How does the reader's understanding of the title of the play "All My Sons" by Arthur Miller change as the play progresses ?

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At the play's beginning, the reader sees Joe Keller as a likeable, decent guy who has worked hard at his business, and done so in part to leave a legacy for both of his sons--Chris, who is a surviving vet of World War II, and Larry, who is missing in action from same.  The tragic flaw of Keller is a decision he made during the war that cost twenty one fighter pilots their lives; although his son Larry did not fly these kinds of jets, it is revealed at the play's end that, devastated by his father's imprisonment for the coverup of the faulty airplane parts, Larry had committed suicide by crashing his plane into the sea near China.  Thus, Joe's tragic mistake first took the lives of many sons, other people's, and then finally, his own son.  When Joe ends his own life at the end of the play, it is to atone for the death of all of the sons who died as a result of his decision.