JEOL Resources

Quantitative NMR Analysis Using JASON SMILEQ: Novel Methods for Improving Accuracy, Part 3. Elucidating Factors through Simulation Analysis

Thu, 02 Oct 2025 12:46:52 GMT

How Does the Uncertainty of Standard Samples Impact Quantitative Analysis Results?

Uncertainty Report and ANOVA Report Results

From the previous analysis, it has been confirmed that repeated errors across the entire measurement system are very small, demonstrating the stability of the measurement process. On the other hand, it is suggested that the uncertainty associated with standard samples may propagate throughout the measurement results.

Analyzing the Impact of Standard Sample Uncertainty

Standard samples are often difficult to substitute, and there are challenges in directly testing their uncertainty impact on measurement results through experimentation. To address these challenges, detailed analyses using simulations prove effective. In this study, computational methods were employed to clarify the tendencies of uncertainty caused by standard samples affecting measurement results.

Analysis Method

The influence of standard sample uncertainty on the integral values obtained through experiments and the resulting quantitative values was investigated. This analysis employed the following methods to examine the impact in detail. Calculations were performed using Python^Ⓡ3 and the report data.

Analysis of Coefficients of Variation: The standard deviation (SD) and coefficient of variation (CV) of integral and quantitative values in experimental data were compared to assess the impact of standard sample uncertainty on the data.
Analysis Using Sensitivity Coefficients: Simulations based on sensitivity coefficients were conducted to analyze the effects of standard sample uncertainty.
Analysis Using Monte Carlo Method: The Monte Carlo method was employed to simulate the influence of uncertainty on the entire measurement and to analyze the detailed characteristics of data distribution.

1. Analysis of Coefficients of Variation

Coefficient of Variation (CV)

The coefficient of variation is a metric that expresses the variability of data relative to the mean. It is calculated by dividing the standard deviation by the mean and is typically displayed as a percentage. This metric is effective in assessing the variability of measurements and serves as an important tool for determining the stability of measurement systems.

Coefficient of Variation After Quantitative Calculations

Figure 1 compares the standard deviation and coefficient of variation for integral values (Non-Normalized) and quantitative values (Normalized) before quantitative calculations. Both sets of values were normalized using their average values to analyze variations more effectively. This approach focused on examining the amplitude of fluctuations and ensured a consistent basis for comparison. After the calculations, the coefficient of variation was found to be as small as 0.21%, confirming that these corrections successfully reduced data variability. Additionally, it was suggested that the final quantitative values might be highly dependent on the characteristics of the standard samples.

Figure 1. Comparison of Standard Deviation and Coefficient of Variation

2. Analysis Using Sensitivity Coefficients

Sensitivity Coefficient

The sensitivity coefficient is a quantitative metric that indicates the extent to which each factor impacts measurement or calculation results. Specifically, it is used to assess how small variations in individual factors contribute to the outcomes. By utilizing this metric, critical factors within a system or analytical model can be identified. Below, the significance and details of simulations based on sensitivity coefficients are explained.

Significance of Simulations Utilizing Sensitivity Coefficients

By applying sensitivity coefficients in simulations, it becomes possible to effectively quantify how specific factors influence the results. In this study, the contribution of standard sample characteristics to overall measurement results was assessed, and their tendencies were clarified.

Simulation Results Using Sensitivity Coefficients

Simulation Range

Simulations were conducted to evaluate the impact on quantitative values when the uncertainty of standard samples (0.25%) fluctuated within its surrounding range.

Simulation Results

From the simulations, the average values and standard deviations of the quantitative values were calculated (Figure 2 (a)). Figure 2 (b) presents a plot comparing the standard deviations of the quantitative calculation results and simulation results against the integral values of the standard samples in the experimental data. The trends in standard deviation were consistent with the experimental results, confirming the accuracy of the simulation's approach.

Characteristics of Experimental Results

The experimental results showed slightly higher values compared to the computational model results, suggesting the possible influence of other factors. Below is an explanation of the impacts of the uncertainties under consideration on the simulation:

Characteristics of Small Uncertainty Ranges
A narrow uncertainty range implies that the variability captured by the model is minimal, making the contribution of specific factors more prominent. In scenarios dominated by the uncertainty of standard samples, external factors are more likely to have a significant impact within this limited range of variability.
Impact on Model Responsiveness
In modeling with small uncertainty ranges, the sensitivity coefficient may not fully reflect the variability. Specifically, the extent to which the model can account for external factors becomes a critical point. Simulations capable of appropriately reproducing the cumulative effects of small fluctuations are more likely to exhibit realistic behavior, even within a narrow range of uncertainty.

Conclusion and Model Applicability

In cases where the uncertainty range is small, the sensitivity and corrections of the model play a crucial role. However, when accounting for complex external factors and interactions, comprehensive methods like the Monte Carlo approach may prove more effective. Especially when experimental data exhibits higher variability or deviation than the model, using such comprehensive methods enables modeling that aligns more closely with the experimental environment.

3. Analysis Using Monte Carlo Method

Overview of the Monte Carlo Method

The Monte Carlo method is a technique that combines random sampling with statistical methods to analyze complex problems. By repeatedly performing numerous simulations based on the distribution of input variables, it identifies the distribution and tendencies of the output results. This method is particularly useful in the following ways:

Reproducing the Behavior of Complex Systems: Capable of analyzing overall behavior even in scenarios involving numerous factors.
Evaluating Uncertainty: Examines in detail how uncertainty impacts results.
Analyzing Entire Distributions: Allows for a visual understanding of not only mean values but also variability and ranges of output results.

Below, we explain the significance and details of simulations utilizing the Monte Carlo method.

Significance of Simulations Using the Monte Carlo Method

The Monte Carlo method was employed to analyze the impact of standard sample uncertainty on the variability and distribution of measurement results. This approach clarified not only the mean values and standard deviations but also the range and shape of variability in measurement results, enabling a comprehensive understanding of the overall data distribution. Additionally, the contributions of standard samples to the stability of the measurement system were quantitatively evaluated, providing direction for improving reliability.

Simulation Results Using the Monte Carlo Method

Simulation Range

Simulations were conducted to evaluate the impact on quantitative values when the uncertainty of standard samples (0.25%) fluctuated around the baseline. The ranges of variation included ±0.05% (i.e., 0.20%-0.30%) and ±0.10% (i.e., 0.15%-0.35%).

Modeling and Statistical Evaluation of Uncertainty

Uncertainty was analyzed using probabilistic models to assess the trends in data distribution. The variations of standard samples were statistically reproduced using uniform distributions and Gaussian distributions (normal distributions), and these results were compared with experimental data. Figure 3 shows a plot comparing the calculated results with experimental results: (a) Distribution of quantitative values. (b) Comparison of normalized mean values, standard deviations, and coefficients of variation.

Evaluation Methods for Simulation Results

To evaluate the simulation results, the most realistic model was considered by calculating the following score. This score was computed as a metric to quantify the variability of measurement results and is based on the formula:
(Score) = (Mean Difference (%) + SD Difference (%) + CV Difference (%)) /3

Mean Difference (%) Evaluates the difference between the average values of experimental results and simulation results, indicating the overall alignment.
SD Difference (%) Assesses the difference in standard deviations between experimental data and simulation data, measuring the degree of alignment in variability.
CV Difference (%) Evaluates the difference in coefficients of variation, focusing on relative variability in the data.

By integrating these three differences and calculating the average, the score was determined. This score is effective for comprehensively evaluating data alignment and the impact of uncertainty.

Figure 3. Simulations Using the Monte Carlo Method: (a) Simulation results (b) Comparison of mean values, standard deviations, and coefficients of variation

Most Consistent Model

A uniform distribution within the uncertainty range of 0.35% (0.9965 to 1.0035) achieved a score of 2.05%, confirming it as the best fit to the experimental data. Figure 4 shows a plot comparing the simulation results and experimental results at an uncertainty of 0.35%. The results are interpreted as follows:

Uncertainty Range of Standard Samples
Although an uncertainty of 0.25% was set as the theoretical standard, the simulation results demonstrated that a range of 0.35% was the most consistent with the experimental data. This difference suggests that the uncertainty of the standard samples may propagate as an error factor throughout the experiment.
Analysis of Distribution Shape
The better fit of the uniform distribution compared to the Gaussian distribution implies that the experimental environment lacks significant variations. In scenarios where a uniform distribution is a better fit, it is likely that the environment and processes are relatively stable, with variations confined to a consistent range.
Ripple Effects and Error Factors
The simplicity and uniformity of fluctuations in the overall experimental system suggest that the uncertainty of standard samples directly impacts the variability of measurement data, reflecting it as an overall error factor.

Figure 4. Comparison of Data Distribution and Experimental Results within a 0.35% Uncertainty Range

Summary of Simulation Results Using Sensitivity Coefficients and the Monte Carlo Method

Differences in Approaches

The sensitivity coefficient was utilized as a method to locally quantify the contribution of standard samples and to analyze in detail the impact of specific factors on measurement results. This approach focuses on particular factors and evaluates their influence in depth. On the other hand, the Monte Carlo method comprehensively analyzes the random behavior of multiple factors, aiming to reproduce the overall behavior of measurement results. It emphasizes visualizing overall distributions and ripple effects.

Differences in Objectives

The objective of sensitivity coefficient analysis was to locally evaluate the influence of specific factors on measurement results. This analysis clarified the extent to which standard sample uncertainty contributes to the results. Conversely, the Monte Carlo analysis aimed to reproduce the overall distribution of measurement data and to examine the ripple effects of uncertainty, as well as the potential influence of external factors and interactions beyond the standard samples.

Overall Conclusions

The simulation results using sensitivity coefficients indicated that the uncertainty of standard samples significantly impacts the overall trend of uncertainty in measurement results. Additionally, the results suggested that external factors and interactions, beyond standard samples, might slightly influence the measurement outcomes. The Monte Carlo results showed that a uniform distribution with an uncertainty of 0.35% (0.9965–1.0035) best fit the experimental data. This finding revealed that the uncertainty of standard samples (0.25%) is a primary source of variability, while its effects are slightly amplified by other factors. Moreover, the suitability of a uniform distribution suggests that the overall experimental environment is relatively simple and exhibits stable fluctuations within a defined range.

SMILEQ Report: Summary of Uncertainty Factor Analysis

Based on the results of the uncertainty report and ANOVA report, the primary factors affecting quantitative analysis results were analyzed. Additionally, simulations were utilized to conduct a detailed analysis of uncertainty factors. In particular, the SMILEQ report's indications regarding the impact of standard sample uncertainty were reproduced, allowing for a more quantitative evaluation of its contribution to overall measurement results. Although evaluations of results influenced by extended uncertainty have been conducted previously, there are few cases where additional factor analysis has clarified the underlying causes. From the findings of this report, it is demonstrated that comprehensive analysis using the SMILEQ report provides specific methods and directions for improving the accuracy and reproducibility of quantitative analysis.

[1] JEOL Analytical Software Network
[2] Spectral Management Interface Launching Engine for Q-NMR
[3] Python is a registered trademark of the Python Software Foundation.

Quantitative NMR Analysis Using JASON SMILEQ: Novel Methods for Improving Accuracy, Part 2. Analysis of Factors through Variance Analysis

Thu, 02 Oct 2025 12:46:18 GMT

From Uncertainty Report to Variance Analysis

Deviation in the Uncertainty Report:
The Uncertainty Report calculates Expanded Uncertainty by analyzing interactions between individual factors and overall data variations. This serves as a critical foundation for integrated analysis of uncertainty across the entire measurement process.

Role of Variance Analysis:
Variance analysis (ANOVA: Analysis of Variance) is a statistical method for determining how multiple factors in data affect the results. It isolates the pure deviations of each factor and clarifies their contribution levels. By separating interactions between factors, ANOVA establishes a solid basis for detailed analysis of uncertainty sources.

Comparison Through the ANOVA Report:
The results of the ANOVA Report allow for thorough analysis of uncertainty sources and the contribution rates of individual factors. This facilitates the development of clear guidelines for improving the measurement process. Such analysis plays an essential role in enhancing data reliability and accuracy.

Variance Analysis: Two-way ANOVA

Two-way ANOVA (Two-factor Analysis of Variance) is a method used to evaluate the effects of two different factors (Factor A and Factor B) on data, as well as their interaction. Below are the primary elements involved in the calculation:

Factor A Evaluates the impact of Factor A on the data.
Factor B Evaluates the impact of Factor B on the data.
Interaction Assesses the effects of the interaction between Factor A and Factor B on the data (Factor A × Factor B).
Error Represents random variability not attributable to the above factors or their interaction.

The Total Variance is determined by combining the contributions of all these elements (Factor A, Factor B, Interaction, and Error). Figure 1 illustrates the mechanism of Two-way ANOVA through a schematic diagram.

Figure 1. Schematic Diagram of Two-way ANOVA

JASON ANOVA: 2 way ANOVA

JASON Variance Analysis provides reports based on two distinct analytical models. The JASON 2 way ANOVA focuses on the effects of independent factors, offering a simple method for individually evaluating elements that influence the data. Its main features include:

Factor A (Sample) Evaluates the independent contribution of Sample without considering direct relationships with Signal, treating it as a background element.
Factor B (Signal) Assesses the direct impact of Signal on the data and evaluates its independent contribution.
Interaction Does not include independent interaction terms.

This approach is particularly suitable when differences between samples are minimal or when the effects of Signal itself are the main focus. Compared to JASON’s other model, the 2-way nested ANOVA, it offers a simpler structure that is effective for analyzing individual factors. Figure 2 presents a schematic diagram illustrating the mechanism of the JASON 2 way ANOVA.

Figure 2. Schematic Diagram of JASON 2 way ANOVA

JASON ANOVA: 2-way nested ANOVA

JASON 2-way nested ANOVA is a comprehensive method for evaluating the relationships and interactions between multiple factors. Its main features include:

Factor A (Sample) Assesses elements influencing data across multiple levels. Similar to the 2 way ANOVA, it is treated as a background factor.
Factor B (Signal) Analyzes the direct impact on data, evaluating it in relation to the levels of Sample.
Interaction Independent interaction terms are not included.

This model is particularly suitable for scenarios where Sample's contribution is critical or where Signal's effect needs to be analyzed in conjunction with Sample interactions. It supports complex data analysis and yields more accurate results. Figure 3 illustrates a schematic diagram of the mechanism of JASON 2-way nested ANOVA. Additionally, Table 1 compares the differences between the two analytical models.

Figure 3. Schematic Diagram of JASON 2-way nested ANOVA

Table 1. Differences Between 2 way ANOVA and 2-way nested ANOVA

Details of the ANOVA Report

In the ANOVA report, variations attributed to each factor are calculated as Mean Square Variance, a key metric for interpreting variance analysis and quantitatively assessing the contribution of each factor. From the Mean Square Variance, deviations for individual factors can be calculated. These deviations, determined independently of other factors or interactions, are referred to as Pure Deviation. By using Pure Deviation, it is possible to extract uncertainty that captures the impact of each factor individually. This process quantitatively evaluates the precision and reliability of the data, laying the groundwork for deeper insights into analytical results. Figure 4 provides an overview of the metrics included in the 2 way ANOVA report, along with detailed explanations.

Figure 4. ANOVA Report: (a) 2 way ANOVA report, (b) Metrics and Descriptions

Comparison Between 2 way ANOVA and Uncertainty Report Results

Figure 5 compares the results of the 2 way ANOVA and the uncertainty report (Application Note NM250002) using a radar chart. The purple color represents the results of the 2 way ANOVA, while the blue color indicates the results of the uncertainty report. The following trends are observed:

Sample Shows lower values compared to the uncertainty report, suggesting that only the pure effects have been extracted.
Signal Displays smaller values, clearly indicating that the influence of other factors and interactions has been reduced.
Repetition Shows very small values, reflecting a high level of stability in the measurement process itself.

Differences between the Results of the Uncertainty Report The differences between the results of the two reports can be explained by the characteristics outlined in Table 2. The uncertainty report provides an evaluation that considers the "worst-case scenario" and tends to assess repeated errors as relatively large. On the other hand, variance analysis offers an approach that reflects the "overall characteristics of the data," extracting uncertainties isolated from other factors. Additionally, variance analysis enables detailed analysis of individual factors.

Figure 5. Comparison Between 2 way ANOVA and Uncertainty Report Results

Table 2. Key Characteristics of the Uncertainty and ANOVA Reports

Analysis of Differences from the Uncertainty Report Results

To analyze the differences from the uncertainty report results, the following steps are undertaken to examine the variance analysis outcomes. First, the validity of the variance analysis results is verified. Then, an analysis of factors is conducted using the results of the two variance analysis models.

Verification of Data Statistical Properties
The statistical properties of the underlying data are evaluated to confirm the validity of the uncertainty and variance analysis results. The report data was analyzed using Python for this evaluation. The following methods were employed:
- IQR Test
- Shapiro-Wilk Test
- QQ Plot
- KDE Plot
Factor Assessment in Variance Analysis
The contribution of data variability and uncertainty to each factor is assessed. This process involves comparing the results of the 2 way ANOVA and the 2-way nested ANOVA to organize the relative impact of each factor.

1. Verification of Data Statistical Properties: Outlier Examination (IQR Test)

The IQR Test (Interquartile Range Method) is one of the techniques used to detect outliers in data. The IQR is defined as the difference between the third quartile (Q3) and the first quartile (Q1), representing the range of the central 50% of the data. In the box plot shown in Figure 6, the following elements are illustrated:

Box (IQR): Represents the range from Q1 to Q3.
Line inside the Box: Indicates the median of the data (50th percentile).
Whiskers: Represent the overall range of the data.

As a result of this analysis, no outliers were detected, and it was confirmed that the variability within the data is small.

Figure 6. IQR Test Results

1. Verification of Data Statistical Properties: Normality Check

Shapiro-Wilk: Test The Shapiro-Wilk test is a statistical method for testing the normality of data. In this test, the null hypothesis assumes that "the data follows a normal distribution." The calculated p-value of 0.6092 is significantly greater than 0.05, confirming that the data follows a normal distribution.

QQ Plot (Quantile-Quantile Plot): The QQ plot is used to compare the distribution of data against a theoretical normal distribution. The closer the points of the actual data align with the straight line representing the theoretical values, the higher the normality. Figure 7 (a) illustrates the QQ plot created using the calculated results. This plot statistically confirms the normality of the data.

KDE Plot (Kernel Density Estimate): The KDE plot is a method for smoothing the distribution of data, providing a more accurate display of data density compared to histograms. Figure 7 (b) shows the KDE plot created using the calculated results. This plot visually confirms the normality of the data.

Assessment of Variance Analysis Validity: Based on the verification results from the above methods, the validity of the variance analysis has been confirmed. Normality has been evaluated both statistically and visually, providing a reliable foundation for trustworthy analytical results.

Figure 7. Verification of Data Statistical Properties: (a) QQ Plot, (b) KDE Plot

2. Factor Assessment in Variance Analysis

Figure 8 compares the results of the 2 way ANOVA and 2-way nested ANOVA using a radar chart. The purple color represents the results of the 2 way ANOVA, while the darker purple indicates the results of the 2-way nested ANOVA. The following trends were observed:

Sample Both models show similar values, confirming the stability of variability. However, the 2 way ANOVA results suggest the potential influence of interactions with other factors.
Signal The 2-way nested ANOVA shows lower values, while the 2 way ANOVA produces relatively higher values. These findings indicate that the Signal might be sensitive to repeated errors, Sample, or interactions with standard samples.
Repetition The values for repeated errors are nearly identical across both models (0.02), confirming a high degree of stability. Additionally, it was noted that the overall variability of the measurement data is kept to a minimum.

Figure 8. Results of JASON ANOVA

Summary of Variance Analysis Results

Based on comparisons with the uncertainty report, the following points have been confirmed through variance analysis:

Validity of Variance Analysis The uncertainty associated with each factor has been statistically validated, and its influence on quantitative analysis results has been clarified.
Repeated Errors Repeated errors show extremely small values, supporting the stability of the measurement process and reliability of the data.
Impact of Standard Samples The uncertainty from standard samples has been found to propagate throughout the measurement, establishing them as key influential factors.
Impact of Interactions Interactions between Signal and Sample may contribute to the uncertainty within the measurement data.

These findings provide critical insights for enhancing the reliability of quantitative analysis.

How Does the Uncertainty of Standard Samples Impact Quantitative Analysis Results?

From the previous analysis, it has been confirmed that repeated errors across the entire measurement system are very small, demonstrating the stability of the measurement process. However, further investigation is needed to explore how the uncertainty associated with standard samples affects the measurement results. To address this issue, detailed analyses using methods such as simulations would be effective. Particularly, evaluating the impact of standard sample characteristics on the overall data can provide crucial insights to improve measurement accuracy and reliability. The detailed exploration of this analysis will be covered in "Part 3. Elucidating Factors through Simulation Analysis."

[1] JEOL Analytical Software Network
[2] Spectral Management Interface Launching Engine for Q-NMR

Quantitative NMR Analysis Using JASON SMILEQ: Novel Methods for Improving Accuracy, Part 1. Evaluation of Uncertainty Factors

Thu, 02 Oct 2025 12:45:49 GMT

Factors of Uncertainty in Quantitative NMR Analysis and Their Significance

The factors contributing to uncertainty in quantitative NMR analysis results can be grouped into three main categories (Figure 1). These categories have a substantial impact on overall uncertainty, emphasizing the importance of addressing each one thoroughly and continually working towards their evaluation and refinement.

Figure 1. Key Elements of Quantitative NMR Analysis

Factors of Uncertainty: Key Points for Each Factor

Standard Samples: The purity and stability of samples are significant contributors to uncertainty.
Analytical Samples: Preparation methods, storage conditions, and physical properties (e.g., homogeneity) play a critical role in affecting uncertainty.
Environment: External conditions, including temperature, humidity, and vibrations, may influence measurement results.
Equipment: Device-specific errors can significantly contribute to uncertainty factors.
Measurement Conditions: Reproducibility of experimental procedures and variations in operational conditions directly impact uncertainty.
Peak Selection: The accuracy and consistency of peak selection greatly influence the reliability of analysis results.
Integration Conditions: Settings for integration ranges and baseline strongly affect the outcomes. Additionally, proper measures to minimize noise effects are essential.

SMILEQ Reports for Comprehensive Evaluation of Quantitative Analysis Results

SMILEQ generates two types of reports for evaluating quantitative analysis results (Figure 2):

Uncertainty Report:
This report complies with ISO 24583. It acts as a reliability-focused analytical tool, providing a comprehensive evaluation of uncertainties throughout the measurement process.
ANOVA Report:
This report employs variance analysis to deliver detailed insights into quantitative analysis results. It offers a systematic approach to isolating and clarifying the contributions of individual factors—such as samples and signals—to the overall data.

Figure 2. SMILEQ Reports

SMILEQ Reports: Key Features

The key features of SMILEQ reports are summarized in Table 1. These reports play a vital role in evaluating quantitative analysis results through two complementary tools:

Uncertainty Report This tool provides an integrated evaluation of uncertainties throughout the entire measurement process. With a reliability-focused and comprehensive perspective, it effectively clarifies overall uncertainty and supports decision-making processes.
ANOVA Report Based on variance analysis, this report isolates and quantifies uncertainties arising from individual factors, such as samples and signals. It offers detailed insights into the contributions of each element, enabling a deeper understanding of data structures.

Significance of Combined Use By combining these two reports, the following benefits can be achieved:

Conduct comprehensive risk assessments based on total uncertainty.
Gaining a deeper understanding of data structures through variance analysis.
Clarifying the factors contributing to uncertainty in quantitative analysis results.

For example, comparing archived Uncertainty Reports using expanded uncertainty values allows for an evaluation of experimental validity. If issues arise with expanded uncertainty, variance analysis results can be utilized for detailed root cause analysis.

Thus, SMILEQ reports are invaluable not only for improving data analysis accuracy but also for enhancing the overall experimental process. By addressing uncertainties methodically and comprehensively, these reports contribute to advancing both measurement reliability and experimental efficiency.

Table 1. Key Features of the Uncertainty Report and ANOVA Report

Details of the Uncertainty Report

The Uncertainty Report outputs Relative Standard Uncertainty (%) for the following factors in quantitative NMR analysis. Relative Standard Uncertainty serves as an indicator to evaluate how each element contributes to the measurement results.

Measurement Repeatability Evaluates variability in reproducibility under identical conditions.
Variations from Different Signals Selected Assesses impacts of signal selection differences on results.
Variations from qNMR Sample Solution Preparations Variations originating from the sample solution used in measurements.
The Purity of the Internal Standard Used Reflects variability due to purity and stability of the standard used.

Combined Standard Uncertainty (%) is calculated by aggregating the Relative Standard Uncertainty of each factor. Furthermore, Expanded Uncertainty (%) is derived by applying a Coverage Factor, which is set based on the confidence level. The Coverage Factor is a statistical coefficient used to expand the uncertainty and define the confidence interval. For example, at a 95% confidence level, the Coverage Factor is set to approximately 1.96. Figure 3 illustrates the metrics included in the Uncertainty Report and provides their respective explanations.

Figure 3. Uncertainty Report: (a) Uncertainty Budget, (b) Metrics and Descriptions

Expanded Uncertainty and Confidence Range

The Expanded Uncertainty, as presented in the Uncertainty Budget, is a key metric for evaluating the reliability of measurement results and assessing the validity of experimental outcomes.

The value obtained for a 95% confidence level in the Expanded Uncertainty (e.g., 0.97% from Figure 3(a)) represents a comprehensive evaluation of uncertainty across the entire measurement process. For a mean measurement value of 99.68%, the true value is interpreted to lie within a range of ±0.97% around this mean. This metric serves as a critical indicator in determining experimental reliability and trustworthiness.

Figure 4 provides an illustration of the quantitative data distribution within the dataset from Figure 3(a), along with its confidence interval. The orange line represents a Gaussian distribution curve derived from the dataset's histogram. It was confirmed that all quantitative values obtained from the experimental data fall within the confidence interval, reinforcing the robustness and reproducibility of the measurement process.

Figure 4. Gaussian Distribution and Confidence Interval in Quantitative Results

Insights from the Uncertainty Report: Contribution Ratio

The contribution ratio is a metric that quantifies how each factor's relative standard uncertainty impacts the combined standard uncertainty of the measurement process. This metric enables a clear evaluation of how significantly each factor contributes to overall uncertainty. The contribution ratio is calculated by dividing the square of the relative standard uncertainty by the square of the combined standard uncertainty, then multiplying the result by 100. This calculation expresses each factor's contribution as a percentage. Figure 5 illustrates the contribution ratios derived from the Uncertainty Report. The following trends can be observed from the contribution rates in Figure 5(b):

Measurement Repeatability Identified as the largest contributor, the standard deviation of repeated measurement data serves as the primary source of uncertainty.
Internal Standard The certified values of the standard sample consistently influence the overall data reliability.
Signal and Sample Although their contribution rates are relatively small, there is potential for further improvements to minimize their effects on uncertainty.

Figure 5. Contribution Rates: (a) Example of Uncertainty Report, (b) Contribution Ratios for Individual Factors

From Uncertainty Report to Variance Analysis

The Uncertainty Report calculates uncertainties that comprehensively reflect the impact of each factor on the entire measurement process. A key feature of this approach is that uncertainties are calculated without separating the mutual interactions between factors or variations in the overall data. This enables a holistic evaluation of uncertainties across the measurement process.　In contrast, Variance Analysis (ANOVA) isolates pure deviations for each individual factor. By eliminating mutual interactions, it clearly quantifies the extent to which each factor contributes to errors. Based on these analyses, specific improvement measures can be formulated to address particular factors.　Furthermore, leveraging the results of the ANOVA Report provides a more detailed breakdown of error factors and contribution rates. Details of this analysis are discussed further in "Part 2. Analysis of Factors through Variance Analysis."

For the latest topics and detailed information on quantitative NMR, please refer to Quantitative NMR (qNMR) on our corporate website.

[1] JEOL Analytical Software Network
[2] Spectral Management Interface Launching Engine for Q-NMR

Integrated Analysis of Fatty Acid Methyl Esters using msFineAnalysis v2 - MSTips 301

Mon, 13 Apr 2020 12:36:36 GMT

Experiment

A commercial 37-component FAMEs standard mixture (Restek, 200-600 ng/μL) was used as a sample. Table 1 shows the measurement conditions used for the GC/EI and GC/FI analyses.

Table 1. Measurement conditions

[GC-TOFMS Conditions]
System	JMS-T200GC (JEOL)
Ion Source	EI/FI combination ion source
Ionization mode	EI+: 70 eV, 300 μA FI+: -10 kV, 50mA, Slope mode
Mass Range	m/z 35-600
GC column	DB-5MSUI, 30 m x 0.25 mm, 0.25 μm
Oven temp.	50°C (1 min) → 10°C/min → 140°C → 3°C/min → 260°C (5 min)
Inlet mode	Split 50:1

Results and discussions

Figure 1 shows the TICC for the GC/EI and GC/FI measurements. While the sample contains 37 components, there were only 36 peaks observed in each chromatogram. The cis-4,7,10,13,16,19-docosahexaenoic acid methyl ester (C₂₃H₃₄O₂) and the heneicosanoic acid methyl ester (C₂₂H₄₄O₂) coelute with exactly the same retention time (RT) at 38.8 min. However, the FI mass spectrum for this peak showed the molecular ions for each component (Figure 2). Because the JMS-T200GC is always measuring high-resolution mass spectra, these components, which are not quite separated in the chromatogram, can be identified by mass separation.

Figure 1. GC/EI and GC/FI total ion current chromatograms for the 37 FAMEs mixture

m/z   Formula   Error
[mDa]   DBE
340.3329   C₂₂H₄₄O₂   -0.7    1.0
342.2536   C₂₃H₃₄O₂   -1.8    7.0

Figure 2. FI mass spectrum (enlarged) at RT 38.8 min and exact mass analysis results

Figure 3. EI and FI mass spectra of 5, 8, 11, 14, 17-eicosapentaenoic acid methyl ester (all-Z)-

The FI mass spectra show molecular ions for all 37 FAMEs in the mixture. Additionally, these molecular ions are the base peak in each FI mass spectrum except for the 15-tetracosenoic acid methyl ester (Z)-, which is detected at a relative intensity of >80%. All of these results demonstrate that FI ionizes FAMEs softly and efficiently. As an example, Figure 3 shows the EI and FI mass spectra for 5,8,11,14,17-eicosapentaenoic acid methyl ester (all-Z)-, which has 5 double bonds and an alkyl group. In this example, the molecular ion was not observed in the EI mass spectrum, but the molecular ion is the base peak in the FI mass spectrum. Figure 4 shows the FI mass spectra and chemical formulas for 6 components that all have a carbon number of 20 (minus the ester bond) and have 0 to 5 double bonds. Lastly, Table 2 shows the integrated analysis report generated by msFineAnalysis. In each case, the FI molecular ion accurate masses were automatically used to determine the molecular formula for each component in the FAMES mixture to help identify the correct match from the EI library database search.

Figure 4. FI mass spectra for the C20 FAMEs

Table 2. Integrated qualitative analysis results report using msFineAnalysis

Conclusions

The msFineAnalysis integrated analysis method produces highly accurate qualitative analysis results for the FAMEs by combining the library search results and molecular formula estimation. This combination of using GC/EI and GC/FI measurements together for qualitative analysis is particularly important for FAMEs as these types of compounds do not produce molecular ions for EI, making it difficult to use database searches alone for identification.

Integrated Analysis of Coffee Aroma by using a Headspace GC-HRMS - MSTips 280

Mon, 13 Apr 2020 12:12:21 GMT

Experiment

A commercial coffee was prepared as follows:

One gram of coffee beans was loaded into a 22 mL HS vial, 15 mL of 100˚C water was added, and the vial was sealed.
After the sample was cooled to room temperature, 10 mL of the supernatant was loaded into a HS vial, and 2 µL of an internal reference (p-Bromofluorobenzene) was added to the sample.
Finally, 2 mL of the above solution was transferred and sealed in a vial that was then used as a sample.

Table 1 shows the measurement conditions used for the headspace/GC-TOFMS system.

Table 1. Measurement conditions

[Headspace Conditions]
System	MS-62070STRAP (JEOL)
Mode	Trap mode
Extract	3 times
Heating condition	60°C, 15 min
[GC-TOFMS Conditions]
System	JMS-T200GC (JEOL)
Ionization mode	EI+: 70 eV, 300 μA FI+: -10 kV, 8mA (Carbotec 5 mm)
GC column	ZB-WAX, 30 m x 0.18 mm, 0.18 μm
Oven temp.	40°C (3 min) → 30°C/min → 250°C (10 min)
Inlet temperature	250°C
Inlet mode	Split 30:1

Results and discussions

Figure 1 shows the operational flow chart for the integrated analysis steps used for the JEOL msFineAnalysis software (chart on the right). First, the data is acquired by using both EI and soft ionization (SI), and all peaks and associated mass spectra are detected in the chromatograms. Afterwards, the mass spectra produced by these ionization methods are linked using their retention times, and these linked mass spectra are recorded as single components. Next, the EI mass spectrum is used for the library database search (1), and the SI mass spectrum is used to identify the analyte molecular ion (2). Afterwards, the molecular ion is used for exact mass analysis to determine possible elemental compositions, and these candidate formulas are then filtered by using the EI library search results (3). Next, the molecular ion is subjected to isotopic pattern analysis to help further limit the candidate formulas (4). Each candidate formula is then used as a search constraint for the exact mass analysis of the EI fragment ions (5). If the molecular ion formula candidate is incorrect, the EI fragment ions will not result in many (if any) compositional formulas, thus indicating that the molecular ion formula is not a good candidate for that particular analyte. These results are then output as an integrated qualitative report (6).

Figure 1. Qualitative Analysis Flow

Figure 2. TIC chromatograms of coffee aroma acquired by a HS/GC/TOFMS

Figure 3. Integrated qualitative analysis results on msFineAnalysis

The msFineAnalysis Auto Analysis function detected 67 components in the GC/EI and GC/FI measurements (Figure 2) that were automatically linked using their retention time. The Auto Analysis function then automatically used the steps in Figure 1 to analyze the linked data, and the results were output as a color-coded table as shown in Figure 3. Each color indicates a level of confidence for the identity of the compound:

Green: A molecular formula candidate was uniquely identified.
Orange: Multiple molecular formula candidates were identified.
White: No significant molecular formula candidates were identified.

The components classified as orange or white can be further reviewed manually to potentially identify a unique candidate formula. In this example, the software was able to automatically determine a unique molecular formula for 63 of the 67 components in the coffee headspace sample.

Conclusions

The msFineAnalysis software produces highly accurate qualitative analysis results by automatically combining the EI library search results and soft ionization (SI) molecular formula determinations. Additionally, this software makes it possible to determine molecular formulas for unknown components not registered in library (match factor score: low), which can not be identified by database search alone (Figure 1, left side). The effectiveness of the msFineAnalysis integrated analysis method effectiveness for GC/MS qualitative analysis was demonstrated by automatically determining molecular formulas from exact masses, regardless of the level of match factor score, to limit the candidate formulas.

Integrated Analysis of an Acrylic Resin using msFineAnalysis v2 - MSTips 300

Mon, 13 Apr 2020 11:34:01 GMT

Software Enhancements

Changes in msFineAnalysis Ver.2:
Version 2 continues to use the integrated analysis work flow (see MS Tips 275) and TICC peak detection developed in Ver.1. Major changes from Version 1 include: 1) Improved graphical user interface (GUI), 2) chromatographic deconvolution, and 3) Group Analysis.

1) Improved GUI:
Version 2 supports two languages: English and Japanese. The GUI was extensively modified to display tabulated integrated analysis results and chromatograms on a single view. Color schemes are now represented by Color Universal Design (CUD) to enhance visibility for people with different kinds of color vision.

2) Chromatographic deconvolution:
Chromatographic deconvolution reconstructs mass spectra by using information (m/z, area) of peaks detected in extracted ion chromatograms (EIC) using the exact masses of the ions observed. This provides high-quality mass spectra for coeluting components that may appear as a single peak in the total ion current chromatogram (TICC).

3) Group Analysis:
Group analysis identifies related compounds in a complex mixture by creating selected ion chromatograms for compounds that have common fragment ions or common neutral losses. This makes it easier to examine component groups and isomers having a similar partial structure.

Experiment

A commercial acrylic resin was used as a model sample. A JEOL JMS-T200GC GC-HRTOFMS was used for analysis, and a Frontier Lab pyrolysis inlet was used for sample pretreatment. Additionally, the system was equipped with an EI/FI combination ion source for this work. The resulting data were analyzed by using msFineAnalysis version 2 (JEOL). Table 1 shows the pyrolysis and GC-HRTOFMS analysis conditions.

Table 1. Measurement conditions

[Pyrolysis Conditions]
Pyrolyzer	PY-3030D (Frontier Lab)
Pyrolysis Temperature	600°C
[GC-TOFMS Conditions]
System	JMS-T200GC (JEOL)
Ion Source	EI/FI combination ion source
Ionization mode	EI+: 70 eV, 300 μA FI+: -10 kV, 40mA/30msec
Mass Range	m/z 35-800
GC column	ZB-5MSi, 30 m x 0.25 mm, 0.25 μm
Oven temp.	40°C (2 min) → 10°C/min → 320°C (15 min)
Inlet mode	Split 100:1
[Data processing Conditions]
Software	msFineAnalysis (JEOL)
Library database	NIST17
Tolerance	±5mDa
Electron	Odd
Element set	C: 0-50, H: 0-100, O: 0-10

Figure 1. Py-GC/EI and Py-GC/FI total ion current chromatograms of an acrylic resin polymer at 600°C

Figure 2. EI and FI mass spectra of related compounds with (a) monomers, (b) dimers, and (c) trimers.

Results and discussions

Figure 1 shows the TICC data for both GC/EI and GC/FI measurements. Methyl acrylate (MA) and methyl methacrylate (MMA) were detected at high intensity. Dimers and trimers were observed at retention times of 10 min and 18 min, respectively. Figure 2 shows typical mass spectra for the monomers, dimers, and trimers. Molecular ions were detected at high relative intensity in FI mass spectra but were weak or absent in the EI mass spectra. Many of the acrylic resin pyrolysates do not have entries in the library database, making it difficult to identify their components by library search alone. Additionally, soft ionization was essential because EI did not produce molecular ions for many compounds as shown in Figure 2b and 2c.

When the msFineAnalysis Auto Analysis was used on for the GC/EI and GC/FI data, 161 components were automatically detected. Ultimately, molecular formulas of 154 components out of the 161 were uniquely identified. Additionally, the formulas of EI fragment ions, which were obtained from accurate mass data, resulted in structural information for the sample molecules. Next, monomers, dimers, and trimers were examined using Group Analysis—the results are shown in Table 2. Out of the 161 components, 46 were directly related to the monomers, dimers, and trimers. In Group Analysis, molecular ions of a desired repeat unit formula are specified and analyzed, speeding up the analysis process. The results for the Group Analysis can be exported, making it easier to calculate the relative intensities using the sum of the chromatogram peak areas shown in Table 2. Other components detected include pyrolysis products in which alkyl chains are bonded with monomers, dimers, and trimers.

Conclusions

The integrated analysis method produces highly accurate qualitative analysis results from the database entries with high match scores by combining the library search results and molecular formula estimation. Additionally, this analysis makes it possible to determine molecular formulas for unknown components not registered in a library database that cannot be identified by database searching alone. The integrated analysis method made it possible to to determine molecular formulas from exact mass results, regardless of the level of match factor score.

Table 2. Integrated qualitative analysis results for monomers, dimers, trimers and their isomers.

This narrowed down the candidate compositions, demonstrating the effectiveness of this software for GC/MS qualitative analysis.

Analyzing a Specific Component using Group Analysis of msFineAnalysis Ver. 2 - MSTips 303

Mon, 13 Apr 2020 10:47:59 GMT

Software Enhancements

Chromatographic Deconvolution:
The msFineAnalysis Version 2 software supports chromatographic deconvolution to reconstruct mass spectra by using the information (m/z, area) from extracted ion chromatograms (EIC) created using exact mass information. Chromatographic deconvolution is effective in separating coeluting components which are detected as a single peak in the total ion current chromatogram (TICC).

Group Analysis:
Group analysis can be used after chromatographic deconvolution to identify compounds that have common substructures. Group analysis is accomplished by creating mass chromatograms from the exact mass data to identity compounds that have the same molecular weight, or that have common fragments or neutral losses. Figure 1 shows the graphical user interface (GUI) for Group analysis.

Experiment

A commercial vinyl acetate resin was used as a model sample. A JEOL JMS-T200GC GC-HRTOFMS was used for analysis, and a Frontier Lab pyrolysis inlet was used for sample pretreatment. Additionally, the system was equipped with an EI/FI combination ion source for this work. The resulting data were analyzed by using msFineAnalysis version 2 (JEOL). Table 1 shows the pyrolysis and GC-HRTOFMS analysis conditions.

Table 1. Measurement conditions

[Pyrolysis Conditions]
Pyrolyzer	PY-3030D (Frontier Lab)
Pyrolysis Temperature	600°C
[GC-TOFMS Conditions]
System	JMS-T200GC (JEOL)
Ion Source	EI/FI combination ion source
Ionization mode	EI+: 70 eV, 300 μA FI+: -10 kV, 6mA/10msec (Carbotec)
GC column	DB-5MSUI, 30 m x 0.25 mm, 0.25 μm
Oven temp.	50°C (1 min) → 30°C/min → 330°C (1.7 min)
Inlet mode	Split 100:1

Figure 1. Group Analysis Window

Figure 2. Group analysis results of C₆H₅ ion

Results and discussions

Figure 1 shows the C₆H₅ fragment ions that were detected in the pyrolysis GC-MS results for the vinyl acetate resin. This fragment ion is characteristic for aromatic compounds. The table on the right shows that there are 26 compounds containing C₆H₅. The view on the left allows the operator to quickly identify where the components containing this ion were detected. The view on the left top shows the GC/EI data with the TICC marked by a solid black line. The bottom left view shows the soft ionization data with the TICC marked by a solid green line. The blue peaks in both views represent the components containing C₆H₅ extracted from the chromatographic deconvolution result. The operator can select an ion such as C₆H₅ from the table and click the OK button at the bottom right of the GUI to immediately create a C₆H₅ tab, thus allowing for extraction of the components containing that specific fragment (Figure 2).

Figure 2 shows the extracted results for components containing C₆H₅. The Group Analysis function displays an “All” tab for the entire analysis results and up to 5 tabs for groups created for ions or neutral losses specified from the exact mass list in Figure 1. For example, the operator can select a fragment ion containing nitrogen, phosphate, or sulfur to find a group of compounds containing the specified elements. The ID and integrated analysis results are then shared between tabs. The results under the C₆H₅ tab represent a group of aromatic compounds.

Conclusions

The msFineAnalysis program is designed to run integrated analysis with or without library search. It is a qualitative program based on a new concept that is effective for non-targeted analysis. The basic functions of the program are capable of identifying numerous components for non-targeted analysis. Group Analysis adds the capability to extract specific compounds or families of related compounds in the same manner as target analysis, speeding up the process of their detailed analysis.

JEOL Resources

Quantitative NMR Analysis Using JASON SMILEQ: Novel Methods for Improving Accuracy, Part 3. Elucidating Factors through Simulation Analysis

How Does the Uncertainty of Standard Samples Impact Quantitative Analysis Results?

Uncertainty Report and ANOVA Report Results

Analyzing the Impact of Standard Sample Uncertainty

Analysis Method

1. Analysis of Coefficients of Variation

Coefficient of Variation (CV)

Coefficient of Variation After Quantitative Calculations

2. Analysis Using Sensitivity Coefficients

Sensitivity Coefficient

Significance of Simulations Utilizing Sensitivity Coefficients

Simulation Results Using Sensitivity Coefficients

Simulation Range

Simulation Results

Characteristics of Experimental Results

Conclusion and Model Applicability

3. Analysis Using Monte Carlo Method

Overview of the Monte Carlo Method

Significance of Simulations Using the Monte Carlo Method

Simulation Results Using the Monte Carlo Method

Simulation Range

Modeling and Statistical Evaluation of Uncertainty

Evaluation Methods for Simulation Results

Most Consistent Model

Ripple Effects and Error Factors The simplicity and uniformity of fluctuations in the overall experimental system suggest that the uncertainty of standard samples directly impacts the variability of measurement data, reflecting it as an overall error factor.

Summary of Simulation Results Using Sensitivity Coefficients and the Monte Carlo Method

Differences in Approaches

Differences in Objectives

Overall Conclusions

SMILEQ Report: Summary of Uncertainty Factor Analysis

Quantitative NMR Analysis Using JASON SMILEQ: Novel Methods for Improving Accuracy, Part 2. Analysis of Factors through Variance Analysis

From Uncertainty Report to Variance Analysis

Variance Analysis: Two-way ANOVA

JASON ANOVA: 2 way ANOVA

JASON ANOVA: 2-way nested ANOVA

Details of the ANOVA Report

Comparison Between 2 way ANOVA and Uncertainty Report Results

Analysis of Differences from the Uncertainty Report Results

1. Verification of Data Statistical Properties: Outlier Examination (IQR Test)

1. Verification of Data Statistical Properties: Normality Check

2. Factor Assessment in Variance Analysis

Summary of Variance Analysis Results

How Does the Uncertainty of Standard Samples Impact Quantitative Analysis Results?

Quantitative NMR Analysis Using JASON SMILEQ: Novel Methods for Improving Accuracy, Part 1. Evaluation of Uncertainty Factors

Factors of Uncertainty in Quantitative NMR Analysis and Their Significance

Factors of Uncertainty: Key Points for Each Factor

SMILEQ Reports for Comprehensive Evaluation of Quantitative Analysis Results

SMILEQ Reports: Key Features

Details of the Uncertainty Report

Expanded Uncertainty and Confidence Range

Insights from the Uncertainty Report: Contribution Ratio

From Uncertainty Report to Variance Analysis

For the latest topics and detailed information on quantitative NMR, please refer to Quantitative NMR (qNMR) on our corporate website.

Integrated Analysis of Fatty Acid Methyl Esters using msFineAnalysis v2 - MSTips 301

Experiment

Results and discussions

Conclusions

Integrated Analysis of Coffee Aroma by using a Headspace GC-HRMS - MSTips 280

Experiment

Results and discussions

Conclusions

Integrated Analysis of an Acrylic Resin using msFineAnalysis v2 - MSTips 300

Software Enhancements

Experiment

Results and discussions

Conclusions

Analyzing a Specific Component using Group Analysis of msFineAnalysis Ver. 2 - MSTips 303

Software Enhancements

Experiment

Results and discussions

Conclusions

Ripple Effects and Error Factors
The simplicity and uniformity of fluctuations in the overall experimental system suggest that the uncertainty of standard samples directly impacts the variability of measurement data, reflecting it as an overall error factor.