Green’s Dictionary of Slang

Andrew Millar n.

also Andrew Millar’s lugger, Andrew Miller, Andrew Miller’s lugger
[generally accepted as a ref. to a contemporary RN Lieutenant (see andrew n.2 ); note also Shakespeare’s Merchant of Venice (1596): ‘But I should think of shallows and of flats, And see my wealthy Andrew dock’d in sands’; although cited as ‘ship, esp. of war’ in the OED, the capital may simply imply the name of a given ship]

(orig. naut.) a man o’war.

[Aus]Vaux Vocab. of the Flash Lang.
[US](con. 1843) Melville White-Jacket (1990) 15: And what did you know, you bumpkin! before you came on board this Andrew Miller? What knew you of gun-deck, or orlop [...] and piping to dinner?
[UK]Hotten Sl. Dict. 67: Andrew Millar, a ship of war.
[UK]D. Sladen in Barrère & Leland Sl., Jargon and Cant I 38/2: Andrew Miller’s lugger, a vessel of the royal navy, is smugglers’ slang taken out to Australia by the convicts, and is used by accomplices in warning the smugglers of the approach of revenue cutters, &c.
[Aus]‘Sea Slang’ in Brisbane Courier 27 Feb. 7/2: [orig. Chambers Jrnl] A curious cant name for a ship of war is ‘Andrew’ or ‘Andrew Millar.’ Its origin is quite unknown.
[Aus]C. Crowe Aus. Sl. Dict 4: Andrew Miller, a war-ship.

In compounds

Andrew Miller’s coach-whip (n.)

some form of on-board flagstaff.

Launceston Examiner (Tas) 12 Aug. 6/1: Has the royal yacht her sails bunted and furled like her? There’s her coachwhip, old ‘Andrew Miller’s’ coachwhip, and her bit of faded red bunting, at the peak hanging ‘straight up and down’ never to be lowered to a foreign hand.