Engineering systems are typically maintained during planned, or unplanned, downtimes in between operation periods. If the duration of the downtime or the budget of the maintenance is an active constraint, all desired maintenance actions cannot be conducted. Seeking of the optimal subset of maintenance actions is referred to as selective maintenance optimization. In this work, we link the statistical analysis of lifetime data into selective maintenance optimization, focusing on datasets with bathtub-shaped failure rates. We also propose two improvements to the efficiency of mixed integer non-linear programming (MINLP)-based selective maintenance optimization. The first is the preclusion of component replacements that, due to the infant mortality period of the component, reduce the reliability. The second is the convexification of two MINLP models, involving only replacement, or replacement and repair, actions. The improvements enable our MINLP-based methods to tackle large-scale selective maintenance optimization problems with up to 700 to 1000 system components.