The operation of packed bed tubular reactors, for exothermic catalytic reactions, presents special challenges provoked by hotspot development. Their potential safety risk can be assessed using different mathematical methodologies, among them, the so-called parametric sensitivity analysis (PSA). This study deals with the identification of safe operational conditions (e.g., feed temperature conditions) for the catalytic oxidation of o-xylene. Three different reaction networks, with different degrees of complexity, were analyzed. Thus, the critical values of the operating parameters, allowing us to define run-away and stable operation conditions, were provided for different reactive configurations. The obtained results were compared with the data reported by various authors who used similar reaction rate laws. The purpose of the present study is to illustrate the peculiarities of the PSA and its application for the design, analysis, and operation of o-xylene multitubular catalytic reactor.