The major shows will run for a few years before they change them. They have to cover the costs for development, staging, etc. Hairspray for example will be around for probably another couple of years at least. Same for Chicago on the Allure. Royal Caribbean spent several million dollars on each show, plus at least on the Alllure the initial Chicago cast was signed to 12 month contracts.
There is no set process for when shows change. The only real variable are the "headliner" shows with specialty acts like comedians and so forth. Those can vary even on a weekly basis.