威布尔分布安全下限对应实际可靠度的预测

PREDICTION OF THE TRUE RELIABILITY CORRESPONGING TO THE ONE-SIDED TOLERANCE LIMIT OF WEIBULL DISTRIBUTION

研究用双指标方法估计威布尔分布的安全下限 (单侧容限 )Ns 时置信度γ、名义可靠度p、子样容量n及实际可靠度r之间的定量关系 ,导出了r的预测公式。计算结果表明 ,对于威布尔分布 ,工程常用的 90 %或 95 %置信度匹配名义可靠度p足以保证r >p ;为了不致使估计的安全下限Ns 过于保守 ,应尽可能增大子样容量n ,使r更趋近于p。

In the structural reliability analysis one-sided tolerance limit N s is usually used for the safe lower limit of Weibull distributed population N with unknown scale parameter β and known shape parameter α. The above N s is usually a function of the sample estimates of distribution parameters, so it is also a random variable. The tolerance interval (N s,+∞) is required to be such that the probability is equal to a preassigned value γ(which is called confidence) that the tolerance interval includes at least a given proportion p of the population(which is called nominal reliability). There is an important question: what is the true reliability rcorresponding to the one-sided tolerance limit N s of Weibull distribution? In the present paper, the relation among confidence γ, nominal reliability p, sample size n and true reliability r is studied, and the formula for predicting r is derived. From the numerical results, for Weibull distribution, the true reliability r can always be larger than the nominal reliability p when the value of confidence γ is 90%(or 95%) conventionally. To avoid an excessively conservative estimate of N s, the sample size nshould be adequate.