Fazlollah Lak

The concept of information theory has many applications in reliability and survival analysis. In particular, it is used to measure the complexity of systems, including the study of the properties of coherent systems. Useful studies based on information theory such as Shannon entropy and Kullback­Leibler’s have been performed to compare systems in terms of uncertainty and information for predicting lifetime, including cumulative entropy, cumulative residual entropy, and generalized entropies. Basic entropy also eliminates some of its weaknesses. In this paper, based on k­th lower record values. We study a new generalization of cumulative entropy as the generalized cumulative entropy criterion, and we obtain this measure of information for the coherent systems lifetime with identically distributed components. Then in the conditional state, we define the conditional generalized cumulative entropy for the the coherent system lifetime and discuss some of its properties.Finally, we propose a generalized cumulative past inaccuracy criterion and introduce the estimators of this criterion using empirical data.