Determination of the mathematical model of the trial

In this step two we will define the mathematical model of the essay. The ISO 4787 guide details two calculation methods to obtain the volume contained in a volumetric flask. The first one indicates the calculation of the volume integrating all the magnitudes participating in the model into the equation. For a test, particularly for a defined temperature, a defined building material (glass), etc. Many of these values, such as water density and coefficient of expansion, can be considered constant, so this standard also proposes a tabulated factor to simplify the calculation. In this case we will use the complete equation to study the variables and their associated uncertainty. The equation (test model) will be:

The equation editor of MCM Alchimia is an ASCII editor that does not have special characters for which the Greek letters will have to be replaced by a common variable name. The main equation that will be put in Set equations will be V20 = ((Ml-Mv) / (Dens_w-Dens_a)) * (1- (Dens_a / Dens_b)) * (1-CDT * (t-20) ) where:

V20: Volume of the flask at 20ºC.
Ml: Mass (read on the scale) of the flask flush with detilated water (g).
Mv: Mass (read on the scale) of the empty flask (g).
Dens_w: Density of the water used in the calibration (g/ml).
Dens_a: Air density (g/ml).
Dens_b: Density of the masses with which the scale has been adjusted (g/ml).
CDT: Coefficient of cubic thermal expansion of the flask material (in 1/ºC).
t: Test water temperature (ºC).

It is advisable to make a deeper analysis of the sources of uncertainty of the input quantities of the model. In this way, if any magnitude has more than one source of uncertainty, it will be broken down into a sum of as many variables as there are sources of uncertainty, one of them will take the value of the magnitude and the rest will have zero value since they are added only for the purpose of evaluation of uncertainties.

More help

• First project – Step 1
• First project – Step 2-A: Basic model
• First project – Step 2-B: Input uncertainties
• First project – Step 2-C: Final model
• First project – Step 3.
• First project – Results.

Several estimations of uncertainty made with MCM Alchimia for advanced models of tests, calibrations or analytical techniques, can be consulted in several published scientific works, both by the software developer, as well as by other researchers in various branches of science. However, for a first contact with the application, in this document we will make a first simple calculation project to know the operation and the possibilities of the application. As an example, we will perform the calculations relevant to the calibration process of a calibration calibrated by the gravimetric method, consistent with the guide ISO 4787: 2010 Laboratory glassware – Volumetric glassware – Methods for use and testing of capacity

• Run the application from the desktop. Estra will already open in step 1.
• We write in the field Title : Calibration of a volumetric flask according to ISO 4787: 2010
• In the field Technical data we replace the pre-existing text with the technical description of our essay. There we can write the following text:
  This project consists of the evaluation of the calibration uncertainty of a 100 ml volumetric flask by the gravimetric method with ISO 4787: 2010. For this, a calibrated 1 mg division scale is available, with its calibration certificate, which tells us that if we assign the maximum correction of the reading in the working range to the uncertainty, it results in an expanded uncertainty of 0.0054 g for k (coverage factor) = 2.
  We also have a mercury glass thermometer of 0.01ºC, which also has a calibration certificate that indicates that at 20.00ºC it has an error of -0.022ºC and an expanded uncertainty of 0.012ºC for k = 2.
  The flask will be completely dried in an oven, cooled to 20°C, filled with distilled water and then weighed on the scale. This operation will be performed 5 times, taking the 5 mass values. To the average of these 5 mass values ​​and the temperature of the water filling, the equations of the standard will be applied to convert the mass value in Volume contained by the flask to 20ºC
• Having entered this data we can continue to the next step. By clicking on the link or the Step 2 button.

More help

• First project – Step 1
• First project – Step 2-A: Basic model
• First project – Step 2-B: Input uncertainties
• First project – Step 2-C: Final model
• First project – Step 3.
• First project – Results.

Although the MCM Alchimia interface has been designed in a modern way, it is also simple and intuitive enough so that the estimation of uncertainties of the test models, can be carry out by technicians who do not necessarily have computer or statistical skills. To facilitate access to the different software features, this interface was designed sequentially and with almost no nested menus. The interface consists of the following sections:

1 .- Main menu: This menu consists of only 6 buttons that manage the files and documents of the program as well as the language modules:

	Save: Allows you to update changes in a previously saved model. If you are working on a new model, it produces an effect identical to the Save as button.
	Save as: Create a new model file with the information added in the screen. The saved model will contain the model information and input quantities with information about its probability distribution function. This option does NOT allow to save curves connected to the model.
	Load model: loads the information of a previously saved model.
	Print results: Send the input data and results of the simulation project to the printer.
	Change language: This option allows you to change the active language of the application’s interface. The detailed procedure for changing the language of the application can be found by following this link .
	Info: Display property data of the application.

2 .- Application bar: : It fulfills the classic functions of the Windows title bar. From this area you can move the MCM Alchimia window through the screen.On the right contains Minimize, Close and Help icons.

3 .- Sequential menu: It determines the work flow recommended for the preparation of a project to estimate measurement uncertainties. While the application allows you to go from one step to another just by pressing the button, it is highly recommended to complete the fields, text areas and drop-down menus each step. In this way, you can not only obtain reliable results, but also reuse the project saved in the future, easily referencing the input data.

• Step 1 .- Project information. This panel allows to indicate a title and the technical description of the project. These fields are part of the final results report that can be sent to the printer, so it is advisable to complete these fields.
• Step 2 .- Model definitionThe upper field of this panel is an equation editor where you must indicate the mathematical model of the test. To break down the contributing parameters of the typed model just click on the Update Parameters link and the application will divide the mathematical model you typed, automatically filling the lower list of that panel, the one of step 3, and correlations matrix with null values.
• Step 3 .- Simulation data. In this panel, the operational characteristics of the simulation are determined. The number of iterations indicated here will determine the size of the vector of pseudo-random values that each variable will contain and, consequently, the amount of output values obtained for the measurand. At the top right, the probability of coverage for the uncertainty analysis may be chosen and in the lower part of the panel, the probability distributions for each contributor are indicated.
• Step 4 .- Correlations matrix. This panel allows the analysis of models with correlated variables, taking into account covariances between them. The parameters of the correlation matrix are automatically filled when the model is defined. The correlation values must be typed manually with values between -1 y 1.
• Step 5 .- Results. After executing the simulation, a list of results and statistical data of the vector is obtained. This panel opens automatically after finishing the simulation.
• Regression data. This version of MCM Alchimia includes support for regression and curves (calibration curve / linear regression), in order to use an interpolation of the curve (in both directions) in the math model of the test.

4 .- Work panel: This is the area of the screen where information is exchanged with the user.

5 .- Simulation button: This button remains inactive until all the necessary data for performing the simulation have been fulfilled. When the probability distribution functions have been indicated for all the parameters of the model, this button lights up allowing to run the simulation and obtain the result of the calculation with its associated uncertainty.

More help

• Installing MCM Alchimia
• Activate the application
• Set your default language
• How to understand the application interface
• Tips and tricks to become an expert in MCM Alchimia

MCM Alchimia can be downloaded in English and Spanish versions by clicking download buttons on the application’s website. Nevertheless, at any time, you can download a new language module (or even generate a new language online) and install it in the application:

• Check if there is a plugin for the language you are looking for, following this link.

1. If the language you are looking for exists, you can download it by clicking on the link with the name of the language.
2. If the language you are looking for does not exist, you can generate it by translating manually the terms from English to your language using the form below. The terms that are not translated will remain in English in the application.
3. By pressing the Submit button at the end of the form, a language file with the extension “.mcl” will be downloaded.

• Click on the button Install language file
• Select the downloaded language file and click Open
• Then MCM Alchimia offers you to use this language as default.If you wish so, click accept, otherwise the software language will be changed back to default language on the next run.

NOTE: Does the language file correspond to an earlier version?
As new software is updated, new terms may appear or change, on account of new specifications or possibilities of the software. In these cases it is possible that the language file has not been updated yet containing fewer terms than necessary.
What to do: In these cases the software automatically solves these problems by adding the missing terms in English. You only need to press Accept in that window and continue.

More help

• Installing MCM Alchimia
• Activate the application
• Set your default language
• How to understand the application interface
• Tips and tricks to become an expert in MCM Alchimia

The licenses of MCM Alchimia have a duration of 1 year and they are totally free.The first time you run the application after installation, you will see a screen with two fields called Short key and Long key. The same will happen after one year using the application with those keys. To activate MCM Alchimia follow these steps:
Run the application. A window with graphic indications to activate the software will be displayed

1. Click on the indicated link to get a free featured one-year licence.
2. If the previous action does not open the web browser on the MCM Alchimia page, follow this link.
3. Copy the short key text in the web page and paste it in the namesake field in the application. Next, do the same with Long key text.
4. Click on Continue button
5. If a message appears saying Successful !!!, that indicates that the program is activated correctly. Now you can press the button Close to start using the application or just wait 5 seconds.
6. If an error is raised, refresh the web page (keys will updated as well) and re-copy the keys in the application’s fields.

More help

• Installing MCM Alchimia
• Activate the application
• Set your default language
• How to understand the application interface
• Tips and tricks to become an expert in MCM Alchimia

MCM Alchimia infinito is the new version of MCM Alchimia. It is a free desktop application that works only in Windows operating system and allows for the estimation of measurement uncertainties by means of the Monte Carlo method. This uncertainty estimation method is consistent with the following reference standards:

• GUM 1995: Guide to the Expression of Uncertainty in Measurement.
• JCGM 101:2008 – Evaluation of measurement data – Supplement 1 to the “Guide to the expression of uncertainty in measurement” – Propagation of distributions using a Monte Carlo method.
  
• EURACHEM / CITAC Guide CG 4. Quantifying Uncertainty in. Analytical Measurement.

Installation of MCM Alchimia in Windows

1. Download the installer using the buttons on this page’s header.
2. If necessary, select Run or Save.
3. If you select Save, double-click on downloaded file to start the installation.
4. You must accept the conditions and then follow installer’s instructions.

NOTE: Is there incompatibility with your Antivirus?
Some antivirus categorize as suspicious file and even, in opportunities, erase the installer of MCM Alchimia .That is due the software is relatively new and does not have a digital signature. However, no antivirus will find viruses or malware in the installer application.
If this is the case, in order to install the application, right click on the antivirus icon and select “deactivate shields for 10 minutes” then retry the installation.

More help

• Installing MCM Alchimia
• Activate the application
• Set your default language
• How to understand the application interface
• Tips and tricks to become an expert in MCM Alchimia