We present a computational tool to develop an exhaust gas recirculation (EGR) - air-fuel ratio (AFR) operating range for homogeneous charge compression ignition (HCCI) engines. A single cylinder Ricardo E-6 engine running in HCCI mode, with external EGR is simulated using an improved probability density function (PDF) based engine cycle model. For a base case, the in-cylinder temperature and unburned hydrocarbon emissions predicted by the model show a satisfactory agreement with measurements [Oakley et al., SAE Paper 2001-01-3606]. Furthermore, the model is applied to develop the operating range for various combustion parameters, emissions and engine parameters with respect to the air-fuel ratio and the amount of EGR used. The model predictions agree reasonably well with the experimental results for various parameters over the entire EGR-AFR operating range thus proving the robustness of the PDF based model. The boundaries of the operating range namely, knocking, partial burn, and misfire are reliably predicted by the model. In particular, the model provides a useful insight into the misfire phenomenon by depicting the cyclic variation in the ignition timing and the in-cylinder temperature profiles. Finally, we investigate two control options, namely heating intake charge and trapping residual burned fraction by negative valve overlap. The effect of these two methods on HCCI combustion and CO, HC and NOx emissions is studied.