Self-adaptive systems need to monitor themselves, to check their internal behaviour and design assumptions about runtime inputs and conditions. This kind of monitoring for self-adaptive systems can include collecting statistics about such systems themselves which can be computationally intensive (for detailed statistics) and hence time consuming, with possible negative impact on self-adaptive response time. To mitigate this limitation, we extend the technique of in-circuit runtime assertions to cover statistical assertions in hardware. The presented designs implement several statistical operators that can be exploited by self-adaptive systems; a novel optimization is developed for reducing the number of pairwise operators fromONtoOlog⁡N. To illustrate the practicability and industrial relevance of our proposed approach, we evaluate our designs, chosen from a class of possible application scenarios, for their resource usage and the tradeoffs between hardware and software implementations.