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A survivor function is $S(t)=\mathbb{P}(T>t)$. For a nonnegative event time it is nonincreasing and right-continuous, with values between zero and one; a proper finite event time has $S(t)\to 0$ as $t\to \infty$. Here $w(0)=1$, $w(t)>0$, $w(t)\to 0$, and $w^{\prime }(t)=-(e^{-t}+6e^{-2t})/4<0$ for $t\ge 0$. Extending it by one for $t<0$ supplies a valid continuous survivor function.

The density is $-w^{\prime }$, so the hazard function isIn particular $h(0)=7/4$ and $\boxed{\underset{t\to \infty }{\lim }h(t)=1}$. The survivor is a mixture of rate-one and rate-two exponential distributions with weights $1/4$ and $3/4$. Among long-term survivors the rate-one component dominates, explaining the limiting hazard. More generally the hazard derivative for a mixture of exponential distributions is minus the variance of the component rate among survivors; the decreasing hazard is selection, not an individual component's changing hazard.

In a population mixture with initial component probabilities $p_i$, conditioning on survival to time $t$ changes them to the displayed probabilities by Bayes theorem. Components with larger survivor functions receive greater relative weight among survivors. The population hazard function is the weighted mean of the component hazards with these time-dependent weights. This selection can change the population hazard even when all component hazards are constant, as shown by the hazard derivative for a mixture of exponential distributions.