Advanced combustion engine concepts, such as the homogeneous charge compression ignition engine, rely on chemical kinetics for their proper operation. Accurate prediction and control of auto ignition time scales are therefore key issues. Real-time prediction and control of ignition using detailed chemical kinetic models is difficult due to the large size of such mechanisms that calls for high computational costs. Ignition models in the form of correlations can overcome these challenges, as long as they are able to predict the time scales that would be obtained using a detailed chemical kinetic model. In this work, a correlation approach based on detailed chemical models is used to simplify the determination of chemical time scales associated with kinetically controlled combustion events. Detailed combustion mechanisms for biodiesel surrogate (methyl decanoate), gasoline surrogates (isooctane/n-heptane/toluene), bio-alcohol (n-octanol) and ethanol/gasoline surrogate blends from the literature are used to generate ignition databases for correlation development, taking into account complex ignition behavior such as pressure-dependent limits of negative temperature coefficient kinetics. We further employ the Livengood-Wu integral method to assess the ability of the resulting correlations to predict ignition in cases where the temperature and pressure are changing prior to ignition. The integral method is compared with results of a single-zone adiabatic homogeneous charge compression ignition engine model simulation using the detailed chemical kinetic model. It is found that the simplified correlations accurately reproduce the predictions of the detailed chemical kinetic models at an insignificant computational cost relative to the detailed simulations. The correlation approach presented here can also be applied to experimental ignition data, as far as these are obtained in a manner that covers a wide range of the relevant parameters with minimal experimental uncertainties. This work enables the incorporation of realistic chemical kinetic effects in the computational analysis and control of kinetically controlled combustion systems.