被測物理量的測量不確定度

Abstract

被測量物的不確定分析在量測科學上是一個重要的課題。然而，被測量物的意義常被誤解，導致所求得的不確定性區間的意義造成混淆。被測量物的真值應屬於參數，而測量結果應屬於隨機變數。通常，在測量科學上估計參數會比預測變數的未來值有意義的多。古典不確定性分析的理論都是將被測量物定義為隨機變數而發展的，但這會喪失不確定性區間對於真值的準確性。我們在這篇文章中會討論被測量物的統計分析。

Uncertainty analysis of measurement of measurand is an important topic in metrology. However, vague statistical concept of measurand results in inefficient inference uncertainty for the true measurand. Measurand and the variable representing its measurement are completely different in probability concept; one is an unknown distributional parameter and the other is a random variable. Generally, a parameter may be estimated more efficiently than the prediction of the future observation of a random variable. The classical uncertainty analysis in literature is developed based on the structure that a measurand is a random variable. This misspecification of statistical model costs serious price of sacrificing efficiency in constructing uncertainty interval for gaining the knowledge of the true measurand. We formally formulate a statistical analysis for measurement of measurand.