Engineering notion of mean-residual-life and hazard-rate for finite populations with known distributions

This article overviews some foundation issues in reliability and argues that generally it does not make sense to use classical notions of the hazard rate (HR) and mean residual life (MRL) to describe the HR and MRL of a device (the HR and failure rate are interchangeable terms). It provides a new methodology, using engineering notions of HR and MRL, to describe the HR and MRL of a device. and discusses the relevance of these methods in comparison to existing methods. In practice, the engineering notions of HR and MRL can be more complicated and more difficult to compute than the classical notions of these functions. Nevertheless, one should adhere to the procedures in this paper insofar as feasible because, as the examples indicate, the engineering notions of these functions dramatically differ from the classical notions. The finite populations have specified joint distributions.