关键词: Bootstrap方法, 小子样, 母体百分位值, 可靠度, 置信下限

Abstract: Bootstrap method is firstly employed to evaluate the confidence lower limit of population percentile under small number of test-sample. Large number of simulation is implemented to verify the advantage of the method. Comparing simulation results of the introduced Bootstrap method to those of traditional and improved one-sided tolerance factor methods, it is found that the Bootstrap method is more accurate than the one-sided tolerance factor method. Especially at small number of test-sample, the results of the introduced Bootstrap method are closer to the actual population percentile than those of other two methods. Under high confidence degree and reliability demand, negative evaluation value may appear in the result of one-sided tolerance factor method, but no one in the Bootstrap method, which shows that the bootstrap method fits the actual population percentile better than other two one-sided tolerance factor methods. A semiparameter Bootstrap method is investigated to determine the confidence lower limit for the reliability as well. Simulations indicate an improvement in accuracy at small number of test-sample and high confidence degree.

Key words: Bootstrap method, small sample, population percentile, reliability, low confidence limit