I took what you are writing as separate sentences as I couldn't figure our how to tie them together this seems like it may be part of a larger article.  You are referring to "processes" and "solutions" but since I don't know the context it is hard to make corrections:

Exercise allows the body to remain flexible which is significant for firefighters, due to encounters of a variety of complex missions.

This technique allows for flexibility as well as increasing the ability of the process to create complex parts, which has received considerable attention recently.

Defining a solutions path is one of complexities of analyzing of the process. I don't see that a solution has a path as it would be an answer....maybe reword or explain your solutions/processes

According to the solution's path equipment of the process was designed and manufactured.

We have designed and manufactured equipment specifically to streamline the process.

I stopped here.  It is too early, i'll come back and attempt to make more corrections after my second cup of coffee.  The terminology and the points you are trying to make seem, almost industrial in nature and it is too early for my brain to be of any use. ^_^
The analysis indicated that "A" has extremely less proportion compare with "B".

Therefore, suitable pressure created at the tool and part conjunction, due to higher height at the point.