Is it ethical to use proprietary (closed-source) software for scientific computation? I have data from an ordinary scientific experiment. Now, in order to analyse the data, the most convenient way for me is to use some proprietary, closed-source software. 

Is it ethical to use such kind of software in research? 

If do use it then this part will be a big black-box in my research. So if someone cannot reproduce my data analysis with the same or with some other software, then it depends on the mercy of the software company if we can find out what went wrong. If the software company does not want to cooperate, then what went wrong might never be found out. I have the feeling that this opposes the principles of science.
I do not think that this is an ethical question in the first place. Reproducibility is not harmed by the requirement that money needs to be spent on buying software or setting up an experiment (or are there open-source particle accelerators?).

While open source solutions are preferable for many reasons, there are clearly cases where using some proprietary software P is appropriate:


When it is known (and has been verified) that P's implementation of method M is correct while the known open-source implementations of M have not (yet) been established as reliable. Conversely, when open-source implementation O is known to give correct results whereas for P this has not been established, then clearly O should be used when there is a choice.
When one can reasonably expect that P is widely available in research institutions (and thus to researchers), like for example certain mathematical / computational packages.
When P allows for a much more (time-/resource-)efficient execution of experiments.
When P is a software package needed anyway to extract / process data from a big-ticket instrument.


Note that I am assuming that P can actually be bought by anyone. If P is not commercially available but rather a closed-source in-house solution then an open-source package is preferable.