Description
In a steelworks chemical laboratory the nickel content of steel is determined using flame atomic absorption spectrometry (FAAS). For the estimation of the within lab reproducibility they use a steel control sample with nickel content of around 8%. An X control chart is maintained with control sample (data are below). The laboratory has participated in 5 interlaboratory comparisons (data are below).
Data
X control chart:
| Date |
Ni content (%) |
| 01.08.2015 |
7.96 |
| 02.08.2015 |
7.77 |
| 05.08.2015 |
8.03 |
| 06.08.2015 |
7.92 |
| 07.08.2015 |
8.21 |
| 08.08.2015 |
8.27 |
| 09.08.2015 |
8.17 |
| 12.08.2015 |
8.10 |
| 11.08.2015 |
8.27 |
| 13.08.2015 |
8.16 |
| 14.08.2015 |
8.00 |
| 15.08.2015 |
8.04 |
| 16.08.2015 |
7.79 |
| 19.08.2015 |
8.08 |
| 20.08.2015 |
7.76 |
| 21.08.2015 |
8.20 |
| 22.08.2015 |
7.72 |
| 23.08.2015 |
7.82 |
| 26.08.2015 |
7.68 |
| 27.08.2015 |
7.96 |
Proficiency tests data:
| No |
Consensus value (%) |
Standard deviation
of participants (%) |
Result of the
laboratory (%) |
No of participants |
| 1 |
7.72 |
0.19 |
8.06 |
30 |
| 2 |
8.49 |
0.20 |
8.67 |
29 |
| 3 |
9.23 |
0.30 |
9.66 |
35 |
| 4 |
7.89 |
0.21 |
8.11 |
30 |
| 5 |
10.25 |
0.16 |
10.01 |
32 |
From the control chart the random component u(Rw) can be calculated. That is actually the standard deviation.
Using the proficiency tests data, calculate the biasi, u(Crefi), RMSbias and u(Cref). Combine RMSbias and the u(Cref). Consensus values can be considered as the Cref values in the Nordtest approach.
Combine the u(Rw) and the u(bias). Calculate the expanded uncertainty from the standard uncertainty (via multiplying with coverage factor).
Task 1
Please calculate the expanded uncertainty of this analysis (at k = 2 level) for a sample with nickel content 10.2% using absolute uncertainties.
Task 2
Please calculate the expanded uncertainty of this analysis (at k = 2 level) for a sample with nickel content 10.2% using relative uncertainties.
