The disclosure relates to a method of utilizing a catalyst system for an oxidation process on a gaseous hydrocarbon stream with a mitigation of carbon accumulation. The system is comprised of a catalytically active phase deposited onto an oxygen conducting phase, with or without supplemental support. The catalytically active phase has a specified crystal structure where at least one catalytically active metal is a cation within the crystal structure and coordinated with oxygen atoms within the crystal structure. The catalyst system employs an optimum coverage ratio for a given set of oxidation conditions, based on a specified hydrocarbon conversion and a carbon deposition limit. Specific embodiments of the catalyst system are disclosed.