To what extent can Willy Loman be considered a tragic hero?

The protagonist of the play Death of a Salesman, written by the prominent American playwright Arthur Miller, is a man named Willy Loman. Willy has a great number of flaws, so it could be argued that he cannot be considered a tragic hero. The notion of a tragic hero is an alluring one for readers nowadays: that a great and virtuous character could fail merely because fate so dictated is a bewitching concept. In this case, however, our protagonist may not be a tragic hero as he does not measure up to the stature of a great and good man: there are too many vices staining his persona.