产品检验中的抽样个数

The Sample Size in the Product Hypothesis Test

设某批产品 (总体 )的次品率为 p,对总体提出假设H0 :p≤ p0 , H1:p >p1其中 0 <p0 ≤ p1<1 .从总体中抽取 n件产品 (容量为 n的样本 )检验上述假设时 ,应选取多大的样本容量 n才合适呢 ?其中次品件数超过多少 (临界值 c)才拒绝 H0 :p≤p0 呢 ?本文从双方 (厂方和用户 )利益相等的原则出发得到了下述结论 .( 1 ) n=1 /p0 ,n的取值与假设 H1无关 ;( 2 )得到了最佳 ( n,c)抽样方案 :n=1 /p0 、c=1 .此时犯弃真错误的概率仍不超过 1 /3.从而在客观上对原假设 H0 仍起到了保护作用 .

Suppose p be the shoddy product ratio in some group of products. For this group of products we propose that H 0: p≤p 0,\ H 1: p>p 1where 0<p 0≤p 1<1. To test the above Hypothesis, what is the reasonable sample size n and what is the maximum shoddy product number c? In this paper we achieved the following result: n=1/p\-0\, c=1 and n is independent of H 1: p>p 1.