Frequently test models are used that contain two or more magnitudes with some degree of correlation, that is, that systematically, when modifying the value of one of them, the other increases or decreases. The correlation coefficients between two variables vary between -1 and 1, where the value indicates the strength of the correlation, while the sign indicates the direction. In this way, we understand that if the correlation is = 1 there is an absolute direct proportionality between the magnitudes whereas if the value is -1 the proportionality is inverse. On the other hand, a zero value for the correlation coefficient indicates that the variables are independent.
If we know the correlation coefficients between the magnitudes of the mathematical model of our trial we can use the correlation panel. The correlation matrix is automatically constructed with the variables of our model so that we indicate the correlation coefficient between them. When we complete the matrix, click on the < connect to the project > and after checking that the matrix is correct, the green light of the button will indicate that it is connected.
In this case, the simulation will be done with correlated variables. If at any time we want to work with independent magnitudes again, we only have to uncheck the checkbox < correlated > on the simulation button. In this way we can alternate between both states without correcting the correlation matrix each time.
This distribution is not a distribution in itself, but a powerful and exclusive form of MCM Alchimia to enter raw values of repeatability to the model of our trial without having to make any kind of previous operations in a spreadsheet.
To the left of the panel we have 5 radio buttons (selectors), which will indicate to the software the form in which the input data will be entered. We will then have 5 input forms:
In the upper right corner of the MCM panel Alchimia has a field where we must indicate the number of repetitions to which we want to estimate the simulation parameters, that is, the mean and the standard deviation of the stockings By default the application has 10 values, however this value can be changed by manually editing the number or with the increment / decrement arrows.
This section of the panel provides two ways to perform the simulation from the parameters of the previously defined distribution from the entered values:
It is usual to assume in all types of analyzes, tests or calibrations, that repetitive events without external stimuli that vary their probabilities, will be distributed according to a normal or gaussian distribution defined by the mean and the standard deviation calculated for the sample. Strictly speaking this is only true when the number of repetitions is large, consistent with the central limit theorem, however when we do not have enough information to describe the properties of this gaussian distribution because our study sample is not large enough, suppose that these conditions are also fulfilled, we will surely throw values of uncertainty underestimated for our measurement, as indicated in the guide JCGM 100 – Guide to the expression of uncertainty in measurement.
The continuous triangular distribution is characterized by being bounded to two extremes as in the case of the rectangular, but also has a mode (or value more probabe) within that range. The probability in any subinterval of equal length will increase linearly until fashion and then descend in the same way to the upper bound. This distribution is widely used in variables where information is limited, as in the case of the uniform, but where we have an approximate knowledge of the Modal value, that is, where, although the exact point of this value is not known, has information of the region or subinterval where to find it.
This continuous distribution is characterized by having the same probability for any value of the interval. It is widely used for contributions of type B uncertainties in which only the major and minor dimensions of the interval are known, for example in the division or resolution of a digital instrument. In many cases this distribution can also be assigned when there is little information about the random variable, in bibliographic data or when the coverage factor of an uncertainty is not known,
This distribution is the one that most frequently is representing natural and social events. Much of the evidence from classical statistics, as well as the estimation of uncertainties, is based on the assumption that the data conform to a normal distribution. From the theoretical perspective, the Central Limit Theorem maintains that given a random sample of sufficiently large size, it will be observed that the distribution of means follows an approximately normal distribution. The general formula of this distribution is:
This distribution represents random variables whose logarithms are distributed according to a normal distribution. The lognormal distribution takes different forms depending on the value of its scale parameter and is often used in the reliability of high technology products and also in microbiological counts since they are based on the multiplicative growth model.
This continuous probability distribution in the field of positive reals is intimately related to the Normal distribution, for example, it is the sample distribution of σ². The Xi (or Chi) Square distribution is defined with a single parameter which are degrees of freedom. The function is always asymmetric and biased to the right. This distribution is very frequently used in various branches of science since it allows analyzing data sets and determining if the difference between them is due to chance (null hypothesis) or to another external factor.