The concept of a stable process is not new to the BIT service team. In the Kanban method, the definition of stability is not based on the (quite difficult) concept of assumption of stationarity but on the more intuitive notion that the arrival rate of new work items and the departure rate of completed work items are (in average) equals.
However, the bottom-line message is the same: if the process is not stable (under control), you cannot make forecasts.
Practically, it is possible to understand if the process is stable through the analysis of a chart: the Cumulative Flow Diagram (CFD).