Enhanced calibration precision: Leveraging RSE and WLS for optimal function optimization

Importance of the Topic

Accurate chromatographic calibration is critical to reliable quantitative analysis in environmental, pharmaceutical and industrial laboratories. Traditional metrics such as r² and RSD can misrepresent calibration quality, especially at low analyte levels. Relative Standard Error (RSE) and Weighted Least Squares (WLS) offer a more robust framework by focusing on standard error relative to mean response and accounting for variance patterns across concentration ranges.

Study Objectives and Overview

This technical note by Thermo Fisher Scientific evaluates the application of RSE, WLS and inverse calibration approaches to enhance the accuracy and precision of calibration in ion chromatography (IC), high-performance liquid chromatography (HPLC) and gas chromatography (GC). The goal is to compare conventional unweighted regression against weighted and non-linear fits, demonstrate their impact on calibration performance, and recommend best practices.

Methodology and Instrumentation

• Data processing was conducted using Thermo Scientific Chromeleon CDS version 7.3.2.
• IC analysis employed a Dionex IonPac AS23 column (4.5 mM Na₂CO₃/0.8 mM NaHCO₃ eluent) with a Dionex ADRS 600 suppressor and suppressed conductivity detection at 5 Hz acquisition.
• HPLC calibration used a Thermo Scientific Acclaim 120 C8 column (3 μm, 2.1 × 150 mm) at 100 °C, UV detection at 245 nm, and a rapid ACN/H₂O gradient at 100 Hz data rate.
• GC experiments utilized a Thermo Scientific TraceGOLD TG ALC1 column with headspace injection, N₂ carrier, FID detection (300 °C), and 25 Hz data rate.
• Cation exchange IC for ammonium used a Dionex IonPac CS12A column with methanesulfonic acid eluent and suppressed conductivity detection.

Key Results and Discussion

• Unweighted linear calibration often met regulatory RSE limits (≤15-20%) but exhibited large relative deviations at low concentrations.
• Quadratic fits with intercepts reduced systematic bias and improved RSE values (down to ~1.6-1.9%) across wide concentration spans.
• Applying 1/Amount² weighting in WLS further homogenized error distribution, lowering RSE to below 1% for GC ethanol and HPLC butyrophenone analyses.
• Inverted calibration in Chromeleon CDS enhanced curve fitting for challenging analytes like ammonium, reducing systematic errors when standard fits failed.
• Comparisons of RSE against RSD and r² revealed that sole reliance on traditional metrics can mislead model selection, favoring unweighted models that underperform at trace levels.

Benefits and Practical Applications

• RSE provides a single criterion for calibration quality that is comparable across models and regulatory frameworks (e.g., US EPA 40 CFR Part 136, IUPAC guidelines).
• WLS with appropriate weighting factors secures consistent precision across broad concentration ranges, critical for trace and environmental analyses.
• Adoption of inverted calibrations offers an alternative when classical and weighted fits cannot capture non-linear detector responses.
• Implementation in Chromeleon CDS streamlines these advanced calibration strategies within routine workflows.

Future Trends and Potential Applications

• Integration of automated RSE calculators and guidance within chromatography software to support method development and validation.
• Expansion of weighting schemes and non-linear models for emerging detector technologies and complex matrices.
• Implementation of machine learning algorithms to select optimal calibration models based on RSE and sample characteristics.
• Broader regulatory acceptance of RSE-driven calibration standards for trace analysis and QA/QC protocols.

Conclusion

Incorporating RSE, WLS and inverted calibration techniques significantly enhances calibration accuracy and precision in LC, GC and IC workflows. By prioritizing relative standard error over traditional metrics, analysts can achieve more reliable quantification across diverse concentration ranges and challenging analytes. These practices, fully supported in Chromeleon CDS, pave the way for robust calibration protocols aligned with regulatory and scientific best practices.

References

1. Sanchez JM. J Sep Sci. 2020;43(16):2708–2717. DOI:10.1002/jssc.202000094
2. Sanchez JM. J Sep Sci. 2021;44(24):4431–4441. DOI:10.1002/jssc.202100555
3. Parr J, Friedman D. EMC Letter to EPA. 2021.
4. Edgerley DA. WTQA ’98. EPA. 1998.
5. EPA. 40 CFR 136.6. 2023.
6. Thermo Fisher Scientific. Chromeleon 7 Help. 2023.
7. IUPAC. Pure Appl Chem. 1998;70(4):993–1014.
8. IUPAC. Pure Appl Chem. 1995;67(10):1699–1723.
9. Wright S. J Agric Res. 1921;20:557–585.
10. Hoisington J. LC·GC Eur. 2004;17:138–143.
11. Tellinghuisen J. Analyst. 2007;132(4):536–543.
12. Burrows R, Parr J. LCGC Supplements. 2020;11:38–38.
13. Thompson M. Why weight? RSC Tech Brief. 2007.
14. Centner V, Massart DL, de Jong S. Fresenius J Anal Chem. 1998;361:2–9.
15. Besalú E. Talanta. 2013;116:45–49.