Introducing redundancy into facility layout designs reduces material handling costs by shortening the total distance travelled by materials and tools, since redundancy allows for shorter flow routes. In our setting, jobs and volumes (demands) are random, and machines have limited capacities. We present a model for determining which machine types should be duplicated (i.e. having more copies than necessary), given the number of extra positions available in the facility. The model is naturally an extension of the quadratic assignment model, and hence very hard, if not impossible, to solve exactly for even moderate problem dimensions. A myopic approach is proposed. We show numerically that the myopic approach is valid, before we, qualitatively, based on the approach, describe a decision-rule determining a good choice of redundant machine types. This very simple description produces the optimal choice of redundant machine types in most situations. In this way, our results add to the understanding of the problem itself, not just to its solution.