In a system composed of n units where at most t of these units are faulty, we consider the following problem introduced by Kim[6]. Identify at least one out of given set with m(≤n) units as faulty or fault-free. In [6], attention is concentrated on the case of m≤2. In this thesis, we consider such an identifiable set of m units for m=3 as a natural extension.
We characterize an identifiable set of three units. Using the identifiable set U with $\mid{U}\mid=3$, sequential t-and t/t+1- diagnosabilities are investigated. We give a new class of sequential t-diagnosable systems with n + t-3 edges which is optimal in the sense that U with $\mid{U}\mid=3$ is identifiable. This class contains a class of optimal sequential t-diagnosable systems by Ciompi and Simoncini[11] whenever n=2t + 1. Also, we obtain a property of t/t+1-diagnosable systems. It S is a t/t+1diagnosable system in which for any set U of three units U is identifiable, a set F of actually faulty units can be isolated to within a set $F^{\ast}$ with $F \subseteq F^{\ast}$ and $\mid{F^{\ast}}\mid \le min \{t+1, \mid{F}\mid+2\}$ instead of a set of t+1 units.
