Thrust-decay time is a term used in rocket engine technology. It is the time (usually in seconds) between engine cut-off as ordered by human or computer guidance input, and the actual complete loss of thrust. Usually engine cut-off is achieved by closing valves that supply propellant to the engine combustion chamber or feed pumps. However, in all practical designs the combustion chamber will still have an amount of propellant in it undergoing the chemical process (or thermal process in the case of nuclear rocket engines) that creates thrust. Thrust decays to zero when chamber pressure is equal to atmospheric pressure (essentially zero in vacuum). Thrust-decay time is not very predictable and can usually only be measured by firing tests of the particular engine.
Thrust-decay time is of some importance in rocket staging, because long thrust-decay times can cause catastrophic collisions between stages if the next-stage rocket engine experiences thrust variations.
However, thrust-decay time is a critical variable in vertical landings of rocket-powered spacecraft (like the Lunar Module or the DC-X) or aircraft, because in the time between actual touchdown and complete loss of thrust the vehicle is highly unstable and may topple over.