  The randomness from a quantum random number generator (QRNG) relies on the
accurate characterization of its devices. However, device imperfections and
inaccurate characterizations can result in wrong entropy estimation and bias in
practice, which highly affects the genuine randomness generation and may even
induce the disappearance of quantum randomness in an extreme case. Here we
experimentally demonstrate a measurement-device-independent (MDI) QRNG based on
time-bin encoding to achieve certified quantum randomness even when the
measurement devices are uncharacterized and untrusted. The MDI-QRNG is randomly
switched between the regular randomness generation mode and a test mode, in
which four quantum states are randomly prepared to perform measurement
tomography in real-time. With a clock rate of 25 MHz, the MDI-QRNG generates a
final random bit rate of 5.7 Kbps. Such implementation with an all-fiber setup
provides an approach to construct a fully-integrated MDI-QRNG with trusted but
error-prone devices in practice.
