"Jumping the Shark" vs. "Growing the Beard": An Analysis of the Rise and Decline of Popular Television Shows

"Growing the Beard" is the definitive moment when a series begins to become noticeably better in quality and "Jumping the Shark" is the opposite.

What is it that gives a certain TV show that first burst of success? What maintains that initial popularity, and what are the signs that a show has endured past its prime?

Focus on shows such as "Happy Days," "Firefly," "Battlestar Galactica," and "Star Trek: TNG".