scheduled review methods for controllable state variables

in many real systems in which a state variable should be controlled for being in appropriate range, the length of control (review) intervals is taken to be constant. in such systems, when the cost of reviews and out-of-range values of the state variable are considerable, this method may not be optimal. in this paper we let the length of review intervals to be variable during each operating cycle and construct the related mathematical cost model. then two scheduled review methods, called u2 and u3, are introduced and the relative annual system costs are analyzed. the model is developed for the case of negative exponential variate as the time between successive consumption points. it is shown that the new methods results a significant reduction in the expected annual cost of the system.