4 replies to this topic

[Tolinorton]

Dear,

 

What does "Expanded uncertainty for the confidence level of 95 %, factor k=2" mean?

 

Is this test result in conformity to EN 590 (see attachment). For this period of time the CFPP in my country should be max - 20 Celsius degree.

 

Or can we accept this result as in conformity to EN 590 standard considering the value of Uncertainty of measurement.

 

 

Attached Files

•  Analysis Report for CFPP.pdf   331.68KB   12 downloads

[P.K.Rao]

Expanded Uncertainty: After getting the combined standard uncertainty, it would be necessary to multiply it by a coverage factor k, to make the uncertainty applicable to a large number values falling within the distribution curve. The value so obtained is “Expanded uncertainty”. A coverage factor of 2 generally gives a value of expanded uncertainty that

 

• it gives the required level of confidence
• it includes underlying distributions
• it encompasses the number of values used to estimate random effects

 

However, this coverage factor 2 will apply when the number of degrees of freedom for calculating the uncertainty are more than 6. If the degrees of freedom are less than or equal to 6, values of k given in the following table should be used.

 

Degrees of

Freedom     Value of  k

1                           12.7

2                             4.3

3                             3.2

4                             2.8

5                             2.6

6                             2.5

More than 6            2.0

 

Example:

 

Let us take the earlier example of flash point of kerosene.

 

Standard uncertainty due to calibration = 0.061

Standard uncertainty due to reading thermometer scale = 0.2256

 

Combined standard uncertainty = Positive Square Root of [(0.061^2) + (0.2256^2) = 0.2337

 

There are 10 observations of flash point viz: 38.0, 38.2. 38.5, 38.1, 37.9, 37.8, 38.0, 38.4, 38.2, 37.8  degrees C

 

Degrees of Freedom are   10 – 1 = 9

 

From the table above, value of coverage factor for 9 degrees of freedom is 2.0

 

So the Expanded Uncertainty for 95 % confidence level = 0.2337 * 2 = 0.4674 or 0.47 deg C in the range of 35 to 40 deg C.

[Tolinorton]

Dear P.K. Rao,

 

Thank you so much for this example, as always you are brilliant in explanation. 

 

Anyway once again I need your personal and professional opinion for CFPP example. Can we accept the result as conformity to EN 590 standard?

 

Best regards

[P.K.Rao]

Dear Tolinorton,

Thanks for your compliments.

 

ASTM D 6371 has given reproducibility (applicable to two different laboratories) as 0.102 x (25 - x) where x is the average of two results under comparison.

The result of CFPP shown in the analysis report is minus 17 deg C

So at this value, the reproducibility would be 0.102 x ( 25 – (-17)) = 0.102 x (25+17) = 4.3 deg C

The uncertainty given in the report at 95 % confidence level = ± 3.5

This appears to be OK compared to ASTM reproducibility

[Tolinorton]

Thank you very much