There has been a substantial increase of the number of direct injection spark-ignition (DISI) engines in the last decade as they can achieve much better efficiency than port fuel injection (PFI) engines. With direct injection (DI) system, engines tend to shift from the larger one to the smaller one coupled with turbocharger, namely engine downsizing. Because of the downsizing, the modern DISI engines are more sensitive to knock. Since knock is correlated to the burning rate of a combustion cycle and the burning rate can be varied significantly due to cycle-by-cycle (CBC) variation, one of the recent study on DISI engines is focused on the correlation between CBC variation and knock. Furthermore, as burning rate, CBC variation, and knock are all the functions of in-cylinder pressure, there should be a correlation among them. In this work, such correlation is studied experimentally by using a PFI and two DISI engines. From the statistical analysis, it has been found that CBC variation and burning rate are linearly correlated. It also has been found there is a linear relationship between knock and burning rate. By connecting the relationship between CBC variation and burning rate to the relationship between knock and burning rate, the relationship between knock and CBC variation is developed. Knock tendency increases with increasing CBC variation, which is attributed to the nonlinear relationship between the maximum in-cylinder pressure (p(max)) and net indicated mean effective pressure (NIMEP). By using the model of limited-pressure cycle with isentropic compression and expansion, it has been demonstrated that pmax increases exponentially with increasing NIMEP. (C) 2017 Elsevier Ltd. All rights reserved.