  Accurate standardisation of Type Ia supernovae (SNIa) is instrumental to the
usage of SNIa as distance indicators. We analyse a homogeneous sample of 22
low-z SNIa, observed by the Carnegie Supernova Project (CSP) in the optical and
near infra-red (NIR). We study the time of the second peak in the NIR band due
to re-brightening, t2, as an alternative standardisation parameter of SNIa peak
brightness. We use BAHAMAS, a Bayesian hierarchical model for SNIa cosmology,
to determine the residual scatter in the Hubble diagram. We find that in the
absence of a colour correction, t2 is a better standardisation parameter
compared to stretch: t2 has a 1 sigma posterior interval for the Hubble
residual scatter of [0.250, 0.257] , compared to [0.280, 0.287] when stretch
(x1) alone is used. We demonstrate that when employed together with a colour
correction, t2 and stretch lead to similar residual scatter. Using colour,
stretch and t2 jointly as standardisation parameters does not result in any
further reduction in scatter, suggesting that t2 carries redundant information
with respect to stretch and colour. With a much larger SNIa NIR sample at
higher redshift in the future, t2 could be a useful quantity to perform
robustness checks of the standardisation procedure.
