Estimation of measurement uncertainty in chemical analysis

Self-test 10.5 A

Task 4

Laboratory has participated in two consecutive years in interlaboratory comparisons (ILCs)of waste water and has obtained the following results for fluoride ion content: 0.99 mg/l and 3.92 mg/l. The reference values of the ILCs for fluoride (obtained by independent expert labs) were 1.14 mg/l and 3.77 mg/l, respectively. The laboratory routinely analyses only drinking water, not waste water (drinking water is a matrix of much simpler composition than waste water). Within-lab long-term reproducibility s_RW of the laboratory’s procedure for fluoride determination at roughly 2 mg/l level as found from the X control chart is 0.04 mg/l. The procedure used at laboratory does not have detectable bias. Which of the following statements are necessarily true?

These data indicate that in one case the laboratory’s result is by 0.15 mg/l below the reference value and in the other case by 0.15 mg/l above the reference value. This proves that the laboratory bias is zero.

The lab has estimated s_RW incorrectly and it should be significantly higher.

It is possible, that the mismatch between the laboratory values and the reference values is caused by the sample matrix, which is different from the one used routinely at the laboratory.

If the laboratory wants to use its procedure for the analysis of waste water then the s_RW and bias should be determined in the waste water matrix.

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:

No	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

Clues

[accordion][acctitle]Clue 1[/acctitle]From the control chart the random component u(R_w) can be calculated. That is actually the standard deviation.[/accordion]

[accordion][acctitle]Clue 2[/acctitle]Using the proficiency tests data, calculate the bias_i, u(Cref_i), RMS_bias and u(Cref). Combine RMSbias and the u(Cref). Consensus values can be considered as the Cref values in the Nordtest approach.[/accordion]

[accordion][acctitle]Clue 3[/acctitle]Combine the u(R_w) and the u(bias). Calculate the expanded uncertainty from the standard uncertainty (via multiplying with coverage factor).[/accordion]

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.

Task 3

Which uncertainty estimation would you rather use?

Calculated by absolute uncertainties

Calculated by relative uncertainties