Risk Assessment

References:

Consider a Spherical Cow by John Harte (University Science Books, 1988).
'The nuclear reactor accident at Chernobyl, USSR', Bernard L. Cohen, American Journal of Physics, vol. 55 No. 12 (1987) p1076.
'Imapcts on the Earth by asteroids and comets: assessing the hazard', C. R. Chapman and D. Morrison, Nature vol. 367, Jan. (1994) p33.
Should We Risk It? Exploring Environmental, Health, and Technological Problem Solving by D. M. Kammen and D. M. Hassenzal (Princeton University Press, 1999).
Consider a Cylindrical Cow by John Harte (University Science Books, 2001).
Risk-Benefit Analysis by R. Wilson and E. A. C. Crouch (Harvard University Press, 2001).
'Traffic Crashes' by Leonard Evans, American Scientist, vol. 90 No. 3 (2002) p 244.
'Resource Letter: RA-1: Risk Analysis', Richard Wilson American Journal of Physics, vol. 70 No. 5 (2002) p475.

Risk

The following is my attempt to summarize the most important points from the above sources. Following each concept is an exercise. We will discuss these in class, along with the two articles we are reading. You should turn in the exercises as one homework.

Probability

Risk assessments primarily are based on probability. The following exercise (adapted from Consider a Spherical Cow) is a simple exercise in calculating probability from know facts.

Exercise:

In 1996 a TWA passenger plane crashed in Long Island Sound. At the time someone suggested that the plane may have been hit by a meteor. Use the following data to determine an approximate risk for a plane being hit by a meteor.

Planes take off about every 5 minutes during daylight hours and the number of commercial airports in the world is about 1000. So in a 12 hour day the number of take-offs is approximately 144,000.
About 3x10³ meteors per day penetrate the atmosphere far enough to hit a plane.
The 'vital' area of a plane, the area that, if hit, might cause the plane to go down, is about 600m².
The area of the earth is about 5x10¹⁴ m² .

Questions:

If a typical flight is 3 hours out of 24, how many planes are in the air at any given time? ans=18000
How much total 'vital' area does this number of planes represent in a 24 hr. period?
What fraction of the area of the earth does this 'vital' area represent?
Multiply the number of meteor hits times the fraction of the earth's area covered by planes per day. If we assume 5% of these hits are deadly we can multiply the number of hits by 5% to get the probability of a crash.
The probability is for a 24 hr period, what is the probability of a crash in a year of travel?
If air traffic continues at the current volume, what is the probability of a crash in the next 50 years?
Was it a reasonable suggestion that a meteor caused the plane to crash or totally absurd? Why or why not?

Historical Risks

Historical risk is calculated based on the assumption that the death rate will remain about the same; this year's death rate is next year's risk prediction. For example, the number of people dying in car accidents in the year 2000 was about 43,000 out of a population of about 281 million. So the rate of death is 43,000/281 million or 15x10^-5. This is a rate of 15 per 100,000 people (150 in a million). In making a prediction of the risk of dying in an automobile accident in the year 2001 we would estimate the risk to be about 15 in 100,000. There are several things to notice here:

There is more than one way to report historical death rates. For example the above calculation does not take into account how much each person drives or how many vehicles are on the road. The number of deaths per 100 million vehicle miles is about 2. The number of deaths per 10,000 vehicles is also about 2.
150 in a million does not sound like a lot but 43,000 people per year does sound like a whole lot. A small risk applied to a large number of people can result in a lot of deaths. A one in a million risk applied to the US population means 281 people die (applied to the world this would be 6000 deaths). If this were to be the result of, say, a plane crash, people would be very upset.
Risks do change over time. The per 100,000 people death rate by vehicle accident dropped from 28 to 22 between 1973 and 1975 as the result of higher oil prices (and less driving) and lower speed limits. It has continued to drop, on average, since then.

Exercise:

553,768 people died of cancer in 2000 out of a population of about 281 million. What was death rate for cancer in 2000?
If you were going to predict the risk of cancer death for the following year, what risk factor would you predict?
If the rest of the worlds population (around 6 billion) had the same risk, how many people would have died of cancer?

New Risks: Technology

Risks due to new technology cannot be assessed directly from historical data. For example there have not been enough nuclear reactor failures to have significant death rate data. In these cases an estimate of the bounds on the probability for failure of the various components per unit of time of the technology are estimated. For example of the probability of a critical water supply pipe breaking in a nuclear reactor can be made from historical experience with similar pipes. The probabilities of failure for each component are then multiplied to get the probability of a failure of the entire device (this is called a 'fault tree' or 'event tree' analysis). Comments:

Upper bounds for failure of a complex system can sometimes be made from historical data where failure has not occurred. For example there have been 8,000 reactor years world wide in light water reactors without a loss of cooling accident. This puts an upper bound on the likely hood of a loss of cooling accident of 1/8,000 = 1.25x10^-4 per reactor year.
An actual calculation of the risk of a reactor leaking radiation into the environment would be much more complicated because of the large number of components in a reactor. The cooling system is one of several lines of defense against a total reactor failure resulting in a release of radioactivity to the atmosphere. Other components of the system would include control rods, water supply pipes, electrical supply failure, and the containment vessel, all of which would have to be evaluated.
The risk of failure is not the same thing as the risk of exposure. In the Three mile Island case, there was a coolant failure but no hazardous exposure to the public.
Risks change over time. As components of a system age we expect the risk to increase.
Estimates of the probability of failure based on a consideration of the components of a system are only as good as the person making the estimate. In complex systems it is possible to overlook a component which might end up being critical to the overall risk of failure. The amount of deterioration of steel water supply pipes in nuclear reactors as a result of radiation damage was not anticipated when the plants were constructed (fortunately this has not resulted in any serious reactor failures).

Exercise:

Given the following probabilities for the failure of various systems and components in nuclear power plant, what is the total probability for failure of the plant (if these are the only parts involved)? P for excess steam pressure is 0.001, P for computer control failure is 0.015, P for the human operator being out of the room is .25, P for a pressure value to fail is .001, P for a back up pressure valve to fail is 0.001.

New Risks: Epidemiology

In the above examples the cause of the risk is clearly and immediately related to the risk directly; it is the car accident that causes the death and the death is very soon after the accident 99% of the time. In many cases, however, the cause and effect relationship is not clear, usually because it is delayed. For example it took many years of data collection before it became clear that smoking causes cancer. In general these cases involve an estimate of the risk associated with exposure of various doses. This information comes from epidemiological studies (comparison of large population groups with different exposures) and/or animal studies. Comments:

'Linear Default' is the assumption that the risk is directly proportional to the dose. For example exposure of 1 to 5 parts per trillion of arsenic in drinking water causes cancer at a rate of one in a million (of the lung, kidney, and bladder, combined risk). Background levels of arsenic in drinking water often exceeds this by a factor of 1000 in which case we would expect the risk to be 1000 in a million (1 in 1000) for people so exposed, assuming a linear dose model.
If we assume the 'Linear Default' model we might try to reduce risk to zero for exposure to anything known to be hazardous at any level. There are at least two reasons not to do this.

For most substances there is probably a threshold dose below which the effects are negligible. It is probably impossible and not necessary to insist that public drinking water be completely free of arsenic. Instead what is usually done in this kind of case is to try to reduce the risk to an acceptable level, for example one in 100 million might be considered acceptable (and would be very hard to detect if the linear model is correct- this would be less than 3 cases in the US per year).
For some substances there is a dose level below which the substance is actually beneficial. The general term for such an effect is Hormesis. An example is alcohol. Alcohol has adverse risks if consumed at doses of more than three drinks per day but it is also true that people drinking less than one drink per day have higher death rates than those drinking one or two drinks per day. The probable cause is that alcohol increases cancer risk but decreases risk from heart disease and these two effects intersect at about 1 drink per day.

Because of the time delay between exposure and illness (cancer for example) it is sometimes difficult to assign values to the dose level which causes a given health problem.
Because epidemiological studies involve humans exposed to many potential harmful agents it is sometimes hard to distinguish between the various substances and their causes and there may be synergistic effects. The interaction between radon and cigarette smoking, for example, required a great deal of research since both cause lung cancer and until recently the amount of radon exposure was not well know. It is now known that the two together cause a greater risk than simply multiplying the risk of each.
Animal study results sometimes do not extrapolate well to humans and it is unethical to experiment with humans.

Exercise:

Suppose the risk of death from an aspirin overdose is 50% if you take 30 aspirins. Assuming a linear dose model, what would be the risk if you take only 1 aspirin?
Using the risk for taking 1 aspirin, how many people in the US would be expected to die as a result if everyone took an aspirin? (Use 281 million for the population of the US.)
Do you think the linear dose model is accurate for aspirin? Why or why not?

Risk Perception

Our perception of risk is sometimes very different from the actual risk. For example, living two months in Denver Colorado carries about the same risk (one in a million) for dying from radiation induced cancer as living 150 years within 20 miles of a nuclear power plant (Denver, being at 6000 feet has a higher incidence of cosmic rays). This is also about the same risk as a single chest X-ray. Many people would choose not to live next to a nuclear power plant but think nothing of having a chest X-ray or moving to Denver. Likewise, traveling 300 miles in a car carries about the same risk (one in a million) as traveling 1000 miles in a plane but many people would rather drive the 1000 miles (and face 3 times the risk) than take a plane. Some factors that affect our perception of risk are:

Choice- do we make the choice to expose ourselves to the risk or does someone else? ATVs are considerably more dangerous than cars but since their use is by choice the risk is not regulated, whereas cars are required to have certain safety features.
Necessity- some people feel compelled to take a risk (for example scuba diving) while others do not. Do you really have to run out to the store or could you get by until tomorrow?
Latency- a delay between cause and effect is sometimes sufficient to decrease the risk perception. Many smokers discount the risk of smoking because they are not yet ill.
Dread- a subjective evaluation of which risk is worse. Cancer by radiation seems worse to some people than cancer from smoking, probably because since radiation is invisible it is more dreaded.
Rare but catastrophic- although plane crashes are rarer (and have a lower risk per mile) than auto crashes plane crashes kill a large number of people all at once. For this reason airplane flights are seen as more risky.
Familiarity- strange risks appear more threatening than known risks. More people die in car wrecks per month than in all terrorist acts in the past 100 years yet the perception is that terrorism is more threatening.
Who is at risk- high risks to small groups (for example coal miners) are not perceived to be as serious as smaller risks to large numbers of people.
Trust- the perception of risk is lower if people trust the person or persons or agency in charge of that risk. As a converse example the perceived risk of nuclear power is much higher than the actual risk in part because of distrust of officials in charge of the nuclear power industry.

Exercise:

The following all have the same risk of one in a million. For each one say whether you think the risk would likely be over or under estimated by an average person and support your answer using the above factors or risk perception.

smoking two cigarettes
drinking 30 diet sodas with saccharin
eating one hundred fifty (1/2 lb) charcoal broiled steaks (aromatic hydrocarbon risk)
eating one hundred 100 gram servings of shrimp (formaldehyde risk)
eating four tablespoons of peanut butter every 10 days for person without hepatitis B1
eating three hundred and fifty slices of stale bread (formaldehyde risk)
drinking seventy pints of beer per year (alcohol cancer risk)
exposure to typical radon levels in drinking water in California for six months
drinking water with the EPA limit of arsenic (50 ppb) for three days
one quarter of a typical chest X-ray
non smoker exposed to average US radon level (1.5 pCi/l) for one week
forty days of living in Denver (compared to Philadelphia)
traveling 100 miles in a motor vehicle
dying from a lightning strike in a 6 year period

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Contact Kyle Forinash, kforinas@ius.edu, for comments/suggestions/corrections.