### LTS statistics

The Tool calculates the expected life time of a reference material in several steps:

1. calculating a linear model for the measurement data $y = b_1 \times x + b_2$, where $y$ represents
measured values and $x$ represents time (expressed in month)
2. correcting the intercept $b_2$ for the difference between the mean obtained from LTS data and 
the mean reported as certified value on import $b_2' = b_2 + \mu_\mathit{LTS} - \mu_c$
3. using the corrected $b_2'$ and $b_1$ to estimate the time point when the value of the certified 
analyte is expected to exceed the interval of $\mu_c \pm U$

![**Fig.L1** LTS data as imported (top) and after adjustment for the certified value (bottom). Selecting a data point by mouse click allows to edit its comment value.](fig/L_Modul_FigL1.png)

The calculation results are depicted in **Fig.L1** and can be exported as a report in PDF format.

***Note!***
The $U$ defining the interval around $\mu_c$, which we expect the property values 
to remain in within the RM life time, is taken from the data read upon initial
Excel import. The user should be careful regarding the value specified here to 
avoid overestimating the life time. LTS monitoring, which is usually performed 
within the same lab, will cover mostly the uncertainty due to stability of a 
material property. The uncertainty defined in the original certificate will
cover additional uncertainty contributions (i.e. from the collaborative trial).
Hence, it might be adequate to use only a fraction of the certified $U$ value to
define the interval.

***Note!***
The parameters of a linear model, i.e. $b_1$, can only be determined with some 
uncertainty. While the current report layout calculates the life time based on 
$b_1$ as described above, a more conservative estimate would be to use the 
confidence interval, $CI_{95}(b_1)$, instead. Calculation based on $CI_{95}(b_1)$
is shown in **Fig.L1** by default.