无失效数据参数估计的模糊回归法

Fuzzy regression method for parametric estimation on zero failure data

由于常规线性回归模型对个别异常数据敏感,导致回归方程欠稳定。建立了实测数据对回归直线的隶属度的计算公式,提出了以该隶属度为权重的模糊加权线性回归模型。由于无失效数据失效概率的确定对分布参数的估计结果有较大的影响,给出减函数法确定指数分布无失效数据失效概率的 Bayes估计式和等效失效数法确定威布尔分布无失效数据可靠度的估计式,并对分布参数进行模糊加权线性回归。回归结果与传统评判结果相比,更接近工程实际。

On account of the conventional linear regression model is sensitive to specific abnormal data, thus leads to instability of the regression equation. The computational formulae to the subordinative degree for the real measured data to the regressive line were established, and the fuzzy weighted linear regression model that takes that degree of subordination as the weight was put forward. Due to the determination on the failure probability of zero failure data has rather big influence upon the estimated result of distributed parameters, the Bayes estimation formula of exponential distributed failure probability of zero failure data determined by method of decrease function and the estimation formula of Weibull distributed reliability of zero failure data determined by method of equivalent failure number were presented, and the fuzzy weighted linear regression was carried out on the distributed parameters. The result of regression is more closed with engineering practice when compared with the result of traditional judgment.