An Investigation of the Burn-In Problem

Abstract
A problem involving the derivation of bounds on distributions with a decreasing failure rate (DFR distributions) is presented. Given that an item has a decreasing failure rate, sharp upper and lower bounds on the burn-in time to achieve a specified mean residual life are derived. The bounds rely only on the DFR assumption and a knowledge of the first moment and a percentile of the failure distribution. In addition, some bounds on the hazard rate and density of a DFR distribution are given.

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