In this paper, a discrete-event dynamical system (DEDS) approach is employed to build a fault-tolerant system under partial observation,vith some diagnostic schemes. We address the issue of detectability for state identification and observability for achievable legal languages in DEDSs. Especially, we introduce C, D-observability conditions to determine the observability in view of supervisor synthesis. Based upon these, we study the diagnostic problems and the construction of fault-tolerant supervisory control systems with partial observations through the behavioural analysis upon a discrete-event model. A case study of a plasma etching system is described to illustrate the proposed approach.