We propose a method by which the set of linear extensions of an interval order may be partitioned into sets of linear extensions of weak orders, using so-called marked configurations of the interval order. The technique relies heavily on the natural linear ordering of maximal antichains in interval orders. We also propose a method whereby sets from this partition can be generated with known probability so as to permit efficient cluster or staged sampling. These techniques, among other uses, may be applied to generate sampling estimates of average rank score statistics for interval censored data similar in construction to that proposed by Prentice (1978) for right-censored data. Keywords: interval censoring, interval orders, weak orders,rank score,nonparametric inference 1 Introduction One of the most intuitively useful facets of a partial order (X; OE) is the set of its linear extensions, that is, the set of all linear or complete orders compatible with OE. This usefulness stems in ...