%0 Journal Article
%@ 0021-9002
%A Foschi, Rachele
%F eprints:1432
%I Applied Probability Trust
%J Journal of applied probability 
%K Burn-in; Bathtub shape; Multiple change points distributions; Reward functions.
%P 1-23
%T Interval bounds for the optimal burn-in times for concave or convex reward functions
%U http://eprints.imtlucca.it/1432/
%X 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.