One of the commonalities of the theory of reliability, economics and insurance is the study of non-negative data, generally skewed (longevity, profit and income), fitting the appropriate model to this data and finding their characteristics. Risk measures play a serious role in the economics of insurance and in the most financial institution. The concepts of inequality measures are an important effect in the evaluation of the inequality of income distributions and wealth in economic, social sciences, and other areas. This paper states some properties of inequality indices and risk measures and applications also, compare them with each other. The main aim of this paper is to investigate the re- lationship between some inequality measures and risk measures with reliability concepts. Specially, we are interested in finding the connection between Lorenz ordering and risk measures. Examining the relationship between inequality indicators, risk and reliability measures allows the researcher to use the criteria of each of these concepts to examine the other concept.

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