Hysteresis Effect in Repair and Replacement Problems with Downtime.

The paper investigates a new class of repair replacement problems called the hysteresis age problem. This problem is concerned with the amount of recovery of service age following a repair, extreme cases of which are minimal repair and age replacement major repair. A mathematical formulation for the discounted hysteresis age problem is presented using the functional equation technique. Optimal age replacement policies which minimize the total expected discounted cost are examined for a linear hysteresis function, for both zero and non-zero downtime. A necessary condition for the classical age replacement problem is determined, extending prior results of Barlow and Hunter, Fox, and Scheaffer. A comprehensive literature survey of the three categories of repair is also presented. Author