How far can we say that the play is a Tragedy?

All my sons was wirtten in the 1940's a short period after the second world war and it is based around the events that happened during the war that involves the keller family. Straight away from the time period we know that something dramatic will happen or has happened to this family as the war has an enormous affect on everyone.
The dictionary definition of Tragedy is : a dramatic composition, often in verse, dealing with a serious or somber theme, typically that of a great person destined through a flaw of character or conflict with some overpowering force, as fate or society, to downfall or destruction.
so how many of these characteristics of tragedy can we see in "All my sons"? so first thing of we see the serious and or somber theme of the after affects of the war, we may not be told the affects of it at first but it is still there in the background, looming.
Then we are told of the great flaw, of the fate filled day that Joe was "sick" this then leading to his inevitable destruction.
This character flaw effects the lives of others, including that of his son Larry, who kills himself, chris and kate who in the end lose their brother and their mother and Joe himself who comits suicide.

So considering we have two suicides, two great losses, all the effect of a fanatical flaw we can consider this to be a tragedy.