Arthur Miller seemed to favor Dunhill My Mixture blends, but was known to smoke other stuff as well, like Walnut.
As to which specific My Mixture I don't know and he may have even had his own personal numbered blend in the books,
you can tell by the 'paint can' style of tin that it was blended at American Dunhill stores:
...although the tin he's using as a catch-all for his pipes appears to be an English-made cutter-top:
"This is a subject as dear to pipemen as their bowls. No one knows how many blends of tobacco there are—Dunhill alone has a list of 50,000, plus its branded blends. Pipemen spend months and even years concocting a blend that suits them, and virtually every pipeshop of any pretensions caters to these amateurs. So the smoking of a pipe, a capital‐intensive avocation, tends to be a vocation for those who take it seriously."
Above quote from an Oct. 6th 1975 NYT article which mentioned Miller, and it's a rather in-depth piece that even mentions estate pipes:
"Pipes of good briar, which are made from the root of the bush, seem to last, if not forever, at least a long time, for there is a brisk business in used ones.
And passing along one such is rated as an act of special friendship."
And Tom Dunn from TPSE even makes an appearance!
I enjoyed reading it: