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This paper focuses on priority assignment for realtime systems using fixed priority scheduling. It introduces and defines the concept of a "robust" priority ordering: the most appropriate priority ordering to use in a system subject to variable amounts of additional interference from sources such as interrupts, operating system overheads, exception handling, cycle stealing, and task execution time overruns. The paper describes a robust priority assignment algorithm that can find the robust priority ordering for a wide range of fixed priority system models and additional interference functions. Proofs are given for a number of interesting theorems about robust priority assignment, and the circumstances under which a "deadline minus jitter" monotonic partial ordering forms part of the robust ordering. The paper shows that "deadline minus jitter" monotonic priority ordering is the robust priority ordering for a specific class of system, and that this property holds essentially independent of the additional interference function.