Measurement uncertainty isn't a static value—it's a living reflection of your process stability. By leveraging Statistical Process Control (SPC), we transform routine QC data into a defensible uncertainty budget.
Section 1: Control Charts
A Control Chart is a graphical tool used to monitor the stability of a measurement process. In the laboratory, it provides "real-time" evidence that an instrument (like an ICP-MS) is operating within its expected statistical limits before sample results are accepted.
Try the SPC CalculatorTable 1.1: Iron (Fe) Trace Data [ppb]
| Run | Value | Run | Value |
|---|---|---|---|
| 01 | 101.2 | 09 | 103.2 |
| 02 | 103.4 | 10 | 101.7 |
| 03 | 99.8 | 11 | 104.1 |
| 04 | 102.1 | 12 | 102.3 |
| 05 | 104.5 | 13 | 100.9 |
| 06 | 101.8 | 14 | 103.8 |
| 07 | 102.9 | 15 | 102.5 |
| 08 | 100.5 | N=15 | S=1.5 | |
Section 2: Combined Uncertainty
The Relative Combined Standard Uncertainty (uc/x) is the "root" of your uncertainty budget. It mathematically merges independent sources of error—random, systematic, and statistical—into a single, standardized metric that represents the total error of your method.
RSD
Random Error: Measures the repeatability of the measurement system. It captures how much individual measurements "drift" from each other.
RBE
Standard Error: Represents the uncertainty of the estimated mean, accounting for sample size (n). It answers: "How much do I trust this average?"
RB
Relative Bias: Measures systematic error. The distance between your experimental average and the certified target value.
u(ref)
Uncertainty of CRM: The inherent uncertainty of the certified standard itself, found on the CoA.
Section 3: RSD — Relative Standard Deviation
The RSD quantifies the random error (or "precision") of your measurement process. It measures how much individual data points deviate from their own average, expressed as a percentage. A lower RSD indicates a more consistent, repeatable method.
Formula
Calculation: Iron (Fe) Dataset
Using the 15 data points from Table 1.1:
Step-by-step:
This means that the ICP-MS measurement of Iron shows a 1.46% shot-to-shot variability during the analyzed runs — a typical precision for trace-level analysis.
Section 4: RBE — Relative Standard Error
The RBE (also known as Standard Error of the Mean) represents the uncertainty in the estimate of the mean. While RSD tells you how much your data scatters, RBE tells you how much you can trust the average you calculated. More data points = smaller RBE = more confidence in your mean.
Formula
Calculation: Iron (Fe) Dataset
Using the RSD from Section 3 and our sample size:
Step-by-step:
With 15 data points, we can be confident that our mean of 102.5 ppb has a statistical uncertainty of only 0.38%. Collecting more samples would reduce this further.
Section 5: RB — Relative Bias
The RB quantifies systematic error (or "trueness"). While RSD measures random scatter, RB measures how far your average result is from the actual target value. This component captures calibration drift, matrix effects, or any persistent offset in your method.
Formula
Calculation: Iron (Fe) Dataset
Comparing our measured mean to the certified target:
Step-by-step:
Our ICP-MS measurements are running 2.5% high compared to the certified reference. This systematic bias will be included in the total uncertainty budget.
Section 6: u(ref) — Reference Uncertainty
The u(ref) represents the uncertainty of your reference standard itself. No standard is perfect — even certified reference materials (CRMs) have an associated uncertainty stated on their Certificate of Analysis (CoA). This component ensures you account for the "truth" not being perfectly known.
Formula
Calculation: Iron (Fe) CRM Certificate
From the Certificate of Analysis for the Iron standard:
Step-by-step:
Even our certified standard has 0.25% inherent uncertainty. This is the baseline "floor" — no measurement can be more accurate than the reference used to calibrate it.
Section 7: Combining All Components
Now we bring together all four uncertainty components using the Root Sum of Squares (RSS) method. This produces the Combined Standard Uncertainty which, when multiplied by a coverage factor (k=2), gives us the Expanded Uncertainty at 95% confidence.
All four components are independent. RSD is divided by √n (sample replicates).
Scenario A: Single Measurement
Sample measured once (n = 1)
Scenario B: Triple Measurement
Sample measured three times (n = 3)