Tool replacement with adaptive control in a non-stationary non-periodic stochastic process

The problem of optimum tool replacement is studied in the case in which tool performance is characterized by progressive decay over time following stochastic laws. A control system is assumed which detects, continuously or at fixed intervals, the service state of the tool. Assuming that the service state of the tool affects the marginal cost of production, the latter is used in order to minimize the unit production cost for an unlimited production horizon. The replacement policy proposed is able to update itself in process by means of an iterative procedure which converges to a conditioned optimum. The effectiveness of such a policy is demonstrated analytically, and illustrative examples obtained by simulation are shown.