Operation safety should be paid more attention for chemical reactor systems in the presence of uncertainty and time delay to prevent environmental pollution events and human injury. The uncertainty deviation maybe unadjustable during the practical operation

such the maximum tolerable delay of chemical reactor systems under uncertainty should be figured out to guarantee the operation safety. A delay tolerability index problem (DTI) and computing framework is proposed to find the maximum tolerable delay for continuous chemical reactor systems. Firstly the continuous reactor system is linearized by Taylor series spreader formula and modeling as transform function by using Laplace transform. Secondly the dynamic response performance is tested for the system with PID control

where the control action is optimized by the nonlinear control design package (NCD). Finally the delay tolerability index problem (DTI) is figured out based on the bisection search method combing with dynamic response analysis. A continuous reactor-separator system is investigated to compute the maximum tolerable delay index when the expected uncertainty deviation is considered as unadjustable condition during the operation. The analysis results demonstrate that the proposed framework/strategy may provide a simple and effective tool for the computing and application of delay tolerability index (DTI)

which is also useful for the operation safety and reliability of chemical reactor system under uncertainty.