Optimal burn-in procedure for periodically inspected systems

Burn-in is a widely used method to improve the quality of products or systems after they have been produced. In this paper, we study burn-in procedure for a system that is maintained under periodic inspection and perfect repair policy. Assuming that the underlying lifetime distribution of a system has an initially decreasing and/or eventually increasing failure rate function, we derive upper and lower bounds for the optimal burn-in time, which maximizes the system availability. Furthermore, adopting an age replacement policy, we derive upper and lower bounds for the optimal age parameter of the replacement policy for each fixed burn-in time and a uniform upper bound for the optimal burn-in time given the age replacement policy. These results can be used to reduce the numerical work for determining both optimal burn-in time and optimal replacement policy.