单侧容限对应实际存活率的预测

PREDICTION OF THE TRUE SURVIVAL PROBABILITY CORRESPONDING TO THE ONE-SIDED TOLERANCE LIMIT

研究了单侧容限系数法中子样容量ｎ、置信度γ及名义存活率Ｐ与实际存活率α之间的定量关系，导出了α的预测公式。计算结果表明：在ｎ较小，γ与Ｐ搭配不当时，将出现α小于Ｐ的不合理情况。此时，名义存活率Ｐ将过高地表示了安全性，从而使人盲目乐观。本文指出：在飞机或直升机结构可靠性分析中，子样容量ｎ通常远小于４３，因此，某些文献中建议取γ＝９０％，Ｐ＝０．９９９９９９是不合理的，本文提出了新的建议。

n the structural reliability analysis one-sided tolerance limit X-KS is usually used hrthe lower limit of a normally distributed population X with unknown mean μand unknown standard deviation σ In the above expression k is called ont-sided tolerance limit factor and X and S are the sample estimates of μand σ,respectively. The tolerance interval(X-KS,+∞)is required to be such that the probability is equal to a preassigned valueγ(which is called confidenee) that the tolerance interval includes at least a given proportion Pof the population(which is called nominal survival probability).There is an important q uestion:what is the true survival probability a corresponding to the one-sided tolerance limil?In the present paper the formula for predictingois derived.From the numerical results,in some instances the true surviv- al probability a may be less than the nominal survival probability P. For example,when γ=90%,P=0.999 999,if the sample size n is less than 43 then α< P.In the aircraft or helicopter struc- tural reliability analysis the sample size n is usually much less than 43.Therefore,γ=90% and P=0.999 999 recommended in some literature are unreasonable.