In this paper we present a heuristic approach to obtain fast numerical approximate solutions for the problem of optimal control of Markov failure prone production systems with failures dependent on the production rate. If the failure rate is characterized by a linear affine dependence on the production rate, for single machine single part type systems, it has been shown that the problem of minimizing a long term average inventory/backlog cost, is solved by the so called hedging point policy, which is not optimal in the general case. In this paper we give a strategy for approaching the general problem, where the dependence of the failure rate on the production rate is characterized by a very general and significant class of functions. For simplicity we illustrate the proposed approach to single machine, single part type, limited inventory production systems, for which starting results needed to apply the method are available.