Len 發問時間： 科學工程學 · 7 年前

# [量測不確定度/統計方法]擴張不確定度及EN值如何計算

7.5 En numbers [See ISO/IEC Guide 43-1:1997, A.2.1.4 item e)]

This performance statistic is calculated as:

En = x - X / √ (Ulab)平方+(Uref)平方

X is the assigned value determined in a reference laboratory;

Uref is the expanded uncertainty of X;

Ulab is the expanded uncertainty of a participant’s result x.

In contrast to the critical values of 2,0 and 3,0 used with z-scores, it is common to use a critical value of 1,0

with En numbers. This is because En numbers are calculated using expanded uncertainties in the denominator

NOTE 1 En numbers should be used with caution when participants may have a poor understanding of their uncertainty

and may not be reporting it in a uniform way. However, incorporating information on uncertainty into the interpretation of

results of proficiency tests can play a major role in improving their understanding of this difficult subject.

When the expanded uncertainties are calculated using a coverage factor of 2,0, a critical value of 1,0 for an En

number is equivalent to the critical value of 2,0 used with z-scores.

NOTE 2 When uncertainties are estimated in a way consistent with the Guide to the expression of uncertainty in

measurement (GUM), En numbers express the validity of the expanded uncertainty estimate associated with each result. A

value of |En| < 1 provides objective evidence that the estimate of uncertainty is consistent with the definition of expanded uncertainty given in the GUM.

2 個已更新項目:

http://tw.knowledge.yahoo.com/question/question?qi...

### 2 個解答

• 7 年前
最佳解答

En numberf 的定義式:

En = (x-X)/√[(Ulab)^2+(Uref)^2]

X 是參照實驗室決定的值,

Uref 是 X 的不確定性, 即相當於 X 可能的誤差.

x 是參與者的結果,

Ulab 是其不確定性指標.

我不大瞭解實際情況. 我猜: "參照實驗室" 結果是一個被認可的結果,

但它仍是有誤差的. 而 "參與者" 的結果大概是需要檢驗其結果 x 是

否與參照值 X 相差超過允許標準. En 就是一個評估指標. 至於 Uref

與 Ulab 是怎樣的一個量數, 可能真正了解工業或工程實務的人了解.

例如 "因為實驗室做比對.共有2家實驗室.故測試電壓數據只有2個."

這是否表示一個是 x 一個是 X, 而無法由這兩個數據去估計誤差, 因

此, 誤差指標 Ulab 與 Uref 要另外由兩實驗室過去的數據去評估.

expanded uncertainty 正式翻譯應是 "擴展的不確定度", 表現測量值

可能範圍. 也就是說測量結果大概會在 目前測量值±擴展的不確定度

範圍內.

In contrast to the critical values of 2,0 and 3,0 used with z-scores, it is common to use a critical value of 1,0

with En numbers. This is because En numbers are calculated using expanded uncertainties in the denominator

上列敘述中 "2,0", "3,0" 及 "1,0" 依次應是 "2.0", "3.0" 及 "1.0".

好像有的國定是用 "," 當小數點的.

這一段敘述是說: 一般統計上用 z 統計量做評估, 可能取 z=2.0 或

z=3.0 做為差異是否顯著的標準 (按: 事實上是 1.96 與 2.58); 而

En 則常用 1.0 做標準. 其理由是 En 分母用的是 "uncertainty" 指

標 (Ulab, Uref) 而不是標準差.

NOTE 1 En numbers should be used with caution when participants may have a poor understanding of their uncertainty

and may not be reporting it in a uniform way.…

這是說: 參與者可能對他們的 uncertainty 不了解而無法提供適當的 Ulab.

(內中隱喻參照實驗室應是精練於此, 不會有問題.) 不過, 這文的作者說,

把 uncertainty 的訊息加入水準檢驗結果的呈現, 對於了解這一概念是重

要的. 若不確定性指標如 Ulab 是採 2.0 為覆蓋因子, 這時 En = 1.0 就相

當於 z-score 用臨界值 2.0. 我不清楚工業或工程實務上怎麼定義與運用

"覆蓋因子" 這東西, 不過既然這樣的 En = 1.0 相當於 z = 2.0, 那也就是

說依 覆蓋因子 = 2.0 為準定出來的 Ulab 相當於 2 倍標準差.

NOTE 2 When uncertainties are estimated in a way consistent with the Guide to the expression of uncertainty in

measurement (GUM), ….

這一個 note 說: 如果 uncertainties 是依據 the Guide to the expression

of Uncertainty in Measurement (GUM, 測量之不確定性表示指導) 的方式

估計的, En 值等於各測量結果之 expanded uncertainty 的有效性. |En| 小

於 1 提供了 uncertainty 的估計與 GUM 定義的 expanded uncertainty 一

致的客觀證據.

2013-07-10 13:52:33 補充：

可參考下列網頁:

physics.nist.gov/cuu/Uncertainty/coverage.html

關於 expanded uncertainty 與 coverage factor.

簡單地說, expanded uncertainty 是 standard uncertainty 的某個倍數,

該倍數就是 coverage factor. 給予一個測量值 y 及其對應的 expanded

uncertainty, 表示真值大概在 y±U 的範圍. U 就是 expanded uncertainty.

2013-07-10 13:58:56 補充：

coverage factor k 的選擇是使 y-U ～y+U 具有適當的信賴度 (讓我們有

足夠的信心真值會落在那個區間中.

standard unceratinty 有點像標準差, coverage factor 就是信賴區間用的

某一標準分布(如 z、t) 臨界值, expanded uncertainty 就是 error margin.

所以, k 常取 2 或 3, 在常態分布下分別對應信賴水準 95% 與 99.7%.

2013-07-10 13:59:51 補充：

原文:

Expanded uncertainty

Although the combined standard uncertainty uc is used to express the uncertainty of many measurement results, for some commercial, industrial, and regulatory applications (e.g., when health and safety are concerned),

2013-07-10 14:00:53 補充：

… what is often required is a measure of uncertainty that defines an interval about the measurement result y within which the value of the measurand Y can be confidently asserted to lie. The measure of uncertainty intended to meet this requirement is termed expanded uncertainty,

2013-07-10 14:01:26 補充：

… suggested symbol U, and is obtained by multiplying uc(y) by a coverage factor, suggested symbol k. Thus U = kuc(y) and it is confidently believed that Y is greater than or equal to y - U, and is less than or equal to y + U, which is commonly written as Y = y ± U.

2013-07-10 14:01:50 補充：

Coverage factor

In general, the value of the coverage factor k is chosen on the basis of the desired level of confidence to be associated with the interval defined by U = kuc. Typically, k is in the range 2 to 3.

2013-07-10 14:02:24 補充：

… When the normal distribution applies and uc is a reliable estimate of the standard deviation of y, U = 2 uc (i.e., k = 2) defines an interval having a level of confidence of approximately 95 %, and U = 3 uc (i.e., k = 3) defines an interval having a level of confidence greater than 99 %.

2013-07-10 21:49:10 補充：

擴充不確定度要如何計算?

不是已在 "意見" 說了嗎?

這裡差不多到上限了.

2013-07-10 21:55:14 補充：

擴充不確定度 = 標準不確定度 × 覆蓋因子

至於 "標準不確定度" 如何得到, 請恕我外行無法解說.

你提到 "要考慮電力分析儀量測解析度產生的不確定度及

儀器校驗報告不確定度." 我想這都應併到 "標準不確定度"

之中, 因為兩者想來都會對結果數字有影響.

• 匿名使用者
6 年前