I have 22 joists to replace over my basement,please advise which is the safest way to go about this,I'm very good with carpentry, but I've never replaced joists,just sistered to existing,please advise.

Sounds like a huge job - yes, you might be handy but I don't think you're doing that one on your own.

A couple of questions...
Are any wires/ pipes/ ducts in the way?
I've never had to work with fire damaged wood. Is the smell a problem? If not, then you can sister them with the new joists - this certainly seems easiest and least risky (assuming the exisitng joists are stable enough even though damaged).
Is this an insurance job or are you having to pay for it yourself?

Yeah I agree with the above post... it's not a one man job... and if you can treat the joists to kill the smell if that's a problem, that would be easier. But what you eventually going to have to do is get in there with a sawsall most likely and start cutting out joists and replaceing areas you cut with a temporary brace... like a mini moveable stud wall. That's assuming there aren't too many obstacles. Pipes etc.