It is currently taking up to 53 weeks (that's a year) to complete non precedent cases and 25 weeks to complete precedent cases.
http://alliancept.org/pdfs/credentialing_wait_times_announcement.pdf
The length of time it takes to complete PLAR depends on a few factors:
1) The amount of courses or deficient areas you need to cover
2) Your option you take to complete each deficient area e.g you decide to complete a course online, register for a classroom work or you take the option to submit proof of post qualification work experience.
All the best.