Let \(A\) be a finite dimensional basic algebra over an algebraically closed field \(k\) and let \(1=\sum^ r_{i=1}e_ i\) be a decomposition of the unit element of \(A\) into primitive orthogonal idempotents. For given \(e_ i\) let \(\Gamma_ i\) be the full translation subquiver of the Auslander-Reiten quiver of \(A\) supported by all indecomposable \(A\)- modules \(M\) with the property \(e_ iM\neq 0\). The author proves that the following statements are equivalent: (a) For all \(i=1,\dots,r\) the quiver \(\Gamma_ i\) is the Auslander-Reiten quiver of a representation-finite poset. (b) For all \(i=1,\dots,r\) the quiver \(\Gamma_ i\) is finite and has no oriented cycles. (c) \(A\) is locally representation directed. (d) Every indecomposable \(A\)-module \(M\) is a brick, i.e. \(\dim_ k\text{End}(M)=1\).