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Remote faulty terminal detection method in the time-division-multiplexing passive optical networks is crucial, especially for the time-slot-violated faulty terminals. We previously demonstrated a detection method using a periodic probing signal. In this paper, we explain the method in details and analyze its performance limitation in multiple terminal cases to evaluate the validity scope of this method. Using a random process model, we show that the proposed method can detect the probing signal even though there is one 15-dB-stronger pseudorandom-binary-sequence bit-stream (PRBS)-type faulty signal using a receiver with the bandpass filter's bandwidth below 0.47 MHz (Q = 21.3). This result shows that the proposed method can be useful for the current 1 Gbps gigabit-capable passive optical network (G-PON) and ethernet PON (E-PON) standards.