  In this study, we investigate signature flips within the framework of
cosmological models featuring a time-varying vacuum energy term $\Lambda(t)$.
Specifically, we consider the power-law form of $\Lambda=\alpha H^n$, where
$\alpha$ and $n$ are constants. To constrain the model parameters, we use the
MCMC technique, allowing for effective exploration of the model's parameters.
We apply this approach to analyze 31 points of observational Hubble Data (OHD),
1048 points from the Pantheon data, and additional CMB data. We consider three
scenarios: when $n$ is a free parameter (Case I), when $n=0$ (Case II), and
when $n=1$ (Case III). In our analysis across all three cases, we observe that
our model portrays the universe's evolution from a matter-dominated decelerated
epoch to an accelerated epoch, as indicated by the corresponding deceleration
parameter. In addition, we investigate the physical behavior of total energy
density, total EoS parameter, and jerk parameter. Our findings consistently
indicate that all cosmological parameters predict an accelerated expansion
phase of the universe for all three cases ($q_0<0$, $\omega_0<-\frac{1}{3}$,
$j_0>0$). Furthermore, our analysis reveals that the $Om(z)$ diagnostics for
Cases I and III align with the quintessence region, while Case II corresponds
to the $\Lambda$CDM model.
