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Previously we developed a theory to estimate the stability of a magnet by statistical estimation of size of disturbance caused by conductor motion. In the theory, various conductor and magnet parameters such as mechanical properties and fluctuation in dimensions of the conductor, electromagnetic mechanical forces to the conductors and configurations of the magnet winding are taken into consideration together with minimum quench energy (MQE). We applied this theory to a large bore magnet developed by Japan Atomic Energy Research Institute (JAERI) for a test facility for large superconductors. The magnet showed training phenomena at excitation tests. In this paper, quench characteristics of the magnet are quantitatively estimated using our statistical method. The reasons for the unexpected quenches are studied and possible modification of the magnet design is discussed to increase the stability.