Optimal trial duration times for multiple change points products lifetime distributions

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 $\mathit{\rho }$ , representing the reward coming from the use of a component in the field. A relevant case in this investigation is the one when $\mathit{\rho }$ 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 $\mathit{\rho }$ is not linear or when the component’s lifetimes distribution is not bathtub (or upside down bathtub) shaped.