I'm sure someone a little more current can help out/correct what I say, seeing as I've been in the pool for 18 months and it has been almost 2 years since I interviewed, but the way I seem to recall.
1. SWA used to guarantee an interview to anyone who met their mins (1000 hour PIC turbine and a 737 type)
2. then they dropped the 737 type requirement to interview but if you successfully completed the interview you had 6 months to obtain the type
3. they have gone back to requiring a type rating but if you had your application on file prior to that date (not sure when it happened exactly) then you'll get a look since they seem to honor their past commitments. example: many guys had interviews scheduled or had a verbal that they were on deck to get an interview prior to 9/11. immediately after many of those interviews were postponed/canceled. But then in Jan-Feb of 02, SWA interviewed all those guys even though it didn't seem likely they were going to need them anytime soon. All of my squadron buddies that had been told 'to expect an interview soon' prior to 9/11 did indeed get an interview there in early 2002. Consequently, many got hired and the pool got large, but small price to pay for guys to get their shot.
4. Another recent change is that SWA used to put out that they offered interviews based on time in the stack. i.e. if you applied and met the minimum qualifications, then you would get called in the order you applied; with the caveat that 737 typed guys had their own (much smaller) stack and would get called first. Recently (again, not sure exactly when) they went to a 'competitive screen' whereas they decided to reserve the right to interview who they thought was more competitive. Which I take as meaning that a guy with 1000 hours of Pilatus time might not get the call before a guy with 3000 hours of 737 time even though he applied a week earlier, in the past he would have.
What is not clear is if their hiring percentages are going to go up now that they have a 'competitive screening' process. I seem to recall back in the glory days of 1999 when 5+ majors were hiring as fast as they could interview, most majors were putting out that 'we wouldn't invite you to the interview if we didn't want to hire you.' well, SWA never really put that out since they said you meet the mins, we'll interview you. Consequently I'm pretty sure their hiring percentages were more like 1 in 4 versus 3 in 4 that some majors had during the heyday.
Many guys have more experience/corporate knowledge on this subject and I'm sure they'll chime in and fix my errors.