User Manual of TOCO19
Institute for FUMI Theory
Introduction
TOCO19 is software for predicting precision of measurements by distinguishing noiseand signals (peaks) in a chromatogram. From the former, mathematical properties of
uncertainty are extracted and analyzed, and to the latter, limits of detection,
quantitation and decision, and precision profiles are given. Users can know thesestochastic properties of each peak by inputting a file of a chromatogram into TOCO19.
Since the theories and methodologies of ISO 11843 Part 7 and JIS Z 8462 Part 7 underlie
the fundamental concepts of TOCO19, repeated measurements of real samples inchromatography can be obviated.
The basic policy of TOCO19 is to provide users with:

explanations of statistical theories cited in TOCO19 (detection limit, etc.)user-friendliness so that TOCO19 can be used without extensive reading of this user
manual.

Upon opening the TOCO19 software, one can see instructions in the TOCO main window.
We hope that following these instructions will be sufficient to users, but if not, thismanual will be of help.
Before TOCO19 was put on the market, its practical suitability had been examinedwith a variety of chromatographic experiments in collaboration with Prof. Akira Kotaniof the Department of Analytical Chemistry, School of Pharmacy, Tokyo University of
Pharmacy and Life Sciences. At present, TOCO19 has been found to be well suited forthe following methods: absolute calibration curve method, internal standard method,isocratic elution, and the gradient elution of HPLC. However, there are some cases inwhich TOCO19 is not effective (see Chapter 3).
We should appreciate it very much if you would kindly let us know of any bugs, if
found, in TOCO19 through the “Contact us” of the Help menu. We will make a maximum
effort to correct, improve, and further develop TOCO19.
August 5, 2020

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Terms and Abbreviations
detection limit

minimum detectable quantity (concentration)

precision

standard deviation (SD) or relative standard deviation(RSD) of measurements (responses) or concentration
estimates

precision profile

plot of measurement RSD against concentration,
defined in ISO 11843-7 and JIS Z 8462-7

quantitation limit

minimum concentration for quantitation

decision limit

criterion for detection, also called critical value,DL

detection limit

FUMI

Function of Mutual Information

FUMI theory

theory to predict the precision of measurements from
noise

and

signalsin theoutput of analytical

instruments
FUMI equation

equation to denote the SD of measurements（=σ(k)）

ISinternal standardPP

precision profile

QL

quantitation limit

RSD

relative standard deviation or coefficient of variation

SD

standard deviation

TOCO

Total Optimization of Chemical Operations

Most of the above terms are specified in views, message boxes, or tool tips of TOCO19.

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Table of Contents
Chapter 1

Fundamentals of TOCO19 ............................................................................. 4

Chapter 2

Operations for different purposes ................................................................. 6

1．Data file import............................................................................................................ 6
2．Input of peak names and concentrations ................................................................... 7
3．Decision limit, DL and QL for a target peak (1) ........................................................ 9
4．Decision limit, DL and QL for a target peak (2) ...................................................... 10
5．Designation and dismissal of target and IS peaks ................................................... 11
6．Precision of a target peak at an arbitrary concentration (precision profile) ......... 12
7．Set of sample injection errors ................................................................................... 12
8．Explanations of DL, QL and decision limit, and PP ............................................... 12
9．Constants for limits of detection and quantitation ................................................. 1210．Signal on noise of limits of decision, detection, and quantitation........................ 13
11．Copy and paste of results from TOCO19 to Excel ................................................. 14
12．Analyses of noise and signals in different files ..................................................... 14
13．A chromatogram lacking a sufficient number of noise data points...................... 14
14. Analyses for internal standard methods............................................................... 15
15．Analyses for gradient elution.................................................................................. 16
16．Import of multiple files and display of one ............................................................ 17
17．Deletion of a file from TOCO19 .............................................................................. 17
18．Comparison of data of different files (routine check) ............................................ 1819．Manual adjustment of peak widths ........................................................................ 19
20．Deletion of a peak from TOCO19 analyses ............................................................ 20
21．Entry of a peak in TOCO19 analyses ..................................................................... 21
22．Setup of a new signal region ................................................................................... 22
23．Analyses of overlapping peaks ................................................................................ 23
24．Complete Manual analyses from scratch ............................................................... 25
25．Statistical reliability of TOCO19 analyses ............................................................ 26
26．SD of area measurements for a peak in the main window ................................... 26
27．Manual calculation of precision (FUMI equation) ................................................ 26
28．Quick display of file data on the chart ................................................................... 27
29．Explanations of labels and figures in TOCO19 ..................................................... 27
Chapter 3

Applicability of TOCO19 in theory and practice ........................................ 27

Chapter 4

Inquiries and general feedback ................................................................... 27

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Chapter 1

Fundamentals of TOCO19

TOCO19 is an automated system for predicting:

precision (RSD of measurements) for a peak in a chromatogram;

detection limit (DL) of the peak.

A data file of a chromatogram containing both noise and signals is the only requirement
for performing TOCO19 analyses.
Figure 1 shows the initial window when TOCO19 is launched. TOCO19 is a fully
automated software and users are only required to input a data file as follows:1.

click the Import menu (see Fig. 1 and for details, see 2.1);

2.

check the input data and analytical results (DL and precision) (see Fig. 2).

After procedure 1, the contents of the file are displayed and automatically detectedpeaks are numbered in the chart (see Fig. 2). In the view of the main window,
measurement RSDs and DLs are shown (see Fig. 2).

ImportUser operation

Menu

View
Chart

User operation

Figure 1 --- Main window at application startup
4Input data

Precision(RSD)

Detection
limit（DL）

Figure 2 --- Analytical results of TOCO19 after a data file has been input
Explanations of almost all of the functions in the main window will appear in the view
when you click on them or in the tool tips when you position the mouse pointer over them.
Manual operations are denoted by purple labels in the main window (see Fig. 2).
Typical operations after the first default analysis shown in Fig. 2 are:

Signals Info button → to input or change a name and concentration of a peak in the
chart



Detection Limit (DL) button → detection limit, quantitation limit, decision limit
and precision profile (plot of measurement RSD versus concentration)



Signal Designation group → manual adjustment of peak widths and designation oftarget and IS peaks.

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Chapter 2

Operations for different purposes

1．Data file import
To import a data file into TOCO19, click the Import menu in the main window, open
a target file on the Open dialog box, and operate the Import dialog box as follows (seeFig. 3)
1.

click the header of a column which contains data;

2.

press the OK button.

The first row of valid data is automatically selected by operation 1 and its value isdisplayed in the text box with yellow background. It is recommended to check its value
for confirmation. If the value is not appropriate, click a row you desire.
Some points to keep in mind are (see Fig. 3):
Ending row denotes the last row to be imported by default;

The value of the Ending row text box (green box) is changeable, and the data fromthe Start at (yellow box) to the End row are imported into TOCO19;

The minimum number of data available for TOCO19 is 300.

Confirm here.

１．click
２．press

Figure 3 --- Import dialog box
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2．Input of peak names and concentrations
The procedures to change a peak name and concentration are:1.

press the Signals Info button after a data file has been imported (see Fig. 4);2.

select a target peak by clicking a row of the view of the Signals Info window (see Fig.
5);

3.

click a cell on the Conc column and input a concentration value;

4.

type a signal name on the Name column;

5.

press the OK button to update the name and concentration and return to the main
window.

Other names and concentration values can also be changed by repeating procedures 2 to4.

１．press

Figure 4 --- Main window

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２．click

４．nameRefresh３．concentration
５．press
View

Figure 5 --- Signals Info window
Some points to note are:

The Refresh button is used to confirm DL recalculation due to a change inconcentration (see Fig. 5). Since a DL is automatically recalculated when anotherrow in the view is clicked, the Refresh button does not have to be used except for
immediate recalculation. If a typed value is illegal, the button will turn red. If not,it will turn green;When you press the OK button, although a new value of Conc is not positive or
numerical, the left message of Fig. 6 will appear. If a newly typed Name consists ofmore than 20 characters, the right message of Fig. 6 will appear. You must close the
Signals Info window after correcting the illegal input.

Figure 6 --- Warning message boxes

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3．Decision limit, DL and QL for a target peak (1)TOCO19 analyses are based on the stochastic properties of noise. Decision limits,
DLs and QLs are quantities inherent in peaks. TOCO19 provides two operation methods
for predicting the precision of a peak from data of noise and signals as follows:（1） press the Detection Limit (DL) button and designate a signal as a target peak;（2） designate a signal as a target peak and then press the Detection Limit (DL) button(see 2.4).
Both operation methods apply to cases where noise and signals are present in the chart(see Fig. 1), but method (1) is also useful if signals are absent in the chart.
The procedures of method (1) are:1.

display a file which contains analyzable noise in the chart (analyzable means thateither SD of w or SD of m has a positive value);2.

press the Detection Limit (DL) button in the main window;

3.

select a file (Signal # > 0) from the view of the Target Signal Selection window (seeFig. 7);4.

select a target peak from the lower-right combo box;

5.

press the OK button to obtain analytical results in the DL & PP…… dialog box (seeFig. 8).
Some points to note are:

If the DL & PP …… window (Fig. 8) appears just after procedure 2, see 2.4;

The light green background (Fig. 7) indicates a file displayed in the main window;The purple border (Fig. 7) denotes a file without peaks (Signal # = 0);An IS signal is not displayed by procedure 4 (it cannot be a target peak).

４．select

５．press

３．selectFigure 7 --- Target Signal Selection dialog box
9Width of a target
peak(Procedure 4)

From left:
Decision limit
Detection（DL）
Quantitation limit（QL）

Target Signal
Selection

precision profile（PP）

Figure 8 --- DL & PP …… window
4．Decision limit, DL and QL for a target peak (2)The procedures of operation method (2) of 2.3 are:1.

confirm that the data in the chart contain both noise (purple blocks) and signals(white blocks) (Fig. 9);2.

select 🔘Target from the Signal Designation group (unless explanations of the next
procedures appear in the view, click the uppermost 🔘 on the left side of the view);

3.

click on or around a target peak in the chart (Fig. 9) (the designated peak is painted
in red and indicated with a T);

4.

press the Detection Limit (DL) button to obtain analytical results in the DL & PP…… window (see Fig. 8).
10３．click

４．press

２．selectFigure 9 --- Selection of a target peak
5．Designation and dismissal of target and IS peaks
Analyses from the Detection Limit (DL) button (decision limit, DL, QL, PP, Signal onnoise (see Fig. 12 or 2.10)) cannot be obtained until a target peak is designated. Forinternal standard methods, precision is also predicted with a designated IS peak.
There are two operations for designating and one for dismissing a target peak:click 🔘Target in the Signal Designation group of the main window and follow the
instructions in the view (unless explanations of the next procedures appear in theview, click the uppermost 🔘 on the left side of the view);click the Target Signal Selection menu in the DL & PP …… window (see Fig. 8) andselect a target peak (see procedures 3-5 of 2.3);

press the Dismiss button to release a target peak from its role, when 🔘Target isselected (see Fig. 9).
The procedures for designation and dismissal of an IS peak are the same as those ofa target, except that it is selected by the 🔘IS radio button and indicated with an IS.
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6．Precision of a target peak at an arbitrary concentration (precision profile)
A precision profile means a plot of measurement RSD (%) against concentration,from which is known a measurement RSD (%) of a target peak at an arbitrary
concentration. The procedures for this purpose are (see Fig. 10):
1.

press the Detection Limit (DL) button to open DL & PP …… (see 2.3 or 2.4);

2.

input a concentration in the green text box on the left side of Precision Profile (PP);3.

check the precision in the yellow text box and the RSD pointed by the yellow ◀.

The blue ▼ indicates a DL and red ▼ a QL.
Click the figure of the Precision Profile (PP) to see an explanation of PP.

precision

２．input
Figure 10 --- A precision profile after a concentration has been input
7．Set of sample injection errors
In chromatographic analyses, the RSD (%) of sample injection errors needs to be input
into the green text box on the right side of “RSD of independent error” (see Fig. 8 or 11).
8．Explanations of DL, QL and decision limit, and PP
Explanations about limits of decision, detection, and quantitation are displayed byclicking one of the colored large labels (see Figs. 11 and 12). Click the figure of Precision
Profile (PP) to see its explanation (see Fig. 11).
9．Constants for limits of detection and quantitation
DLs and QLs are defined as a constant times an SD of blank sample measurements(= σ(k)). The default values of the constant are 3.3 and 10 for DLs and QLs, respectively.
The latter constant is fixed, but the former is changeable. An arbitrary constant can be
assigned to a DL by typing a value in the green text box on the right side of the label“DL” (see Fig. 11). The Default button restores the default values (3.3 and 10).
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10．Signal on noise of limits of decision, detection, and quantitation
The Signal on noise, shown in Fig. 12, is a Gaussian peak which is superimposed onreal noise and is useful to confirm a signal-to-noise ratio (S/N) for decision limits, DLs
and QLs . The following procedures are necessary for the Signal on noise:1.

press the DL Signal button in the DL & PP …… window (see Fig. 11) after pressing
the Detection Limit (DL) button on the main window;

2.

select one of the three radio buttons (🔘) in the Detection Limit Signal on Noise
window (see Fig. 12).
An explanation about the Signal on noise will appear by clicking one of the labels of

the limits.

Precision profile（PP）

１．press

Figure 11 --- DL & PP …… window
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２．select

Signal on noise

click a label

Figure 12 --- Detection Limit Signal on Noise window
11．Copy and paste of results from TOCO19 to Excel
Clicking the Copy menu leads to the copying of the TOCO19 results to the clip board
and you can paste the contents into Excel for further examination. The following
TOCO19 results can be copied:main window (noise and signal analyses);

Signals Info window (items in the view);



DL & PP …… window (decision limit, DL, QL and PP);

Files Info window (items in the view and control chart);

Detection Limit Signal on Noise window (selected Signal on noise);

FUMI Equation window (σ(k)).
These results are useful for technical reports, etc.

12．Analyses of noise and signals in different files
In cases where noise and signals are in different files, see 2.3.
13．A chromatogram lacking a sufficient number of noise data points
There often arise situations where enough noise data points are not secured in adata file due to densely populated peaks or narrow noise regions around a peak. In
these cases, TOCO19 can also be performed by analyzing noise of another file (see 2.3).
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14. Analyses for internal standard methods
The procedures for analyses of internal standard methods are (see Fig. 13):1.

select the 🔘IS button in the Signal Designation group (see instructions in the view);

2.

click on or around a desired peak in the chart;

3.

follow one of instructions appearing in the view
① DL, QL, decision limit and PP → Detection Limit (DL) (see 2.3 or 2.4);② Detection limit → the third or fourth radio button (🔘) on the left side of theview (a DL for an IS peak is described as IS, but other peaks are given predicted
DLs; meanings of columns appear in the view by clicking one of them).
A point to note is:IS peak selection in procedures 1 and 2 should be performed from a file containing
both noise and signal. This selection is also possible with a file containing signal
alone, but the precision cannot be calculated without noise.

２．click

３．①

press

３．②

select１．selectFigure 13 --- The main window after an IS peak has been selected15

15．Analyses for gradient elution
In gradient elution of HPLC, baselines (backgrounds) of chromatograms are notusually horizontal, but oblique. However, TOCO19 can cope with these cases. As isshown in Fig. 14, if the observed histogram (zigzag line) of areas created by the
background noise is in good agreement with the theoretical line (smooth line) of a normal
distribution, TOCO19 analyses can be considered successful (for details, see 2.25).

good agreement between
theory and practice

Figure 14 --- An example of gradient elution analyses

1616．Import of multiple files and display of one
The procedures to import multiple files and display one in the main window are:1.

execute the Import menu repeatedly to import multiple files (see 2.1);

2.

press the Files Info button on the left side of the main window (see Fig. 14);3.

select a radio button (🔘) of the Sh* column which contains the file you want to show
in the main window (see Fig. 15);

4.

press the OK button to return to the main window.
TOCO19 analyses are based on noise and signals in the chart of the main window.

17．Deletion of a file from TOCO19
In the Files Info window (see procedure 2 of 2.16), click a row of the desired file inthe view, unselect its radio button (🔘) of Sh* and uncheck its check box (☑) of Join, andthe selected file will be deleted (see Fig. 15). Deletion will not be executed until the OK
button is pressed. Click the Undo button to undo the deletion.

View

Delete or

３．select

Undo

Control chart

４．press

Figure 15 --- Files Info window
1718．Comparison of data of different files (routine check)An abnormal condition of an instrument can often be found by a daily check ofbackground noise. TOCO19 provides this function as a control chart. To see a control
chart, import multiple files and press the Files Info button.
The procedures to select a specific peak for a control chart are (see Fig. 16):
1.

click a row of a file containing a desired peak in the Files Info window;

2.

select a desired peak from the combo box on the right side of label “(time unit)”;3.

confirm the DL in the yellow text box and also compound name.
Some points to note are:

DL values are described in terms of absolute calibration curve methods. Even if an
IS peak is designated, DL values of IS methods are not shown;Files with no peaks are shown by purple borders in the view (see Fig. 16);

In procedure 2, IS peaks cannot be selected as a peak for the control chart.

１．click

２．select

３．confirm

Figure 16 --- Files Info window (no signals in file #2 with purple borders)1819．Manual adjustment of peak widths
Users can manually adjust a width of a peak (a white block in the chart) (see Fig.
17). For this purpose, the Signal Designation group is used as follows:1.

select a radio button, 🔘Target or 🔘IS.

Instructions of the next procedure will appear in the view as shown here (see Fig. 17)
2.

click on or around an objective peak in the chart;

3.

click or double-click the ◀ or ▶ button to adjust a width of the peak;4.

confirm the width, peak area (red or blue) and peak number.
Change in a peak width affects the precision (DL and RSD). The designation of atarget or IS peak can be dismissed by the Dismiss button.

２．click

Procedures 2-4
１．select

Dismiss

４．confirm

３．click or double-click

Figure 17 --- Main window

19

20．Deletion of a peak from TOCO19 analyses
If a peak is deleted from TOCO19 analyses, it will no longer have the peak numberin the chart or analytical results (precision and DL) in the view. Users can limit the
information of peaks by releasing insignificant peaks from analyses. This peak deletioncan be done with the Signal Entry group as follows (see Fig. 18):
1.

select the 🔘Delete button;

Instructions for the next steps will appear in the view as follows:2.

click on or around a peak with a number to select as a candidate (indicated with ▲);3.

press the Do button.
In the updated chart (see Fig. 19, but neglect the green ▼), the red block is retained,

but the white block for the selected peak is erased.
A point to note is:A peak designated as T or IS cannot be deleted by the above procedures. However,this is feasible, if the designation of T or IS is dismissed by the Dismiss button.

２．click

Instructions

３．press
１．select

Dismiss button

Figure 18 --- Main window for signal deletion
2021．Entry of a peak in TOCO19 analyses
The procedures to enter a peak in TOCO19 analyses are (see Fig. 19):1.

select the 🔘Add button in the Signal Entry group.

The instructions for the next steps will appear in the view as follows:2.

click on or around a peak without a number to select it as a candidate (indicatedwith ▼);

3.

press the Do button.
In the updated window (see Fig. 18), the red block is retained, but a new white block

will be created.
Some points to note are:


A peak with a non-positive area cannot be analyzed;A region outside the red blocks cannot be designated as a new peak to be analyzed.
For setting a new signal region (red block), the procedures of 2.22 are useful;A peak width (white block) is changeable (see 2.19).

２．click

Instructions

１．select
３．press

Figure 19 --- Main window for signal entry
21

22．Setup of a new signal region
The Manual SE group is used to set up a new signal region. The chart of Fig. 20
shows an example of data which are all recognized as noise by unchecking the ☑Signal
Elimination (SE) check box. If ☑Signal Elimination (SE) is checked, automatic peakdetection of TOCO19 is carried out. The procedures to set up a new peak region are
1.

check the ☑Select a signal check box in the Manual SE group;

The instructions for the next steps will appear in the view as follows:2.

draw a square with the mouse to designate a new region as a signal in the chart;3.

press the Eliminate button.
Figure 21 shows that the red and white blocks are created after procedure 3. The

width (white block) of a peak is changeable (see 2.19).
The setup of a new signal region is referred to as Signal Elimination (SE), becausesignal components in the noise regions (purple blocks) spoil the noise analyses of
TOCO19 and elimination of them improves the reliability of the TOCO19 analyses.

２．draw a square

Instructions

１．check

３．press

Figure 20 --- Main window (manual signal elimination)22

a new
signal region

Figure 21 --- Chart after procedure 3
23．Analyses of overlapping peaks
Each overlapping peak can be analyzed by virtually separating them as follows:1.

check ☑Select a signal of the Manual SE group (see Fig. 20);

2.

draw a square around one of the overlapping peaks with the mouse (see Fig. 22);

3.

press the Eliminate button to create a new signal region (white block) (see Fig. 23,
but neglect ▼);4.

select 🔘Add of the Signal Entry group and click the other peak to set a new region(see ▼ of Fig. 23);

5.

press the Do button to let the new peak participate in analyses; (see Fig. 24).
Instead of procedures 1-3, the ◀ and ▶ buttons of the Signal Designation group canbe used to adjust the signal region of the first peak.
Instead of procedures 4 and 5, procedures 1-3 can be used to create another signal
region of the second peak (see Fig. 25). If a square drawn by the mouse overlaps with theexisting signal region (white block) of the first peak, the latter region will be erased.

２．draw a square

Figure 22 --- Chart (a framed box around one of two peaks)
23

４．selectFigure 23 --- Chart (selection of the second peak)Figure 24 --- Chart (Participation of the second peak)draw a square

Figure 25 --- Another example of separation of overlapping peaks

2424．Complete Manual analyses from scratch
TOCO19 is automatic software for analyzing noise and signals, but it also provides
the following complete manual operations from the very beginning which are conducted
through the Manual SE group (see Fig. 26):
1.

uncheck ☑Signal Elimination (SE), while a data file is displayed on the chart;

2.

check ☑Select a signal in the Manual SE group;3.

draw a square with the mouse to designate a signal region in the chart;

4.

press the Eliminate button.

Repeat procedures 2-4 to set more signal regions. If necessary, you can use the ◀ and ▶
buttons to adjust the signal regions.
Checking ☑Signal Elimination (SE) restores the initial state of file import. The
Default button leads to the default state, whether or not ☑Signal Elimination (SE) is
checked. For the adequacy of these manual operations, Histogram of measurement
errors needs to be checked (see 2.25).

３．draw a square

Elimination

１．uncheckof a signal
region２．check

４．press

Figure 26 --- Main window (manual operations of a signal region)25

25．Statistical reliability of TOCO19 analyses
The FUMI theory approximates a distribution of measurement errors as a normal
distribution of areas created by background noise, but sometimes this approximation is
not effective. The adequacy of the FUMI theory in a specific problem can be confirmedby the Histogram of measurement errors shown in the lower-right of the main window.
In the histogram of Fig. 27, the normal distribution (smooth line) coincides with the
distribution observed from real background noise (zigzag line) and the TOCO19 analyses
can be concluded to be successful. Note that the signals (white blocks) are all eliminatedfrom the noise regions (purple blocks). The histogram of Fig. 28 shows a failure of the
TOCO19 analyses due to insufficient signal elimination (left figure).

Figure 27 --- Right prediction of measurement precision

Figure 28 --- Wrong prediction of measurement precision
26．SD of area measurements for a peak in the main window
Click the FUMI equation menu, and you can obtain a theoretical SD (σ(k)) of a peakdesignated in the main window. This analysis is based on the noise in the chart.
27．Manual calculation of precision (FUMI equation)
Press the FUMI equation menu and input four parameters (SD of w, SD of m, φandpeak width (k)), and you can obtain a measurement SD (σ(k)). The FUMI equation
window also gives an explanation of the FUMI theory.
26

28．Quick display of file data on the chart
The upper limit of data in TOCO19 is 20,000 points, and the display of data close
to the limit is rather slow. In this case, checking Skip Plot in in the Chart of the Tools
menu will be able to improve the display time by decreasing the number of data
displayed in the chart. The density of the dots in the chart will look thin, but themanner of the analyses is exactly the same.
29．Explanations of labels and figures in TOCO19
The procedures to see explanations of labels and figures in TOCO19 are:1.

click labels and figures;2.

position the mouse pointer over the labels or figures when the Tooltip Assistance of
the Tools menu in the main window is checked.

This function applies to the major labels and figures, but not to all of them.
Chapter 3

Applicability of TOCO19 in theory and practice

The FUMI theory underlying TOCO19 analyses has the following assumptions:
1.

background noise is a major source of measurement errors at low concentrations in
instrumental analyses;

2.

background noise is assumed to be approximated by mixed random processes ofwhite noise and AR(1) (first order autoregressive process).

Therefore, analytical methods which violate the above assumptions are beyond thescope of the FUMI theory. If the RSD of other errors than noise is less than 7%,
TOCO19 can be considered to be effective.
The following are examples in which TOCO19 fails (based on the above-mentioned
assumptions):large sampling errors (1);large preparation errors (1);large injection errors or ionization errors (1);

too steep a slope of background in the gradient elution (2);a large amount of spike noise in background (2).

The applicability of TOCO19 can be confirmed by a histogram of errors (see 2.25).
Chapter 4

Inquiries and general feedback

Let us know your theoretical or technical questions, comments, and requests about
the FUMI theory and TOCO19 through the Contact us menu of Help of TOCO19. We
appreciate your cooperation and feedback.
27