The time on stream during which the
rate constant for the catalytic reaction,

, falls to a specified fraction of its original value, often 0.5.
Source:
PAC, 1976, 46, 71
(Manual of Symbols and Terminology for Physicochemical Quantities and Units - Appendix II. Definitions, Terminology and Symbols in Colloid and Surface Chemistry. Part II: Heterogeneous Catalysis)
on page 83