  Despite recent experimental progress towards observing large zero-bias
conductance peaks (ZBCPs) as signatures of Majorana modes, confusion remains
about whether Majorana modes have been observed. This is in part due to the
theoretical prediction of fine-tuned trivial (i.e., non-topological) zero-bias
peaks that occur because of uncontrolled quantum dots or disorder potentials.
While many aspects of the topological phase can be somewhat fine-tuned because
the topological phase space is often small, the quantized height of the ZBCP
associated with a Majorana mode is known to be robust at sufficiently low
temperatures even as the tunnel barrier is pinched off to vanishingly small
normal-state conductance. The key shortcoming of the existing experimental
works is an acute lack of stability of the putative Majorana mode features,
indicating the probable absence of a topological phase, and the current paper
suggests specific experimentally accessible measures for a careful quantitative
analysis of the measured ZBCP stability. In this paper, we study how the
counter-intuitive robustness of the ZBCP height to the tunnel barrier strength
can be used to distinguish Majorana modes from non-topological ZBCPs. To this
end, we introduce a dimensionless quality factor $F$ to quantify the robustness
of the ZBCP height based on the range of normal-state (i.e. above-gap)
conductance (which depends crucially on the tunnel barrier height) over which
the ZBCP height remains within a pre-specified range of quantization. By
computing this quality factor $F$ together with the topological characteristics
for a wide range of models and parameters, we find that Majoranas are
significantly more robust (i.e., have a higher value of $F$) compared with
non-topological ZBCPs in the ideal low-temperature limit. Even at a temperature
as high as the experimentally used $20$ mK, we find that we can set a threshold
value of $F\sim 2.5$ (for $\epsilon=0.1$) so that ZBCPs associated with a
quality factor $F>2.5$ are likely topological and $F\ll 2.5$ are topologically
trivial. More precisely, the value of $F$ is operationally related to the
degree of separation of the Majorana modes in the system, although $F$ uses
only the experimentally measured tunnel conductance properties. Finally, we
discuss how the quality factor $F$ measured in a transport setup can help
estimate the quality of topological qubits made from Majorana modes. In
particular, we show that if the induced gap can be enhanced somehow beyond the
currently available $\sim 30$ $\mu$eV in InAs/Al samples, large (small) values
of $F$ could easily distinguish between stable topological (unstable trivial)
ZBCPs with the quantum dot induced quasi-Majorana bound states occasionally
behaving similar to topological Majorana modes in short wires.
