For a flexible manufacturing system, determining the feasible production set at a given time is essential for production management. In this paper, we propose methods for estimating the production set for a general multi-part type failure prone flexible manufacturing system. We also discuss how to get an open loop control that can control the system producing at the margin of its expected production set and how to estimate the corresponding variance. Some special cases are discussed where we also suggest some simple approximations. Numerical examples are presented to illustrate our algorithm.