To meet rapidly changing market demands, manufacturers strive to increase both of productivity and diversity at the same time. As a part of those effort, they are applying flexible manufacturing systems that produce multiple types and/or options of products at a single production line. This paper studies such flexible manufacturing system with multiple types of products, multiple Bernoulli reliability machines and dedicated buffers between them for each of product types. As one of the prevalent control policies, priority based policy is applied at each machines to select the product to be processed. To analyze such system and its performance measures exactly, Markov chain models are applied. Because it is too complex to define all relative transient and its probabilities for each state, an algorithm to update transient state probability are introduced. Based on the steady state probability, some performance measures such as production rate, WIP-based measures, blocking probability and starvation probability are derived. Some system properties are also addressed. There is a property of non-conservation of flow, which means the product ratio at the input flow is not conserved at the succeeding flows. In addition, it is also found that increased buffer capacity does not guarantee improved production rate in this system.