Bayes feature fusion reliability evaluation model based on data migration
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摘要:
基于同种产品的多类试验源寿命数据信息，利用不同数据源间的映射关系，将多源数据迁移至现场数据源中形成混合数据源，以此作为产品可靠性贝叶斯统计分析基础。对于不同应力下加速寿命数据，将其折算至常应力水平下确定参数分布密度函数解析，以此作为产品可靠性贝叶斯统计分析的先验条件。将贝叶斯统计模型与数据迁移模型进行结合，融合多源数据的同时确定其参数估计值，得到产品密度函数解析并完成产品可靠性分析。算例表明：该类模型利用数据源间映射关系可有效实现数据迁移，且能实现加速寿命数据与其他各类数据源的同步融合，融合样本数据后的产品可靠性综合评估比单一寿命数据源的产品可靠性评估更全面、客观。
Abstract:Based on the life data information from multiple test sources, using the mapping relationship between different data sources, the multi-source data were migrated to the field data source to form a mixed data source, which was used as the basis for the Bayesian statistical analysis of product reliability. For the accelerated life data under different stresses, it was converted to the constant stress level to determine the parameter distribution density function, which was used as the priori condition for the product reliability Bayesian statistical analysis. By combining the Bayesian statistical model with the data migration model, and fusing multi-source data while determining the parameter estimates at the same time, the product density function and the product reliability analysis were obtained. The example showed that this model can effectively achieve data migration by utilizing the mapping relationship between data sources, and can accelerate the synchronous fusion of life data with other types of data sources. The comprehensive evaluation of product reliability after fusing sample data was more comprehensive and objective than that of a single life data source.
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Key words:
- data migration /
- Bayesian /
- data fusion /
- exponential distribution /
- reliability
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图 5 不同融合方法产品寿命分布函数对比图
Figure 5. Comparison of product life distribution functions with different fusion methods
图 6 不同融合方法产品寿命分布函数对比图
Figure 6. Comparison of product life distribution functions with different fusion methods
表 1 多源数据结构表
Table 1. Multi-source data structure table
数据源类别 数据结构 A类 $ {y_1},{y_2},\cdots,{y_{{n_1}}},{y_{_i}} > 0,i = 1,2,\cdots,{n_1} $ B类 $ {x_{11}},{x_{12}},\cdots,{x_{1{n_2}}},{x_{1j}} > 0,j = 1,2,\cdots,{n_2} $ C类 $ {x_{21}},{x_{22}},\cdots,{x_{2{n_3}}},{x_{2k}} > 0,k = 1,2,\cdots,{n_3} $ D类 应力条件为$ {S_a},a = 1,2,\cdots,n $
寿命数据为$ {t_{a1}},{t_{a2}},\cdots,{t_{a{r_a}}} $
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产品可靠度 产品失效率 产品平均寿命 $ R （ t ） = 1 - \displaystyle\int_0^t {f （ {{x_i};{\boldsymbol{\varPsi }}} ） } {\text{d}}x $ $ \lambda （ t ） = \dfrac{{{F'} （ t ） }}{{1 - F （ t ） }} = \dfrac{{f （ {t;{\boldsymbol{\varPsi }}} ） }}{{R （ t ） }} $ $ E （ X ） = \displaystyle\int_0^\infty {tf （ t ） } {\text{d}}t $
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表 3 某产品电子元件试验寿命数据初始数值
Table 3. Initial value of product electronic component test life data
h 试验种类 寿命数据值 A类 742.79, 2878.35, 2723.95, 3752.92, 4391.46, 1102.8, 1222.4, 3400.68, 830.10, 870.62 B类 1225.18, 737.35, 526.60, 649.87, 3399.11, ···, 980.47, 22.99, 772.24, 4029.56 C类 8260.48, 1782.21, 611.91, 2491.37, 2765.02, ···, 2980.49, 5465.17, 592.64, 888.10
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表 4 恒定电压加速寿命试验数据
Table 4. Constant voltage accelerated life test data
试验条件 $ {S_1} = 12 $
$ {r_1} = 10 $$ {S_2} = 15 $
$ {r_2} = 15 $$ {S_3} = 19 $
$ {r_3} = 20 $$ {S_4} = 25 $
$ {r_4} = 25 $$ {S_5} = 35 $
${r_5} = 30$失效时间
$ {t_{al}} $/h4915.23
1060.47
$ \vdots $
563.14
2380.15438.03
4124.38
$ \vdots $
728.86
58.44353.50
726.93
$ \vdots $
684.05
705.74180.36
370.88
$ \vdots $
161.04
279.4036.42
146.84
$ \vdots $
101.93
27.98
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表 5 三源样本顺序统计量
Table 5. Three-source sample order statistics
h 数据源分类 样本顺序统计量 A源 742.79, 830.10, 870.62, 1102.80, 1222.40, 2723.95, 2878.35, 3400.68, 3752.92, 4391.46 B源 6.18, 22.2, 22.99, 29.53, 37.41, ···, 5320.39, 7694.58, 7793.3, 8970.31, 9031.32, 9265.99 C源 10.31, 11.77, 15.9, 55.2, 68.98, 71.79, ···, 10783.7, 11256.8, 11454.9, 13073.3, 20468.0
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表 6 基于分位点的三源样本配对表
Table 6. Three-source sample pairing table based on quantile
h 样本对 样本配对值 A源与B源 （225.24, 742.79）,（455.74, 830.10）, ···, （3508.84, 3752.92）, （4955.55, 4391.46） A源与C源 （315.16, 742.79）, （574.70, 830.10）, ··· , （4693.42, 3752.92）, （7501.01, 4391.46）
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表 7 B、C两源迁移数据表
Table 7. B and C two source migration data table
h 数据源分类 折算数据 B类 1721.74, 1299.1, 1116.61, 1223.31, ···, 1509.74, 680.21, 1329.33, 4151.37 C类 5508.77, 1735.96, 1054.40,2148.96, ···, 2433.81, 3880.84, 1043.18, 1215.25
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表 8 不同应力下折算数据表
Table 8. Conversion data table under different stress
h 应力水平 折算至常应力下样本数据 $ {S_1} = 12 $ 7633.9, 1466.77, 352.67, ···, 3491.81, 671.10, 3578.11 $ {S_2} = 15 $ 1544.12,5310.3,3050,36, ···, 2563.29, 1842.24, 1156.30 $ {S_3} = 19 $ 1792.73, 3327.34, 4454.96, ···, 5769.81, 1284.01, 3151.12,3240.25 $ {S_4} = 25 $ 1831.09, 3451.93, 4642.90, ···, 1055.61, 1666.79, 2673.67 $ {S_5} = 35 $ 1887.88, 5547.53, 3083.96, ···, 1385.83, 4059.09, 1608.34
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表 9 加速寿命试验折算样本参数估计表
Table 9. Parameter estimation table of the converted sample of accelerated life test
应力水平 折算样本参数估计值 $ {S_1} = 12 $ $ {\tilde \lambda _1} = \dfrac{1}{{2\;417.109}} $ $ {S_2} = 15 $ $ {\tilde \lambda _2} = \dfrac{1}{{2\;451.604}} $ $ {S_3} = 19 $ $ {\tilde \lambda _3} = \dfrac{1}{{2\;365.011}} $ $ {S_4} = 25 $ $ {\tilde \lambda _4} = \dfrac{1}{{2\;371.819}} $ $ {S_5} = 35 $ $ {\tilde \lambda _5} = \dfrac{1}{{2\;363.386}} $
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表 10 产品可靠性评估指标结果表
Table 10. Product reliability evaluation index results table
可靠度 失效率 平均寿命 $ R （ t ） = {{\text{e}}^{ - 0.000\;422x}} $ $ \lambda （ t ） = 0.000\;422 $ $ E （ x ） = \theta = 2\;369.67 $
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