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A drill-down on a MAD means giving "more detail" by descending the dimension hierarchies. It is proposed in Gray et al. (1996), and subsequently in Lehner (1998), Nguyen, Tjoa, & Wagner (2000), and Pedersen, Jensen, & Dyreson (2001).
An implicit aggregation function, e.g., count or sum, is assumed. Thus, a drill-down corresponds to performing aggregate formation on "lower" category types with the given aggregate function. To get to the lower category types, a reference to the original MAD is needed. In fact, this operator is, in reality, a facility for retrieving the original MAD after having applied the roll-up operator to it. It cannot be applied to any MAD without the previous operation, because we are not able to generate more disaggregate data than the original MAD carried out by the aggregation process. In other words, only if we know a disaggregative law which estimates the distribution of the summary data (probabilistic data) are we able to compute (to estimate) such data.
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