This paper investigates the replacement strategy in which aging equipment is completely rejuvenated (through replacement or overhaul) when its service age reaches a certain critical level. The equipment is also partially rejuvenated (through repair) following a random breakdown, in which case its service age is brought to a level which is a constant fraction of its service age justprior to breakdown. This results in a repair discipline which is between the previously studied cases of minimal repair and major repair. The optimal replacement policy which minimizes the total expected discounted cost, including cost of replacement, cost of repair, and cost of operation, is examined.