The application of certain models of substitution ((The Certain Replacement Models (Case study)


Replacement models deal with the problem of finding the optimal random time for a preventive replacement of a technical system. A large class of such models has been considered in the literature recently. In this research a unifying approach to the replacement problem is given regarding it as an optimal stopping problem. The generalization allows to weaken a necessary monotonicity condition and to consider different information levels. Measuring information in this context leads to discussing the problem in general terms of stochastic process theory. An example shows how to get explicit solutions and how the information level influences the optimal replacement policy. We can be applied in modeling machine replacement problem. We begin with a deterministic model to illustrate the concept of a machine cycle, then follow by a stochastic model with a general cost. We then compare popular replacement policies: the time-based replacement policy for a single machine replacement problem. We also prove an interesting result that the optimal costs of this policy