为解决计量测试工作中合成标准不确定度评定问题。首先,对简单的两均匀分布进行了概率密度函数合成,得到了半区间不等的两均匀分布合成为梯形分布,半区间相等的两均匀分布合成为三角分布,并给出其合成概率密度函数表达式;其次,将三角分布与均匀分布的概率密度函数进行了合成,得到了合成概率密度函数的表达式,并绘制出其图像,从概率密度函数的角度和合成标准不确定度计算的角度分别计算出合成分布的方差,2种方法得到的结果一致,并用蒙特卡洛法对60000个服从均匀分布和60000个服从三角分布的数据进行模拟,所得到的曲线与合成概率密度函数曲线完全一致。
Abstract
In order to solve the uncertainty evaluation problem of synthetic standard in measurement and test. First, the probability density function synthesis of simple two uniform distributions is carried out, and the two uniform distributions with different half-intervals are synthesized into trapezoidal distribution, and the two uniform distributions with equal half-intervals are synthesized into triangular distribution. Secondly, the expression of synthetic probability density function is given. The probability density functions of triangular distribution and uniform distribution are synthesized, and the expression of synthetic probability density function is obtained, and its image is drawn. The variance of synthetic distribution is calculated from the point of view of probability density function and the point of view of calculation of synthetic standard uncertainty respectively. The results obtained by the two methods are consistent, and the Monte Carlo method is used to simulate 60000 data which obey the uniform distribution and 60000 data which obey the triangle distribution. The curve obtained is completely consistent with the curve of the composite probability density function. The results are consistent and the correctness of the synthetic probability density function is verified.
关键词
计量学 /
均匀分布 /
三角分布 /
概率密度函数
Key words
metrology /
uniform distribution /
triangular distribution /
probability density function
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参考文献
1 DumebiO, RichardB. A generative model for motion synthesis and blending using probability density estimation［J］. Lecture Notes in Computer Science, 2008, 5098: 218-227.
2 AndrzejP, MarekL. Average prior distribution of all possible probability density distributions［J］. Advances in Intelligent and Soft Computing, 2010, 80: 181-190.
3 PhilippeC, José-VictorC G. Process capability indices dedicated to bivariate non normal distributions［J］. Journal of Quality in Maintenance Engineering, 2008, 14(1): 87-101.
4 林世曾. 均匀分布与反正弦分布的误差合成［J］. 计量技术, 1996, (5): 37-39+36. LinX Z. Error synthesis of uniform distribution and arcsine distribution［J］. Measurement Technique, 1996, (5): 37-39+36.
5 徐宝, 马艺光, 赵志文, 等. 简单均匀分布参数同等最短置信区间的求法［J］. 统计与决策, 2017, (19): 84-86. XuB, MaY G, ZhaoZ W, et al.Solution of Simple Uniform Distribution Parameters with the Same Shortest Confidence Interval ［J］. Statistics and Decision, 2017, (19): 84-86.
6 单长吉, 徐楠, 李林. 基于分布合成求展伸不确定度方法的研究［J］. 佳木斯大学学报(自然科学版), 2011, 29(1): 120-122. ShanC J, XuN, LiL. Study on the Method to Acquire the Expanded Uncertainty Based on Distribution Synthesis［J］. Journal of Jiamusi University (Natural Science Edition), 2011, 29(1): 120-122.
7 吴石林. 误差分析与数据处理［M］.北京: 清华大学出版社, 2010．
8 茆诗松. 数理统计学［M］. 北京: 中国人民大学出版社, 2016.
9 甘晓川, 周鑫, 赫明钊, 等. 一种不确定度的卷积评定方法［J］. 计量技术, 2012, (4):3-6.
10 刘智敏. 不确定度与分布合成［J］. 物理实验, 1999, (5): 17-19. LiuZ M. Composition of Uncertainty Distribution［J］. Physics Experimentation ,1999, (5): 17-19.
11 胜亚楠, 管志川, 罗鸣, 等. 基于不确定性分析的钻井工程风险定量评价方法［J］. 中国石油大学学报（自然科学版）, 2019, 43(2):91-96. ShengY N, GuanZ C, LuoM, et al.A quantitative evaluation method of drilling risks based on uncertainty analysis theory［J］. Journal of China University of Petroleum (Edition of Natural Science), 2019, 43(2): 91-96.
12 宁丽娟. 几种常见的连续型分布［J］. 价值工程, 2018, 37(25): 237-238. NingL J. Several Kinds of Conventional Continuous Distributions［J］. Value Engineering, 2018, 37(25): 237-238.
13 孟令川, 朱泽熙. 圆柱螺纹塞规中径不确定度评估的蒙特卡洛模拟［J］. 计量学报, 2017, 38(z1): 98-103. MengL C, ZhuY N. Uncertainty Estimate on Effective Diameter of Thread Plug Gauge by Monte Carlo Simulation［J］. Acta Metrologica Sinica, 2017, 38(z1): 98-103.
14 刘园园, 杨健, 赵希勇, 等. GUM法和MCM法评定测量不确定度对比分析［J］. 计量学报, 2018, 39(1): 135-139. LiuY Y, YangJ, ZhaoX Y, et al.Comparative Analysis of Uncertainty Measurement Evaluation with GUM and MCM［J］. Acta Metrologica Sinica, 2018, 39(1): 135-139.
基金
重庆市自然基金面上项目(cstc2019jcyj-msxmX0701,cstc2019jcyj-msxmX0383,cstc2019jcyj-msxmX0800,cstc2019jcyj-msxmX0783); 重庆市技术创新与应用发展专项面上项目(cstc2019jscx-msxmX0051); 重庆市市场监督管理局科技项目(CQZJKY2019004)
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