Help Documentation of S updated.

inst/app/www/rmd/help_start.Rmd

@@ -34,8 +34,13 @@ output:
 ```
 
 <style>
-p.caption {
-  font-size: 0.75em;
+div.figcaption {
+  font-size: 0.8em;
+  background: rgba(0, 0, 0, 0.04);
+  padding-top: 2px;
+  padding-bottom: 2px;
+  margin-top: 4px;
+  margin-bottom: 10px;
 }
 </style>
 

inst/app/www/rmd/lts_fig_L1.Rmd

@@ -2,13 +2,31 @@
 
 The Tool calculates the expected life time of a reference material in several steps:
 
-1. calculating a linear model for the measurement data $y = m \times x+n$, where $y$ represents
+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 $n$ for the difference between the mean obtained from LTS data and 
-the mean reported as certified value on import $n' = n + \mu_\mathit{LTS} - \mu_c$
-3. using the corrected $n'$ and $m$ to estimate the time point when the value of the certified 
-analyte is expected to exceed the range of $\mu_c \pm U$
+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.
+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.

inst/app/www/rmd/stability_uncertainty.Rmd

@@ -2,22 +2,26 @@
 
 The parameters of all linear models are collected in **Tab.S1** and the potential
 uncertainty contribution of the material stability is obtained from formula 
-$u_{stab}=|t_{cert} \times err|$ where $t_{cert}$ is the expected shelf life of
-the CRM (in month) and $err$ is the standard error `SE` of the slope of the linear model.
+$u_{stab}=|t_{cert} \times s(b_1)|$ where $t_{cert}$ is the expected shelf life 
+of the CRM (in month) and $s(b_1)$ is the standard error `SE` of the slope of 
+the linear model.
 
-The expected shelf life can be set by the user and should incorporate the time until
-the first certification monitoring and the certified shelf life of the material. 
-This estimation of stability uncertainty is based on section 8.7.3 of ISO GUIDE 35:2017
-and valid in the absence of a significant trend.
+The expected shelf life can be set by the user and should incorporate the time 
+until the first certification monitoring and the certified shelf life of the 
+material. This estimation of stability uncertainty is based on section 8.7.3 of 
+ISO GUIDE 35:2017 and valid in the absence of a significant trend.
 
-To determine if the slope $m$ is significantly different from $m=0$ we perform a t-test by 
-calculating the t-statistic $t_m = |m| / s(m)$ and comparing the result with the two-tailed 
-critical value of Student's $t$ for n - 2 degrees of freedom to obtain the P-values in column `P`.
+To determine if the slope $b_1$ is significantly different from $b_1=0$ we 
+perform a t-test by calculating the t-statistic $t_m = |b_1| / s(b_1)$ and 
+comparing the result with the two-tailed critical value of Student's $t$ 
+for n - 2 degrees of freedom to obtain the P-values in column `P`.
 
 ![**Tab.S1** Calculation of uncertainty contributions from stability assay](fig/S_Modul_Tab1.png)
 
 ***Note!***
-Clicking on a table row will display the analysis for the analyte specified in this row.
+Clicking on a table row will display the analysis for the analyte specified in 
+this row.
 
-Values from column `u_stab` can be transfered to the material table of the certification module 
-in case that matching analyte names are found (analyte names are depicted in red if not found).
+Values from column `u_stab` can be transferred to the material table of the 
+certification module in case that matching analyte names are found (analyte 
+names are depicted in red if not found).