A single, unreliable machine producing n part types is considered. Using a continuous flow model, conditions are found for the optimality of a just-in-time, or zero-inventory, policy via a stochastic coupling analysis. These conditions are proven to be necessary and conjectured to be sufficient for optimality. This correspondence extends the results of Veatch and Caramanis [5], in which necessary and sufficient conditions are found for a single machine producing two part types, and it strengthens the results of Perkins and Srikant [3], in which sufficient conditions are found for n part types.