Some Existence Theorems for Probabilistically Diagnosable Systems

This correspondence is concerned with probabilistic fault diagnosis for digital systems. The model considered in this correspondence is the diagnostic model introduced by Maheshwari and Hakimi where each unit has a probability of failure. For this model under both fault assumptions by Maheshwari-Hakimi and by Barsi-Grandoni-Maestrini, some existence theorems are obtained for probabilistically diagnosable systems. 1) Necessary and sufficient conditions for the existence of testing links to form probabilistically t-diagnosable systems with and without repair. 2) Necessary and sufficient conditions for the existence of probabilities of failure of all units to form probabilistically t-diagnosable systems with and without repair which have no hardcore.