The manufacturing system considered in the paper consists of possibly unreliable machines, whose inputs may be random and may be in batches. The key assumption on the system is that events of unsatisfactory processing independently occur at all machines. We derive a set of inequalities relating processing rates with probabilities of successful processing at unreliable machines. It is shown that the manufacturing system with a CFWL scheduling policy applied is stable if these inequalities are satisfied simultaneously; by CFWL policy we mean the policy that chooses any part-type with a work load exceeding a certain portion of the total one for the next run. This policy is motivated by CAF policy introduced in [7] and is the stochastic extension of CFW policy used in [9].