“There are many factors that affect the security of an operating system or application, from the code level to the user level. Whether or not the source code is open is probably one of the least important factors.”

The use of Open Source software such as PHP and Ruby on Rails is widespread and in the opinion of Savantis is no less secure than Closed proprietary software. There are some compelling arguments for adopting Open Source, such as the reasons given here - Why Open Source Software.

. “In short, the effect on security of open source software is still a major debate in the security community, though a large number of prominent experts believe that it has great potential to be more secure.”

There are also sceptics : here, but even in this article there are concessions:

“Comparing all open source software with all commercial software is tough. Certainly, when it comes to security, there are good cases and disasters in each camp. I do believe that from a security point of view, Apache is probably better off than Microsoft's IIS and that djbdns is better off than almost anything competitive. While I do think the open source community has a long way to go in general, I don't think it is necessarily worse on the whole. I would evaluate it only on a case-by-case basis. In the end it doesn't matter if open source systems tend to be more secure than proprietary systems, because on the whole they aren't yet coming close to being "secure enough."

Further strong arguments for not using Open Source come from DevX’s Executive Editor A. Russell Jones, but these opinions are challenged extensively here.

In the end, in the words from this article sum it up...

“There are many factors that affect the security of an operating system or application, from the code level to the user level. Whether or not the source code is open is probably one of the least important factors.”

Indeed Open Source is under continual scrutiny. There is an initiative by the US government to improve the security of Open Source software.