In OLAP models, or data cubes, aggregates have to be recalculated when the underlying base data changes. This may cause performance problems in real-time OLAP systems, which continuously accommodate huge amounts of measurement data. To optimize the aggregate computations, a new consistency criterion called the tolerance invariant is proposed. Lazy aggregates are aggregates that are recalculated only when the tolerance invariant is violated, i.e., the error of the previously calculated aggregate exceeds the given tolerance. An industrial case study is presented. The prototype implementation is described, together with the performance results.