We analyzed the interrelationships between mixture heterogeneity and reaction in a premixed charge compression ignition (PCCI) combustion, using large eddy simulation (LES) in conjunction with a reaction kinetics model. The aim of this analysis is to find the statistical characteristics of the mixture heterogeneity in a turbulent flowfield for moderating the PCCI combustion and for increasing an output limit, which is restricted by a severe knock. Several different initial conditions of heterogeneity of an air-fuel or air-fuel-EGR gas mixture were given at the intake valve closing time by a new method, which generated statistically reasonable turbulent fluctuations in both velocity and fuel mass fraction fields. The autoignition and combustion behaviours were analysed for several different sets of the r.m.s. and the length scale of the fluctuations in the fuel mass fraction. The analyses show that the combination of a larger r.m.s. value and a longer-length scale of the fluctuations in fuel mass fraction is effective to slow the combustion in a hot flame reaction phase and to avoid knocking. The analytical results also show that the heterogeneous distribution of an EGR gas has a considerable effect in making the combustion slower, even when a fuel-air mixture is homogeneous.