The growing size of a multiprocessor system increases its vulnerability to component

failures. In order to maintain the system’s high reliability, it is crucial to identify and

replace the faulty processors through testing, a process known as fault diagnosis. The

minimum size of a largest connected component in such a networked system is typically

used as a measure for fault tolerance of the system. For this measure, the conditional

diagnosability of the system in terms of an alternating group network is important, which

is studied in the present paper under a comparison model, with some precise and useful

bounds of tolerance derived.