A systematic approach for performing a holistic reactivity insertion analysis in research reactors using the RELAP5/MOD3 code is proposed. The intention is to demonstrate, in an orderly manner, a method for determining the limiting reactivity insertion in a research reactor facility. Indispensable constituents of the algorithmic approach are the introduction of the "time-to-failure" parameter, the selection of the reactivity insertion duration, the evaluation of the control rod drop time, and the computation of engineering factors. The methodology is demonstrated through a RELAP5/MOD3 parametric study performed to determine the limiting reactivity insertion values for the Greek Research Reactor-1 (GRR-1). In the framework of this study, the core nodalization effect on reactivity limits and the degree of conservatism introduced by the engineering factors are discussed. The results obtained confirm the applicability of the approach and reveal the effect of the parameters mentioned above on the performance of reactivity insertion analysis.