime distributions for a variety of interval degradation models when the degradation path is an exponential function. Numerical integration and Monte Carlo simulation are used to calculate the lifetime distribution for interval degradation models and single-point degradation models; in addition, we determine the relationship between the respective models. The simulation results reveal that the performance of the interval degradation model is more reasonable and effective than that of single-point degradation model.
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图 1 正态分布-均匀分布-均匀分布模型下的分布函数
Fig. 1 Cumulative distribution function of a normal-uniform-uniform model
图 2 正态分布-正态分布-均匀分布模型下的分布函数
Fig. 2 Cumulative distribution function of a normal-normal-uniform model
图 3 伽马分布-均匀分布-均匀分布模型下的分布函数
Fig. 3 Cumulative distribution function of a gamma-uniform-uniform model
图 4 伽马分布-正态分布-均匀分布模型下的分布函数
Fig. 4 Cumulative distribution function of a gamma-normal-uniform model
图 5 威布尔分布-均匀分布-均匀分布模型下的分布函数
Fig. 5 Cumulative distribution function of a Weibull-uniform-uniform model
图 6 威布尔分布-正态分布-均匀分布模型下的分布函数
Fig. 6 Cumulative distribution function of a Weibull-normal-uniform model
图 7 指数分布-均匀分布-均匀分布模型下的分布函数
Fig. 7 Cumulative distribution function of an exponential-uniform-uniform model
图 8 指数分布-正态分布-均匀分布模型下的分布函数
Fig. 8 Cumulative distribution function of an exponential- normal - uniform model
图 9 对数正态分布-均匀分布-均匀分布模型下的分布函数
Fig. 9 Cumulative distribution function of a lognormal-uniform-uniform model
图 10 对数正态分布-正态分布-均匀分布模型下的分布函数
Fig. 10 Cumulative distribution function of a lognormal-normal-uniform model
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