1. A system for monitoring the clearance between a plurality of turbine blade shroud segments configured in a row and a stationary portion of a turbine, comprising; means for measuring the clearance between the stationary portion of the turbine and each of the shroud segments a number of times along each shroud segment under dynamic conditions; means for averaging said measurement to produce an average clearance value for each shroud segment; means for analyzing said average clearance values for each shroud segment to determine when the clearance between a shroud segment and the stationary portion of the turbine is approaching a critical value; and means for developing control signals in response to said means for analyzing.