Replacement policies based on cost limits are widely acknowledged as particularly user friendly and e¢ cient strategies for organizing the maintenance of technical systems. Di¤erent from the maintenance policies considered so far, repair cost limit replacement policies explicitly take into account that repair costs are random variables. Likely the …rst paper suggesting the use of repair cost limits and demonstrating their application was Gardent and Nonant [132], followed by Drinkwater and Hastings [111], Hastings [152].