﻿ 测绘地理信息产品抽样检验的两类错误概率
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1. 国家测绘产品质量检验测试中心, 北京 100830;
2. 中国测绘科学研究院, 北京 100830

Probabilities of two types of errors in sampling inspection for surveying and mapping products
CAI Yanhui1, CHENG Pengfei2, ZHANG Li1, XU Yantian2
1. National Quality Inspecting and Testing Center of Surveying and Mapping, Beijing 100830, China;
2. Chinese Academy of Surveying and Mapping, Beijing 100830, China
Abstract: Based on theory of hypothesis testing, a function of calculating probabilities of two types of errors is proposed, which is adopted inanalyzing the advantages and disadvantages of different sampling schemes given in the National Standard GB/T24356-2009. Under the circumstance of large lot size, the sampling inspection should be carried out lot by lot with the lot size less than 200 and the least lot number. Investigations on such procedure are made base on the probability distributions of two types of errors. Numerical results of type Ⅰ error show that the whole lot inspection is equivalent to the sub-lot inspections sequence from the point of probability of positive null hypothesis. At the same time, experiment results of type Ⅱ error with the typical sampling scheme show that the conclusions of sampling inspection according to the requests of GB/T24356-2009 may be badly wrong under the situation of low percentage of defectiveness.
Key words: surveying and mapping    quality inspection    sampling schemes    type Ⅰ error    type Ⅱ error

1 假设检验的两类错误 1.1 两类错误的定义

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1.2 两类错误概率的计算

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 图 1 两类错误拒绝域集合 Fig. 1 The reject sets of two types errors

2 测绘地理信息产品抽样检验的两类错误 2.1 抽样检验的抽样方案

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L(p)构成的曲线称为该方案的抽样操作特性曲线[23]，即OC曲线。OC曲线反映了抽样方案的检验通过概率与产品不合格率的分布关系。对给定的质量水平p0p1，在不考虑检验误差的条件下，式(4)即为

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2.2 GB/T24356-2009标准抽样的两类错误概率

GB/24356-2009采用了计数型一次简单随机抽样方法[1, 23-25]，并规定当不合格数为0，判定批合格；当不合格数大于等于1，判定批不合格，即Ac=0，Re=1。该抽样方案(N, n, 0, 1)可表述为从批量为N的产品中随机抽取n个样品进行检验，若其中不合格品数为0，就可以较高的概率接受该批产品；若其中不合格品数大于等于1，则以较高的概率拒绝该批产品。表 1为该标准规定的抽样表。当测绘地理信息成果的批量超过200，需要进行均匀分批，再按此表抽样，进行检验。

 批量 样本量 批量 样本量 1-20 3 101-120 11 21-40 5 121-140 12 41-60 7 141-160 13 61-80 9 161-180 14 81-100 10 181-200 15 201- 分批次提交，批次数应最小，各批次的批量应均匀 说明 当样本量等于或大于批量时，则全数检查

 序号 N n α(p0=0) β(p1=1) β(p1=2) β(p1=5) 1 20 3 0.00 0.850 0.716 0.399 2 40 5 0.00 0.875 0.763 0.493 3 60 7 0.00 0.883 0.779 0.525 4 80 9 0.00 0.887 0.786 0.542 5 100 10 0.00 0.900 0.809 0.584 6 120 11 0.00 0.908 0.824 0.613 7 140 12 0.00 0.914 0.835 0.635 8 160 13 0.00 0.918 0.844 0.651 9 180 14 0.00 0.922 0.850 0.664 10 200 15 0.00 0.925 0.855 0.674

3 测绘地理信息产品大批量抽样检验 3.1 大批量产品检验总体通过概率的等价性

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 图 2 大总体分批抽样方案的OC曲线 Fig. 2 OC-curve lines of different sampling plans With big lots

3.2 大批量的质量检验两类错误概率

 N n α(p0=0) β(L(p1)(p1=2) β′(p1=2) 302 26 0.000 0.835 0.165

 N n α(p0=0) β(L(p1))(p1=1) β′(p1=1) L(p1)×L(p1)(p1=2) β′×β′(p1=2) 151 13 0.000 0.914 0.086 0.835 0.007

3.3 大批量抽样检验的失真性

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 N n β(L(p1))(p1=2) β(L(p1))(p1=6) β(L(p1))(p1=12) β(L(p1))(p1=18) β(L(p1))(p1=30) 302 26 0.835 0.580 0.333 0.189 0.058

4 结论与展望

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http://dx.doi.org/10.11947/j.AGCS.2019.20180108

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#### 文章信息

CAI Yanhui, CHENG Pengfei, ZHANG Li, XU Yantian

Probabilities of two types of errors in sampling inspection for surveying and mapping products

Acta Geodaetica et Cartographica Sinica, 2019, 48(8): 954-959
http://dx.doi.org/10.11947/j.AGCS.2019.20180108