We study peak Age of Information (PAoI) violation guarantee in a periodic multi-source status update system. The system is served by a shared base station, which requires scheduling. Our main contribution is a randomized scheduling framework that targets heterogeneous PAoI requirements. To that end, we derive numerically trackable upper bounds on the PAoI violation probability in two traffic regimes (long and short period) by leveraging the multivariate noncentral hypergeometric Wallenius distribution and the geometric distribution, respectively. Guided by these bounds, we design two low-complexity randomized scheduling schemes that meet diverse PAoI violation probability targets without the traffic assumption. Simulations validate the bounds and demonstrate feasible operation across a wide range of configurations.