  While there have been many studies examining the stability of hierarchical
triple systems, the meaning of ``stability'' is somewhat vague and has been
interpreted differently in previous literatures. The present paper focuses on
``Lagrange stability'', which roughly refers to the stability against the
escape of a body from the system, or ``disruption'' of the triple system, in
contrast to ``Lyapunov-like stability'' that is related to the chaotic nature
of the system dynamics. We compute the evolution of triple systems using direct
$N$-body simulations up to $10^7 P_\mathrm{out}$, which is significantly longer
than previous studies (with $P_\mathrm{out}$ being the initial orbital period
of the outer body). We obtain the resulting disruption timescale $T_\mathrm{d}$
as a function of the triple orbital parameters with particular attention to the
dependence on the mutual inclination between the inner and outer orbits,
$i_\mathrm{mut}$. By doing so, we have clarified explicitly the difference
between Lagrange and Lyapunov stabilities in astronomical triples. Furthermore,
we find that the von Zeipel-Kozai-Lidov oscillations significantly destabilize
inclined triples (roughly with $60^\circ < i_\mathrm{mut} < 150^\circ$)
relative to those with $i_\mathrm{mut}=0^\circ$. On the other hand, retrograde
triples with $i_\mathrm{mut}>160^\circ$ become strongly stabilized with much
longer disruption timescales. We show the sensitivity of the normalized
disruption timescale $T_\mathrm{d}/P_\mathrm{out}$ to the orbital parameters of
triple system. The resulting $T_\mathrm{d}/P_\mathrm{out}$ distribution is
practically more useful in a broad range of astronomical applications than the
stability criterion based on the Lyapunov divergence.
