Estimating measurement uncertainty in high-performance liquid chromatography methods

In every measurement procedure, it is important to know the components of measurement uncertainty affecting the quality of measured result and reliability of quantified result. The procedure for recognizing measurement uncertainty is not universal but depends on the method and sample type. It has to be made according to good laboratory practice. This paper aims at showing the comparison of measurement uncertainty component estimations for three methods using the high-performance liquid chromatography techniques: determination of the type and content of aromatic hydrocarbons in diesel fuels and petroleum distillates by normal phase high-performance liquid chromatography, determination of nitrates in water samples by ion chromatography, and determination of molecular weights of polystyrene by size exclusion chromatography technique. Both similarity and differences were found during the measurement uncertainty component estimation, and conclusions about influences of certain components on the result uncertainty were made.     

Prediction of precision from signal and noise measurement in liquid chromatography: Limit of detection

Summary A method to determine the limit of detection (LOD) in high performance liquid chromatography (HPLC) is described. The power spectral density of instrumental baseline variation is fitted by the simplex least squares methods with a mixed random process of white noise and Markov process as a model. The white noise is characterized by standard deviation (SD),; the Markov process by the SD, , and auto-correlation degree, ρ. All required parameters for calculating the LOD signal are obtained by experiment without repeat measurements. No arbitrary constants are needed. The LOD signal is uniquely determined and is characterized by 33.3 % relative standard deviation (RSD) of analyte measurements and 0.13 % of the error of the first type. This signal also specifies that the signal-to-noise ratio =3, using the definition of noise originating from the white noise and Markov process. The theoretical conclusion is verified by the Monte Carlo simulation using real baseline and peaks. The LOD concentrations for naphthalene, acenaphthene, pyrene and perylene are given. First part of series cited as Ref. [1].     

Prediction of precision from signal and noise measurement in liquid chromatography: Limit of detection

Summary A method to determine the limit of detection (LOD) in high performance liquid chromatography (HPLC) is described. The power spectral density of instrumental baseline variation is fitted by the simplex least squares methods with a mixed random process of white noise and Markov process as a model. The white noise is characterized by standard deviation (SD), w; the Markov process by the SD, m, and auto-correlation degree, . All required parameters for calculating the LOD signal are obtained by experiment without repeat measurements. No arbitrary constants are needed. The LOD signal is uniquely determined and is characterized by 33.3% relative standard deviation (RSD) of analyte measurements and 0.13% of the error of the first type. This signal also specifies that the signal-to-noise ratio=3, using the definition of noise originating from the white noise and Markov process. The theoretical conclusion is verified by the Monte Carlo simulation using real baseline and peaks. The LOD concentrations for naphthalene, acenaphthene, pyrene and perylene are given.First part of series cited as Ref. [1].     

Determination of pesticides in apples by liquid chromatography with electrospray ionization tandem mass spectrometry and estimation of measurement uncertainty

A liquid chromatography/electrospray ionization-tandem mass spectrometry (LC/ESI-MS/MS) method was developed and validated to determine 90 pesticides in apple samples. MS/MS data acquisition was achieved by applying multiple-reaction monitoring of 2 fragment ion transitions to provide a high degree of sensitivity and selectivity for both quantitation and confirmation. Matrix-matched standard calibration curves with the use of isotopically labeled standards (or a chemical analog) as internal standards were used to achieve the best accuracy for the method. Both a conventional method validation procedure and a designed experiment were applied to study the accuracy and precision of the method. A compiled computer program that provided a semiautomated procedure for handling a large number of calculations was used to calculate the overall recovery, intermediate precision, and measurement uncertainty (MU). In general, the overall recoveries from samples spiked at levels of 10, 50, and 80 microg/kg, ranged from 60.8 to 121.1%, intermediate precision was <10%, and MUs were <30%. Poor accuracy and/or repeatability was observed for pyridate and etofenprox. The method limits of detection based on a signal-to-noise ratio of >3 were usually <1 microg/kg (ppb), except those for aldicarb sulfoxide and pyridaphenthion, which were about 5 microg/kg.     

Urinary testosterone measurement by gas chromatography after solid-phase extraction and high-performance liquid chromatography.

A method was developed for the rapid determination of testosterone in urine. The procedure consists of solid-phase extraction (SPE) followed by high-performance liquid chromatographic (HPLC) clean-up before gas chromatographic determination. Recovery was evaluated by adding [3H]testosterone (10(4) cpm) to urine samples; the mean recovery of radioactivity after SPE and HPLC was 82%. Precision was estimated by repeated measurement of testosterone in four different urine samples; the coefficient of variation was 7.9% (95% confidence limits 6.1-11.4%). Accuracy was evaluated by standard addition and dilution assays; a linear relationship was found between the expected and observed values (r2 = 0.982). The method is rapid, effective and suitable for routine analysis.     

Prediction of precision from signal and noise measurement in liquid chromatography: Mathematical relationship between integration domain and precision

Summary The precision of integration over noisy instrumental output for quantitative analysis is studied. A probability theory is developed to predict the relative standard deviation (RSD) of integration results over an integration domain from one-point integation (peak height measurement) to entire area integration in HPLC. Common integration modes of horizontal zero line and oblique zero line are taken into account, but no peak overlap is assumed. The question of the analytical superiority of peak height measurement or integration for quantitation is answered. In the HPLC apparatus used, the minimum RSD of measurements is found in the integration domain of ca. ±0.5 for analytes [peaks are approximated by the Gaussian signal of width, (standard deviation)]. The RSD of integration measurements is also shown to depend on the stochastic properties of back-ground noise (uncorrelated noise and correlated 1/f type noise). The theoretical conclusion is verified by Monte Carlo simulation and HPLC experiments for some aromatic compounds.Second Part of series cited as Ref. [1].     

Prediction of precision from signal and noise measurement in liquid chromatography: Mathematical relationship between integration domain and precision

Summary The precision of integration over noisy instrumental output for quantitative analysis is studied. A probability theory is developed to predict the relative standard deviation (RSD) of integration results over an integration domain from one-point integration (peak height measurement) to entire area integration in HPLC. Common integration modes of horizontal zero line and oblique zero line are taken into account, but no peak overlap is assumed. The question of the analytical superiority of peak height measurement or integration for quantitation is answered. In the HPLC apparatus used, the minimum RSD of measurements is found in the integration domain of ca. ±0.5 σ for analytes [peaks are approximated by the Gaussian signal of width, σ (standard deviation)]. The RSD of integration measurements is also shown to depend on the stochastic properties of background noise (uncorrelated noise and correlated 1/f type noise). The theoretical conclusion is verified by Monte Carlo simulation and HPLC experiments for some aromatic compounds. Second Part of series cited as Ref. [1].     

Prediction of measurement uncertainty in isotope dilution gas chromatography/mass spectrometry

An equation is theoretically derived which describes the relative standard deviation (RSD) of the amount ratios of analyte to its isotope-labeled variant in gas chromatography/mass spectrometry (GC/MS) using the stable isotope dilution method. The determination of methyltestosterone is taken as an example. The uncertainty equation proposed is justified by comparing the theoretical RSD values with the experimental RSD values obtained by replication over a wide range of analyte amount. The detection limit and quantitation limit are estimated from the continuous plot (precision profile) of the theoretical RSD against analyte amount.     

The measurement and meaning of void volumes in reversed-phase liquid chromatography

The seemingly simple process of measuring the mobile phase volume, V0, in reversed-phase liquid chromatography has eluded unambiguous agreement for over 25 years. Examples exist in the literature where the reported volume is physically impossible, either equal to or larger than the empty column volume, or being so small that it would represent a total porosity of half the theoretical limit for well-packed columns. Here we review the many proposals for methods of measurement, and compare and critique them. At this time, there is still no consensus for the best method of measurement, and workers are urged to critically examine values they measure, to insure they are at least physically possible.     

Amnesic shellfish poisoning toxins in shellfish: estimation of uncertainty of measurement for a liquid chromatography/tandem mass spectrometry method

A liquid chromatography/mass spectrometry (LC/MS) method for amnesic shellfish poisoning toxins in shellfish was developed and validated. Tissue homogenate (4 g) was extracted with 16 mL methanol-water (1 + 1, v/v). Dilution into acetonitrile-water (1 + 9, v/v) was followed by C18 solid-phase extraction cleanup. Domoic acid (DA) and epi-domoic acid were determined by LC/MS/MS with electrospray ionization and multiple reaction monitoring. External calibration was performed with dilutions of a certified reference standard. Advantages of this method include speed, lower detection limits, and a very high degree of specificity. The LC/MS response was highly linear, and there were no significant interferences to the determination of DA. Formal method validation was performed on 4 shellfish species. Fortification studies gave recoveries (mean +/- SD; n = 24) of 93 +/- 14% at 1 mg/kg, and 93.3 +/- 7.6% at 20 mg/kg over all the species. Analysis of a mussel certified reference material showed the bias as < 5%. The limits of detection and quantitation were 0.15 and 0.5 mg/kg, respectively. Routine application of the method over 4 months gave a recovery for the QC sample (1 mg/kg fortified blank mussel homogenate) run with each batch of 88.9 +/- 5.5% (mean +/- SD; n = 37). The total uncertainty of measurement results were estimated as 0.12 (12%) at 0.25-5 mg/kg and 0.079 (7.9%) at 5-50 mg/kg. The major contribution to the uncertainty was the repeatability of the LC/MS determination, probably arising from subtle matrix effects.     

Estimating measurement uncertainty in an afternoon. A case study in the practical application of measurement uncertainty

The ISO/IEC 17025:1999 standard requires chemical testing laboratories to have an estimate of the uncertainty of their measurements. This is a new requirement for many laboratories and there is confusion as to how to estimate uncertainty. Concerns have been raised about the time and effort required to obtain uncertainty estimates.Uncertainty budgets were prepared for the measurement of benzene, toluene, ethyl benzene and xylenes (BTEX) in water using purge and trap coupled with GC/MS. A time limit of one working afternoon (2 pm–5.30 pm) was imposed for preparing the uncertainty estimate. Details of the uncertainty estimate for toluene are described.The method in question had been in routine use for several years and the laboratory held third party (NATA) accreditation for the test. Consequently a considerable amount of performance data was readily available. Relevant information was extracted from the documented test method, validation data, instrument calibration and from routine quality control. This data was combined according to the principles of the ISO Guide to the Expression of Uncertainty, as promulgated in the Eurachem document "Quantifying Uncertainty in Analytical Measurement."The uncertainty estimates were compared to estimates obtained from generalised empirical models (the Horwitz and Lowthian equations), and from interlaboratory studies of this analysis.A traceability chain from routine measurements to the SI units of metre, kilogram and mole is described.Realistic and useful uncertainty estimates were obtained with a few hours work using data extant in the laboratory.     

Baseline compensation for gradient elution high-performance liquid chromatography with a dynamically referenced flow cell

Stable baselines were obtained with a gradient test system of acetone in methanol by using a secondary pump circuit at atmospheric pressure to simulate the gradient formed by the primary (high pressure) circuit. The secondary gradient system is used dynamically to reference the flow cell, thus eliminating baseline drift when detector-active mobile phases are used in gradient elution.     

Purity verification and measurement uncertainty

In chemical analysis, laboratories are required to verify the purity of reference material being used. Also, the contributions from the verification procedure, where significant, have to be included in the estimation of the total measurement uncertainties of the test results. One common verification procedure is to use another source of the same material if an appropriate certified reference material were not available. This involves a comparison test where the purity value of the reference standard is determined using a second source reference standard as the “calibrant”. In normal practice, the standard uncertainty of the purity value of a reference standard is estimated according to the probability distribution function (PDF) of the possible purity values of the reference standard concerned. With the use of Monte Carlo simulation technique, this paper attempted to study the effect of verification process on that PDF and thus the associated standard uncertainty as well. Also, the effects of parameters like the purity of the second source reference standard, the method precision and the acceptable range set for the comparison test on the verification outcome were discussed.     

Interlaboratory study of a liquid chromatography method for erythromycin: determination of uncertainty

Erythromycin is a mixture of macrolide antibiotics produced by Saccharopolyspora erythreas during fermentation. A new method for the analysis of erythromycin by liquid chromatography has previously been developed. It makes use of an Astec C18 polymeric column. After validation in one laboratory, the method was now validated in an interlaboratory study. Validation studies are commonly used to test the fitness of the analytical method prior to its use for routine quality testing. The data derived in the interlaboratory study can be used to make an uncertainty statement as well. The relationship between validation and uncertainty statement is not clear for many analysts and there is a need to show how the existing data, derived during validation, can be used in practice. Eight laboratories participated in this interlaboratory study. The set-up allowed the determination of the repeatability variance, s(2)r and the between-laboratory variance, s(2)L. Combination of s(2)r and s(2)L results in the reproducibility variance s(2)R. It has been shown how these data can be used in future by a single laboratory that wants to make an uncertainty statement concerning the same analysis.     

The measurement of nucleoside deaminases by high performance liquid chromatography and their use in clinical chemistry.

The measurement of the nucleoside deaminases--cytidine deaminase, guanosine deaminase and adenosine deaminase--by reversed phase high performance liquid chromatography is reviewed. The clinical value of assaying the enzyme activity is discussed for each of these enzymes. Both cytidine deaminase and adenosine deaminase measurements have proven clinical value, although the use of the assay of cytidine deaminase in the diagnosis of pre-eclampsia is probably not helpful.     

Method validation and measurement uncertainty evaluation for measurement of mass concentration of organic acids in fermentation broths by using ion chromatography

In the present paper, a methodology for method validation and measurement uncertainty evaluation for the measurement of mass concentration of organic acids in fermentation broths was developed. Acetic acid was selected as a representative of organic acids. A detailed procedure for in-house method validation based on simple experimental design and consistent statistics is presented. In addition, a step-by-step illustration of ??Bottom-Up?? approach for measurement uncertainty evaluation of acetic acid in fermentation broths is also provided. The major sources of uncertainty of the result of measurement were identified and the combined uncertainty was calculated. Our analytical protocol allowed us to quantify acetic acid in fermentation broths in mass concentrations up to 75?g?L^?1 with satisfactory recovery (102.3%) and repeatability lower than 2%. We also estimated within-laboratory reproducibility over 3-month period, which was 2.3%. We proved that the method was selective for the measurement of mass concentration of acetic acid in fermentation broths. Measurement uncertainty of results was evaluated to be 6.2% with 95% confidence level. After validation and measurement uncertainty evaluation steps, results obtained showed that the method can be applied to efficiently monitor fermentation processes.     

Application of gas liquid chromatography to the measurement of industrial liquid effluent flow rates

Summary The measurement of liquid effluent flow rates by injection of a tracer into the effluent stream and measurement of the resulting tracer concentration by gas chromatography is described. The technique is capable of good precision and has been applied to flowrate measurements in the range 0.6–1.7 m lb/hr.