Optimal production run for processes with constant and random drifts

In this paper, we consider a production process with a continuous drift in the mean of a quality characteristic of the product. We develop models for this problem in which we consider the drift to be either known in advance and constant, or occurs in a random fashion. We analyse the developed models and discuss the shape of the resulting cost function for one of the models which helps in obtaining a global solution of the problem. We suggest several schemes for solving the resulting models which give policies for optimal tool replacement. We also present some numerical examples.