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Diagnosability without fault repair of a digital system containing at most t faults is considered. A system-level diagnostic model defined in an earlier paper  is employed. The model is to an extent independent of the means used to implement diagnostic procedures, i.e., whether the tests are accomplished via hardware, software, or combinations thereof. Two parameters, the masking and exposure indices, are defined. Conjoined with the previously defined closure index, the parameters fundamentally characterize the capability for executing valid tests in a multiple-fault environment. Necessary and sufficient conditions for a system to be t-fault diagnosable without repair are derived in terms of these parameters. Examples are presented to illustrate the application of the model for systems close to those encountered in actual practice.