Environmental Engineering FOURTH EDITION

36 ENvIRONMENTAL,ENGINEERING

observdfrequency. However, it allows us to estimate that the average annual prob-
ability of a truck accident in the United States is 3.5 x If there are 20,000
truck shipments of hazardous materials per year for 10 years, and the average distance
traveled is 1000 km per shipment, there would be

(10 years) x (3.5 x 10-~ accidents/year-shipment-km)

x (2 x io4 shipments) x (1000 km/shipment)

= 70 accidents involving trucks carrying hazardous materials.

This result can be expressed by at least four different expressions:

0 The frequency of accidents involving trucks carrying hazardous materials is 70

0 The 10-year average frequency of accidents involving trucks carrying hazardous

0 The 10-year average frequency of accidents involving trucks carrying hazardous

0 The average frequency of accidents involving trucks carrying hazardous materials

accidents in 10 years, or

materials is 7 accidents per year, or

materials is 0.007 accidents per kilometer per year, or

is 0.07 accidents per kilometer for this 10-year period.

The probability of an accident involving a truck carrying hazardous materials is

3.5 x

The unconditional probabilities of a set of alternative outcomes of the same event

always add to unity. That is, assume that an automobile trip, when a driver and one

passenger occupy the car, has ten possible outcomes:

as estimated from the observed accident frequency.

1. The car will arrive safely at the destination without incident.


2. The car will be involved in an accident but no occupant will be injured.


3. The car will be involved in an accident and an occupant other than the driver will


4. The car will be involved in an accident and the driver will be injured, but the


5. The car will be involved in an accident and an occupant other than the driver


6. The car will be involved in an accident and the driver will be killed while the


7. The car will be involved in an accident and an occupant other than the driver


8. The car will be involved in an accident and the driver will be killed while the


9. The car will be involved in an accident and driver and occupant will both be


10. The car will be involved in an accident and driver and occupant will both be

be injured. The driver will be uninjured.

occupant will be uninjured.

will be killed, while the driver is uninjured.

occupant will be uninjured.

will be killed, while the driver is injured.

occupant is injured.

injured.

killed.