An interesting problem in reliability is to determine the optimal burn-in time. In Foschi and Spizzichino (Decis Anal 9:103-118, 2012), the solution of such a problem under a particular cost structure has been studied. It has been shown there that a key role in the problem is played by a function ρ, representing the reward coming from the use of a component in the field. A relevant case in this investigation is the one when ρ is linear. In view of more general applications to management of production processes, 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 ρ is not linear or when the components lifetimes distribution is not bathtub (or upside down bathtub) shaped
