Variation propagation in a multi-station manufacturing process (MMP) is described by the theory of Stream of Variation. Given that the measurements are obtained via certain sensor distribution scheme, the problem of whether the stream of variation of an MMP is diagnosable is of great interest to both academia and industry. We present a comprehensive study of the diagnosability of MMPs in this paper. It is based on the state space model and is parallel to the concept of observability in control theory. Analogous to the observability matrix and index, the diagnosability matrix and index are first defined and then derived for MMP systems. The result of diagnosability study is applied to the evaluation of sensor distribution strategy. It can also be used as the basis to develop an optimal sensor distribution algorithm. An example of a three-station assembly process with multi-fixture layouts is presented to illustrate the methodology.