In view of the growing importance of the reversed residual lifetime in reliability anal- ysis and stochastic modeling, in this paper, we try to study some of the reliability properties of reversed residual lifetime random variable based on doubly truncated data and complete the preceding results such as Ruiz and Navarro (1995, 1996), Navarro et al. (1998), Nanda et al. (2003), Nair and Sudheesh (2008) and Sudheesh and Nair (2010). The monotonicity properties of the doubly truncated reversed resid- ual variance and its relations with doubly truncated reversed residual expected value and doubly truncated reversed residual coefficient of variation are discussed. Further- more, an upper bound for it under some conditions is obtained. We also discuss and find the similar results and some characterizations for discrete random ageing, which are noticeable in comparing with continuous cases.

Keywords