It is known that for single-part-type production systems with homogeneous Markovian machine failure rates, special single threshold feedback policies, called hedging point policies, are optimal, and the stationary probability distribution of the part-type surplus, for given tentative hedging point values, can be obtained analytically. This approach is extended to multiple threshold policies with production rate-dependent machine failure rates. It is shown that the stationary distribution of the part-type surplus can be obtained under the extended policy and in the presence of production rate-dependent failure rates. The advantage of multiple threshold policies is that they can provide a piecewise constant (step function) approximation of any feedback policy. It is observed that hedging point policies are not always optimal and, in fact, feedback policies are not always optimal either.