  The concept of entanglement witnesses form a useful technique to detect
entanglement in realistic quantum devices. Measurement-device-independent
nonlinear entanglement witnesses (MDI-NEWs) are a kind of entanglement
witnesses which eliminate dependence on the correct alignments of measurement
devices for guaranteeing the existence of entanglement and also detect more
entangled states than their linear counterparts. While this method guarantees
entanglement independent of measurement alignments, they are still prone to
serving wrong results due to other loopholes. Here we study the response of
MDI-NEWs to two categories of faults occurring in experiments. In the first
category, the detection loophole, characterized by lost and additional events
of outcomes of measurements, is investigated, and bounds which guarantee
entanglement are obtained in terms of the efficiency of measurement being
performed. In the second category, we study noise associated with the sets of
additional quantum inputs required in MDI-NEW scenarios. In this case, a type
of noise is identified which still allows the MDI-NEWs to guarantee
entanglement. We also show that MDI-NEWs are less or equally robust in
comparison to their linear counterparts under the same noise in additional
quantum inputs, although the former group detects a larger volume of entangled
states in the noiseless scenario than their linear cousins.
