小偏度数据下通用质量特性评估最小样本量确定方法

doi:10.12305/j.issn.1001-506X.2025.10.22

摘要/Abstract

摘要：

针对航空装备面临作战任务复杂多样、战场环境动态多变，其状态鉴定、作战试验等通用质量特性评估常常面临数据样本量少、波动大等问题，从偏度和中心极限定理入手，提出通用质量特性参数小偏度数据下最小样本量要求的确定方法。首先，确定一定参数的目标分布，计算该参数下该分布的偏度。其次，取一定的初始样本量，生成该分布的多个随机数，计算其均值。再次，对其均值进行正态性检验，判断在给定样本量下是否通过正态性检验。最后，用试验中装备的平均故障间隔时间进行案例分析，证明了小偏度样本在小于推荐值情况下，计算结果仍具有参考意义。所提方法可为小样本量下航空装备通用质量特性的准确评估提供技术性指导。

关键词: 最小样本量, 偏度, 中心极限定理, 通用质量特性

Abstract:

In response to the complex and diverse combat tasks faced by aviation equipment, as well as the dynamic and changing battlefield environment, the evaluation of general quality characteristics such as state identification and combat testing often faces problems such as small sample sizes and large fluctuations in data. Starting from the skewness and central limit theorems, a method for determining the minimum sample size requirement for general quality characteristic parameters is proposed with small skewness data. Firstly, determine the target distribution of a certain parameters and calculate the skewness of the distribution with that parameters. Secondly, take a certain initial sample size, generate multiple random numbers for the distribution, and calculate their mean. Thirdly, perform a normality test on its mean to determine whether it passes the normality test with the given sample. Finally, a case analysis is conducted using the average time between failures of the equipment in the experiment, which proves that the calculation results of small skewness samples still have reference value even when they are less than the recommended value. This provides technical guidance for the accurate evaluation of general quality characteristics of aviation equipment in small sample sizes.

Key words: minimum sample size, skewness, central limit theorem, universal quality characteristic

中图分类号:

U 462.3+5

李娇, 彭文胜, 曾照洋, 邵英华, 张宝良. 小偏度数据下通用质量特性评估最小样本量确定方法[J]. 系统工程与电子技术, 2025, 47(10): 3378-3388.

Jiao LI, Wensheng PENG, Zhaoyang ZENG, Yinghua SHAO, Baoliang ZHANG. Method for determining minimum sample size for general quality characteristics evaluation with small skewness data[J]. Systems Engineering and Electronics, 2025, 47(10): 3378-3388.

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正态性检验通过率p	偏度范围	适用样本量（建议大于此值）
0.9	±0.5	30
0.9	±0.15	5
0.8	±0.5	20
0.8	±0.2	5
0.7	±0.5	15
0.7	±0.3	5

正态性检验通过率p	偏度范围	适用样本量（建议大于此值）
0.9	±0.35	50
0.9	±0.15	20
0.8	±0.5	28
0.8	±0.2	5
0.7	±0.66	27
0.7	±0.25	5

正态性检验通过率p	偏度范围	适用样本量（建议大于此值）
0.9	±0.5	25
0.9	±0.15	5
0.8	±0.5	17
0.8	±0.3	5
0.7	±0.5	10
0.7	±0.36	5

组别	实验数据	试验次数	成功次数
1	2.650 5，2.170 6，1.690 2，0.703 0，0.658 8	5	3
2	2.384 8，1.998 9，1.553 9，1.256 8，2.718 7	5	4
3	2.115 3，1.755 5，1.751 7，1.172 2，1.224 7	5	3
4	2.530 4，0.781 7，0.710 6，1.641 6，2.824 6	5	3
5	2.517 6，1.038 7，1.633 9，1.685 1，2.490 7	5	4
6	1.040 4，2.704 2，1.942 9，2.209 1，1.212 9	5	3
7	1.874 9，1.975 4，1.288 2，1.223 9，2.376 3	5	3

组别	偏度	均值
1	0.011 5	1.574 62
2	0.003 6	1.982 62
3	0.024 3	1.603 88
4	0.084 3	1.697 78
5	−0.110 3	1.873 20
6	0.036 3	1.821 90
7	0.051 8	1.747 74