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So I guess that for Part 91, a piece of equipment doesn't have to be TSO'd?
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Yes and no.
If something is going to be permanently installed on an aircraft and it does not have an STC or it is not original equipment/official replacement for original equipment it MUST be TSO'd for Part 91 ops.
So, for example, when we replaced our Attitude Indicator, Turn and Slip Indicator and our Magnetic Compass we had to replace each with a TSO'd version because we were not replacing them with new "identical" instruments.
As DE said all TSO means is it meat a "stricter" set of certification standards. It could be nothing more than every piece of equipment is actually tested (as oppesed to every fifth piece, etc.) or it could meant they use "better" parts for the TSO'd version. All that really matters is TSO'd stuff can fail just like non-TSO'd stuff and it costs more, usually a lot more.
PMA is similar to TSO when it comes to implimentation but it's more along the lines of "I'm going to replace my Gizmo with the identical Gizmo and on my airframe this particular Gizmo is PMA'd for use (meaing it doesn't need to be TSO'd in order to mount it)."
When you're dealing with an olde raircraft, essentially, EVERYTING you want to add to it needs to be TSO'd because finding original equipment is almost impossible - short of overhauling what you have.