Determination of the detectability and diagnosability of a digital system containing at most t faulty system components is considered. The model employed 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. A parameter, called the closure index, is defined which characterizes the capability for executing valid tests in the presence of faults. The closure index can be thought of as the size of the smallest potentially undetectable multiple-fault in the system as modeled. On the basis of this parameter, results are presented which permit the determination of t-fault detectability and t-fault diagnosability with repair for the system. Examples are presented to illustrate the application of the model for systems close to those encountered in actual practice.