Can anyone recommend freeware (if possible) QbD and Statistical Analysis software? Ideally something similar to SAS JMP (a hefty task, I know). Anything can help!
Are you looking for complete range of solutions are specific to topics such as DOE, process monitoring, multivariate etc. It is good to use open source but in case you want to work in regulated environment, that could be a challenge. Apart from above try SAS university edition, softstat or data language tools
R - project Programming Language seems to be the best option for OpenSource, see 4 likes for http://alternativeto.net/software/jasp/ vs 121 for R at the same link.
I suspect: if you try to find/ search at the community from R... then you will get plugin, extension or subproject for regulated environment if needed, or at least you can pay to a developer to customize those needs.
next a sample search http://alternativeto.net/browse/search?q=statistical+analysis+doe I suggest you try the search that fit your needs, get familiar with tags on alternativeto.net the site is user maintaned so not everything are posted or at the velocity one might want.
Dear Jehad, depending on your budget, design complexity and desired output (mainly in graphical terms and for instance inference on suitable acceptance "spaces") options include general purpose calculation tools as a scientific calculator or Excel as all the calculations involved are fairly simple. However if you can afford it I would advise to get a package like Modde from MKS or JMP from SAS (the ones I'm familiar with). Design-Expert is also a common choice but I never used it as I'm very happy with Modde which is quite powerful yet does not requires a heavy load on learning to use it - there's also lots of free courses and learning material from the software company. I found JMP more powerful but more expensive and requires more effort to learn (my opinion/experience).
You will be able to find R packages to perform the design, analysis and plotting (all for FREE) as already pointed out by Jose Castroesquivel.