As various types of products are produced in a single production system, it is important to determine a scheduling policy that selects one of the different types. In addition, the failure of processes in a line need to be considered due to machine failure, raw material supply and demand, quality issues, and worker absence, etc. Therefore, we studied production systems with various product types, dedicated buffers for each product type, Bernoulli equipment, and WIP-based scheduling or cyclic scheduling. To analyze such system exactly, we introduced a method to analyze the performance such as production rate, WIP level, blocking probability and starvation probability based on Markov chains and derived various characteristics. Especially, assuming that equipment does not need to select the type it just tried, the flow rate is no longer conserved and increasing buffer capacity does not guarantee increase production rate. The performance comparison between WIP-based and cyclic policy is studied as well.