Resumen
Recently, Rao et al. [(2004) Cumulative residual entropy: a new measure of information. IEEE Trans. Inform. Theory 50(6), 1220–1228] have proposed a new measure of uncertainty, called cumulative residual entropy (CRE), in a distribution function F and obtained some properties and applications of that. In the present paper, we propose a dynamic form of CRE and obtain some of its properties. We show how CRE (and its dynamic version) is connected with well-known reliability measures such as the mean residual life time.

Resumen
In the study of reliability of the technical systems and subsystems, parallel systems play a very important role. In the present paper, we consider a parallel system consisting of n identical components with independent lifetimes having a common distribution function F. It is assumed that at time t the system has failed. Under these conditions, we obtain the mean past lifetime (MPL) of the components of the system. Some properties of MPL are studied. It is shown that the underlying distribution function F can be recovered from the proposed MPL. Also, a comparison between two parallel systems are made based on their MPLs in the case where the components of the system are ordered in terms of reversed hazard rate. Finally a characterization of the uniform distribution is given based on MPL.