One of Willy's major delusions in Death of a Salesman is his conjuring of Ben. Whenever Willy begins to think about his dreams, he imagines talking to Ben about making it big. The audience knows that Ben died long ago; however, Willy constructs Ben's persona as if he were alive and well. Willy's hallucinations go much farther than simply remembering times past with Ben--he imagines that he tells Ben about all that is going on in the present. Therefore, Ben represents a form of Willy's madness. In the play, Willy's madness is created by his illusions of what he believes is the American Dream, so his delusions are all rooted in Willy's irrational efforts to achieve "the dream."
Willy Loman gives himself over to many delusions in Death of a Salesman. One could make a distinction between the delusions (lies) he believes in and the madness he seems to be falling into--or one could argue that Willy's failing mental state is just a continuation of his failure to live in reality most of his life. The primary example of his madness, if one wants to call it that, is his interaction with Ben, his brother who is not really there but with whom Willy keeps falling into conversation. Another example of his madness is his tendency to lapse into the past and have conversations aloud that relive past events. In Act One, while Biff and Happy are upstairs, Willy is downstairs talking to himself, reliving the past. Happy goes down to try to get him to go to bed.
Beyond these obvious disconnects with reality, Willy lives with many delusions--lies he tells himself and others. He often lies to Linda about how much money he has made on a sales trip, grossly inflating his success until she pulls the specifics out of him. He allows himself to believe that Biff was a top salesman for Bill Oliver, when in fact he was only a shipping clerk. He says that he never told the boys to steal, when it's evident that he taught them to steal from the nearby construction site and downplayed Biff's stealing balls from Oliver. He also conveys to Bernard that he doesn't know what came over Biff, causing him to not go to college, but in fact he knows that Biff did it "for spite" because of Willy's affair.
As Biff says, "We never told the truth for ten minutes in this house!" Willy has willfully deluded himself for most of his life, perpetuating lies about himself and others to make himself feel important. Those delusions take over at the end of his life, causing a disconnect with reality that can be considered a type of madness.