Burn-in procedure is a manufacturing technique that is intended to eliminate early failures of the system or product. Burning-in a component or system means to subject it to a period of use prior to being used in field. The time period during which the burn-in procedure continues is called the burn-in time. Generally burn-in is considered to be expensive and so the length of burn-in is typically limited. Thus burn-in is most often accomplished in an accelerated environment in order to shorten the burn-in process. A new failure rate model for an accelerated burn-in procedure, which incorporates the accelerated ageing process induced by the accelerated environmental stress, is proposed. Under the proposed model, two-dimensional optimization problem of determining optimal burn-in time and optimal replacement policy is considered. Numerical examples will also be given for illustration.