小样本无失效寿命试验数据的轴承可靠性评估

针对小样本无失效寿命试验数据可靠性问题提出了评估模型。模型采用Bayes理论构造服从原始样本的抽样函数，结合Bootstrap法生成大量服从抽样函数的随机数作为增广样本，再通过最佳线性不变估计法分析原始样本及增广样本得到Weibull分布双参数估计值作为可靠性评估结果。通过Monte-Carlo法仿真生成服从Weibull分布的随机数，分别采用该模型、配分布曲线法及现有Bayes理论对此随机数做评估，对比发现:该模型得到的参数估计较现有Bayes理论和配分布曲线法更接近Weibull双参数真值，且形状参数和尺度参数估计值的相对误差均低于10%，验证了模型分析小样本无失效数据进行可靠性评估的可行性。借助文献实例对模型进行分析，对比得出模型能得到较现有Bayes理论和配分布曲线法更符合工程实际的评估结果；模型在小样本情况下的双侧可靠度置信区间长度低于现有Bayes理论和配分布曲线法，有效提高了小样本无失效数据可靠性评估精度。 

Reliability evaluation of bearings based on small samples and zero-failure life test data

A reliability evaluation model of small samples and zero-failure life data was proposed.The Bayes theory was used to construct a sampling function subjecting to the original small samples.The Bootstrap method was used to generate a large of random numbers subjecting to the sampling function as augmented samples.Both of the original and augmented samples were analyzed by the best linear invariant estimation method to obtain the two-parameter estimation value of Weibull distribution for reliability evaluation.The Monte-Carlo method was used to generate random numbers subjecting to the Weibull distribution.These random numbers were evaluated by the model，the match distribution curve method and the existing Bayes theory respectively.The results showed that the parameter estimates obtained by the model were closer to the Weibull two-parameter true value than the existing Bayes theory and the match distribution curve method.Meanwhile，the relative error of the estimated value of the shape parameter and the scale parameter was less than 10%，indicating the feasibility of the model to analyze the small sample of zero-failure data for reliability evaluation.The model was verified with examples in reference，and the results showed that the reliability evaluation obtained by the model was closer to that used in actual engineering practice than the other two methods；moreover the model's two-sided reliability confidence interval length was smaller than the other two methods，effectively improving the accuracy of reliability evaluation of small samples and zero-failure data .