Tolerable and ALARP
I work as a safety engineer in the UK rail sector. Although the rail sector has its own standards (national and European), all of these are subservient to the law of the land, i.e. the Health and Safety at Work Act.
It's a long time since I worked for the MoD in any capacity, and my service predates the MAA and a lot of the new thinking surrounding safety of military aircraft, so please forgive me if I make any erroneous statements or assumptions about the manner in which the law applies to military aircraft in the 21st Century.
The ALARP principle (or SFAIRP - So Far As Is Reasonably Practicable in HASAW terms) is quite simple to apply in theory. All risks must be reduced to a level that is tolerable (what is meant by "tolerable" must be defined in the responsible organisation's Safety Management System) and furthermore must also be reduced to a level that is As Low As Reasonably Practicable. At this stage, as has been pointed out, cost comes into the equation.
Basically, what has to be done is this. For each risk, once it has been mitigated down into the "tolerable" region, further mitigation measures should be sought, and MUST be implemented UNLESS it can be shown that the cost of doing so is grossly disproportionate to the safety benefit to be realised through implementation of this mitigation.
In the UK rail industry, grossly disproportionate is generally taken to mean more than three times the safety benefit, measured in terms of equivalent fatalities. The VPF (Value of Preventing a Fatality) is around £1.7m, more if we are talking about multiple deaths (due to public aversion to this sort of accident).
So, if your identified safety measure will cost £3m to implement, but will save at least £1m in equivalent fatalities, then it must be implemented in order to justify ALARP.
Of course, it's never this easy in practice, as the true cost and value is always open to argument and horse trading. And we don't expect, with any complex system, to ever achieve zero fatalities. The word "safe" actually means "acceptably unsafe", although no-one will ever use that phrase in a safety case...