关键词: Weibull分布, 可靠性, 平均无故障工作时间, 区间估计, 似然比

Abstract: To evaluate reliability of multiple numerical control machine tools with field time truncated failure and small sample data, a two-step and bisectional interval method of likelihood ratio test is proposed, this method consist of firstly rough estimation and lastly accuracy estimation, and iterative formula of interval estimation for model parameters of 2-parameter Weibull distribution and reliability indices including mean time between failures, operational time given reliability and reliability at given time are all derived. In rough estimation process, a larger calculating step can be used to search maximum value of convex carve and minimum value of concave curve for assessment indices; At accuracy estimation stage, to obtain more accuracy computing results, bisectional interval of the two sides of maximum (minimum) value can be recalculated until the evaluation results meet the requirement of estimated accuracy. By using the proposed method, point estimation of model parameters and interval estimation of reliability indices for a detail example are presented. The results show that this method is suitable for reliability assessment to small sample data and can reduce computing and improve iterative speed.

Key words: Interval estimation, Likelihood ratio, Mean time between failures, Reliability, Weibull distribution