The use of chemical kinetic mechanisms in computer aided engineering tools for internal combustion engine simulations is of high importance for studying and predicting pollutant formation of conventional and alternative fuels. However, usage of complex reaction schemes is accompanied by high computational cost in 0-D, 1-D and 3-D computational fluid dynamics frameworks. The present work aims to address this challenge and allow broader deployment of detailed chemistry-based simulations, such as in multi-objective engine optimization campaigns. A fast-running tabulated chemistry solver coupled to a 0-D probability density function-based approach for the modelling of compression and spark ignition engine combustion is proposed. A stochastic reactor engine model has been extended with a progress variable-based framework, allowing the use of pre-calculated auto-ignition tables instead of solving the chemical reactions on-the-fly. As a first validation step, the tabulated chemistry-based solver is assessed against the online chemistry solver under constant pressure reactor conditions. Secondly, performance and accuracy targets of the progress variable-based solver are verified using stochastic reactor models under compression and spark ignition engine conditions. Detailed multicomponent mechanisms comprising up to 475 species are employed in both the tabulated and online chemistry simulation campaigns. The proposed progress variable-based solver proved to be in good agreement with the detailed online chemistry one in terms of combustion performance as well as engine-out emission predictions (CO, CO2, NO and unburned hydrocarbons). Concerning computational performances, the newly proposed solver delivers remarkable speed-ups (up to four orders of magnitude) when compared to the online chemistry simulations. In turn, the new solver allows the stochastic reactor model to be computationally competitive with much lower order modeling approaches (i.e., Vibe-based models). It also makes the stochastic reactor model a feasible computer aided engineering framework of choice for multi-objective engine optimization campaigns.