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A statistical approach to performance prediction is applied to a system development methodology for pipelines comprised of independent parallel stages. The methodology is aimed at distributed memory machines employing medium-grained parallelization. The target applications are continuous-flow embedded systems. The use of order statistics on this type of system is compared to previous practical usage which appears largely confined to traditional Non-Uniform Memory Access (NUMA) machines for loop parallelization. A range of suitable performance metrics which give upper bounds or estimates for task durations are discussed. The metrics have a practical role when included in prediction equations in checking fidelity to an application performance specification. An empirical study applies the mathematical findings to the performance of a multicomputer for a synchronous pipeline stage. The results of a simulation are given for larger numbers of processors. In a further simulation, the results are extended to take account of waiting-time distributions while data are buffered between stages of an asynchronous pipeline. Order statistics are also employed to estimate the degradation due to an output ordering constraint. Practical illustrations in the image communication and vision application domains are included.