System effectiveness in crude oil processing industries can be constrained by operational efficiency of the constitutive units. Thus ascertaining availability status of all system units can provide decision makers with an effective means of improving the technical performance of complex processing systems. Most of the works found in literatures focused on either models specifically for estimation of interval, instantaneous or stationary availability with specific repair distributions or models with mathematical complexities whose underlying assumptions impose ample application constraints to industries. This paper proposes a proof of concept compact generalized model for determination of availability of complex processing industries. The approach is clearly presented as an off-shoot of earlier but independent availability models (Lie et al. 1977, Ebeling, 2010). The applicability of the models has been illustrated using data obtained from a typical crude oil refinery company located in Nigeria. The unit availability for the studied period as well as mean annual availability of the system can all be computed with the models. The lowest and highest availability values recorded for the units were 0.083 and 0.692 respectively at the Kero Hydro-treating unit and second boiler unit. The mean system availability during the period stood at 0.451. The result shows that the proposed model is a good means of computing system availability. The results have also updated decision makers support tools for system performance improvement.