Skeletal reaction models for n-butane and iso-butane combustion are derived from the detailed gas phase chemistry model of USC Mech II through directed relation graph (DRG) and DRG aided sensitivity analysis (DRGASA) methods. The skeletal models generated from various combustion systems, e.g. auto-ignitions versus premixed flames, n-butane versus i-butane, are compared, and analyzed based on the temperature and species profiles during ignition and within the flames. The reduced models are further optimized through the method of uncertainty minimization by polynomial chaos expansion (MUM-PCE) to enhance model performances. The uncertainty of the optimized model is quantified by the spectral expansion technique, exploring the relationship between the model size and uncertainty.