The RUL Loss Rate for a Special Class of Time-to-Failure Distributions*

This chapter focusses on a special class of time-to-failure (TTF) distributions, defined by the property that their mean residual life (MRL) is a linear function of time. For that class of distributions, the properties of the remaining useful life (RUL) and the RUL loss rate are investigated. A fundamental relation between the slope of the MRL (i.e. the average RUL loss rate) and the standard deviation of the RUL is derived. This leads to closed-form expressions for the RUL confidence intervals.

This special family of TTF distributions is shown to include the exponential distribution, the Dirac distribution, and the uniform distribution.