A certain type of dwelling has a probability of a fire at night in any year of 2 in 100,000. If there is a fire and the smoke alarm fails there is a 50% chance of a fatality. The smoke alarm fitted to the building has a MTTF of 15 years. How often should the smoke alarm be inspected if the likelihood of a fatality in a dwelling with a failed alarm is to be kept below 1 in a million?

If the cost of inspection is $50 what value is being placed on the cost of a fatality if the interval is determined as above?