[en] A Criticality Accident Alarm System (CAAS) has an important role in minimizing the potential dose from a criticality accident should one occur in a process. The presence of one does not imply an intolerable or unacceptable risk of a criticality accident; it is there in order to mitigate the effects if an accident were to occur. In the UK the decision is largely based on a test of either 'reasonably foreseeable' after the loss of controls designated to maintain criticality safety, or based on consequences of dose below a certain threshold. The decision is also made with consideration of the benefits and harms, as any system must provide a net benefit in terms of risk. This can be a difficult and subjective process. This paper sets out a method to estimate the significance of unforeseen criticality risk. The method can be used to assist in the decision to install a CAAS. It sets out a structure by which meaningful discussion may be had with stakeholders in order to arrive at a more informed decision for CAAS. The method employs a simple means of estimating the unforeseen risk contribution to the overall risk of criticality. By this means it may be determined whether the unforeseen risk is trivial, of concern (warranting further consideration) or significant (where a CAAS would likely be installed). The approach is illustrated by the application of the method to 3 facilities: an old plutonium fuel processing glovebox line, a solid waste compaction facility and a plutonium powder store.The trial results compared with the actual arrangements shows differences, although not large. (authors)