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This paper deals with a method of estimation of robust dead-time for first order plus time delay (FOPTD) process which does not violate the closed loop stability when Proportional-Integral (PI) parameters and Proportional-Integral-Derivative (PID) parameters as suggested by popular tuning techniques, have been used. Using the Hermite-Biehler Theorem applicable to quasi polynomials, we estimate the lower bound value of (T/L) and then the range of L for the two controller modes. This investigation will help to infer the amount of system parameters that can be tolerated before control system becomes unstable for the two controller modes.