The class of life time distributions with a mean residual life linear in time:

Abstract

Prognostics and Health Management (PHM) elicits increasing interest in view of its potential economic impact both through service-affecting failure avoidance and maintenance cost reduction. One of the key challenges in the PHM discipline is the estimation of Remaining Useful Life (RUL), i.e. the time remaining until failure in the absence of maintenance. The expectation of RUL, Mean Residual Life (MRL), has long been studied by reliability engineers, dating back to the nineteen sixties. There is a one-to-one relationship between MRL, reliability function and failure rate (also called hazard rate): each one of three functions uniquely determines the other two. Usually, MRL varies with time. We study here a special class of life-time distributions characterized by the fact that their MRL is a linear, non-increasing function of time, and highlight the central role of the time derivative of the MRL, called ageing rate, for PHM; and then generalize to piecewise-linear MRL.