  Considering possible solutions to the $S_8$ tension between the Planck cosmic
microwave background (CMB) measurement and low-redshift probes, we extended the
standard $\Lambda$CDM cosmological model by including decay of dark matter
(DDM). We first tested the DDM model in which dark matter decays into a form of
noninteracting dark radiation. Under this DDM model, we investigated the
impacts of DDM on the Sunyaev Zel'dovich (SZ) effect by varying the decay
lifetime, $\Gamma^{-1}$, including the background evolution in cosmology and
the nonlinear prescription in the halo mass function. We performed a
cosmological analysis under the assumption of this extended cosmological model
by combining the latest high-redshift Planck CMB measurement and low-redshift
measurements of the SZ power spectrum as well as the baryonic acoustic
oscillations (BAO) and luminosity distances to type Ia supernovae (SNIa). Our
result shows a preference for $\Gamma^{-1} \sim 220$ Gyr with a lower bound on
the decay lifetime of $\sim$ 38 Gyr at 95\% confidence level. Additionally, we
tested the other DDM model in which dark matter decays into warm dark matter
and dark radiation. This model supports $\Gamma^{-1} \sim 137$ Gyr to resolve
the $S_8$ tension with a lower bound on the decay lifetime of $\sim$ 24 Gyr at
95\% confidence level. Comparing these two models, we find that the second
leads to slightly better reconciliation of the $S_8$ tension.
