The results of the first inspection contain information which laboratory experiments can hardly furnish, such as crack initiation time parameters. Moreover, it is pure in a sense that it is not infected by noise coming from previous, imperfect, inspections. In other words, it is a rich source of information that can be analyzed by Bayesian methods. The first inspection time also heavily influences the overall structural reliability, and therefore the overall costs as was noticed from previous works. By minimizing a loss function based on mean Shannon information, a suitable criterion for selecting the first inspection time is proposed.