How Often Will the Firemen Get their Sleep?

We calculate the expected additional fire protection cost to a city implied by the 1974 amendments to the Fair Labor Standards Act. Under the amendments, if a city chooses not to pay its men who are on duty for more than 24 hours at a time for sleep and meal time, it may exclude up to eight hours of sleep time, but must compensate them at overtime rates for the entire sleep period if one or more alarms prevent them from obtaining at least five uninterrupted hours of sleep in that period. Interalarm times are modeled as a Poisson process, and both point and interval estimates of the additional annual overtime cost are computed for the city of Monterey by estimating the annual number of interrupted sleep periods. A model that permits the rate at which alarms are received and the length of die designated sleep period to be varied is developed for computing the proportion of nights in the year during which the firemen get five uninterrupted hours of sleep. A procedure for adjusting the model to allow for the time spent in response to an alarm is also described.