等精度测量中粗大误差的评估及其在Mathematica上的实现

The Assessment of Gross Error in Equal Precision Measurement and the Fulfillment on Mathematica

摘要: 由于偶然因素带来的误差称之为粗大误差，在等精度测量中，判定和剔除数据系列中的粗大误差，对测量结果的最佳值、不确定度、置信概率都十分重要，将直接影响到测量结果的最佳表达式和相对误差的可信程度。本文从置信概率的角度，探讨粗大误差的判别和处理过程，以及如何在数学工具Mathematica上实现的。这种结论同样可以应用到工程实践中。

Abstract: Since the errors caused by accidental factors are called gross errors, it is very important to determine and eliminate gross errors in data series in equal precision measurement for the best value, uncertainty and confidence probability of measurement results, which will directly affect the best expression of measurement results and the reliability of relative errors. This paper discussed the determination and treatment process of gross error from the probability point of view, and explained how to implement the process on the tools of Mathematica. The conclusion can also be applied to the engineering practice.