One of the main subject of engineering , is the information theory. This topic is related to entropy , compress information and the other related topics. In this thesis after expresstion the initial reliability introductions , we introduce generalized cumulative entropy. we find their relations with the lower record values of a iid random variables. After that , we express the properties of generalized cumulative entropy and its dynamic. In the following , we introduce a risk measure based on cumulative entropy and consider its application in stock market in member of the Organization for Economic Co.operation and Development(OECD) countries.