a method , and a system for implementing the method , for detecting whether a flame is an on state or alternatively is in an off state . the method includes detecting the flame and generating therefrom a flame signal capturing one or more attributes of the flame ; using a high - order cumulant - to - moment formula to determine high - order cumulants for a random variable process representation of the flame signal ; and determining whether the flame is on or off using the high - order cumulants . the method includes the step of applying the high - order cumulant - to - moment formula in a self - learning algorithm to determine flame - on high - order cumulants and flame - off high - order cumulants for the flame . step includes comparing the high - order cumulants to the flame - on high - order cumulants and the flame - off high - order cumulants to determine whether the status of the flame is on or off .