Thank you Arun for your time!
Your idea is maybe only the first step to what I want but it was
nevertheless a new tool for me and interessing to learn. 

I added a "week"-column to your data set: 
dattrial<-data.frame(a=c(1,NA,rnorm(4,10)), Week=c(3,3,3,4,4,4))

I am looking for a way to count the number of rows for each week which do
contain data (without NA).
In the next step I want to create a graph which shows the week on the x-axis
and the counted number of data for each week on the y-axis. 

Thank you! 

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