# Interval bounds for the optimal burn-in times for concave or convex reward functions

Foschi, Rachele Interval bounds for the optimal burn-in times for concave or convex reward functions. Journal of applied probability . pp. 1-23. ISSN 0021-9002 (Submitted)

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An interesting problem in reliability is to determine the optimal burn-in time. In a previous work, the authors studied the solution of such a problem under a particular cost structure. It has been shown there that a key role in the problem is played by a function $\rho$, representing the reward coming from the use of a component in the field. A relevant case in this investigation is the one when $\rho$ is linear. In this paper, we explore further the linear case and use its solutions as a benchmark for determining the locally optimal times when the function $\rho$ is not linear or under a different cost structure.