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Livengood-Wu integration model is acknowledged as a relatively simple but fairly accurate autoignition prediction method which has been widely recognized as a methodology predicting knock occurrence of a spark-ignition (SI) engine over years. Fundamental idea of the model is that the chemical reactivity of fuel under a certain thermodynamic test condition can be represented by inverse of the acquired ignition delay. However, recent studies show that the predictability of the model seems to deteriorate if the tested fuel exhibits negative temperature coefficient (NTC) behavior which is primarily caused by two-stage ignition characteristics. It is convincing that the cool flame exothermicity during the first ignition stage is a major cause that limits the prediction capability of the integration model, therefore a new ignition delay concept based on cool flame elimination is introduced in order to minimize the thermal effect of the cool flame.