加速寿命试验三参数威布尔分布的极小变异-极大似然估计

目的 在加速试验中，对寿命服从三参数威布尔分布的产品进行可靠性评估与寿命预测，解决形状参数小于1时传统方法难以计算的问题。方法 利用三参数威布尔分布与指数分布之间的转换关系，以变异系数误差最小为优化目标，在确定最优位置参数估计值的基础上，应用拟极大似然方法估计分布模型中的其余参数，建立极小变异–极大似然估计（MV-MLE）。根据加速寿命试验中失效机理不变的原则，在失效机理等同条件下，将该方法推广至多应力水平下的可靠寿命评估。结果 在单一应力与多应力水平下，通过仿真模拟验证了所提方法的有效性。与传统方法相比，在小样本条件下，所提方法可提高形状参数（机理等同性参数）估计精度40%以上。结论 所提方法对于三参数威布尔分布的参数估计和寿命评估具有较高精度，能够有效克服传统方法的不足，在加速寿命试验评估中具有良好的应用效果。

Minimum Variation-Maximum Likelihood Estimation of Three-parameter Weibull Distribution under Accelerated Life Test

The work aims to estimate the reliability and predict the lifetime of the products subject to three-parameter Weibull distribution under accelerated life test, so as to solve the problem that the traditional methods are difficult to complete the calculation when the shape parameter is less than 1. Through the conversion relationship between three-parameter Weibull distribution and exponential distribution, the best estimated value of the location parameter was determined with the error of coefficient of variation as the optimization objective. Then, the analogue maximum likelihood method was used to estimate the remaining parameters of the Weibull distribution, based on which the minimum variation-maximum likelihood estimation (MV-MLE) was constructed. According to the principle of constant failure mechanism in accelerated life test, the proposed method was extended to evaluate the reliable lifetime of products under multiple stress levels while ensuring the failure mechanism equivalence. The effectiveness of the proposed method was verified by simulations under both single stress level and multiple stress levels. Compared with traditional methods, the proposed method improved the estimation accuracy of shape parameter (i.e. mechanism equivalence parameter) by more than 40% with small samples. The proposed method performs high accuracy for parameter estimation and lifetime prediction of three-parameter Weibull distribution, which overcomes the defects of traditional methods, and has good application effects in the evaluation of accelerated life test.