Optimization of single machine, single part-type dedicated Kanban policies in multi-part transfer lines with unreliable machines is considered. At each production stage, available machine production time is shared according to either one of two modes: (i) a synchronized mode in which distinct part-type work-in-process (wip) levels at any given stage can be shown to remain proportional to each other at all times, thus in effect reducing the analysis to that of a single part-type transfer line problem (ii) a more general prioritized mode such that at any stage the wip levels instead provably reach their maxima and minima in a fixed priority dependent sequence. A standard cost function which is a combined measure of long term storage and backlog costs under a constant vector of demand rates for different part types is employed to measure performance for any given choice of Kanban parameters. For the synchronized mode, approximate performance computation is achieved via a modification of an existing transfer line decomposition /aggregation technique, while the prioritized mode requires the development of a new approximation technique. Both approximate performance evaluation algorithms are validated against Monte Carlo simulations and are subsequently incorporated within dynamic programming schemes which compute best choices of Kanban parameters.