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October 30, 2007

What are the Chances?

Written by  Mark Jablonowski
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No one knows when and where the next disaster will strike. Catastrophes are, by their very nature, unpredictable. The best we can do is assign some estimate of long-run relative frequency, or probability, to the occurrence of these untoward events. A knowledge of the probability of catastrophic events can, however, provide valuable information on which to base disaster planning and recovery decisions.

To this end, disaster recovery specialists may want to gain a better understanding of the probabilities of events that entail serious consequences. Most of us have an intuitive feel for the probabilities of everyday events. These probabilities figure prominently in our decision making processes. My choice as to whether or not to take an umbrella with me today, for example, depends on my estimate of the probability of rain. The probabilities of catastrophes, on the other hand, are usually out of the realm of our individual experiences. The probabilities of these (thankfully!) rare events must be determined from statistical data, or from logical analysis.

Statistical analysis is feasible when there is a large body of data available. For example, records of dam failures in the United States go back to at least the 1800's. This data provides information on thousands of dams for over a hundred years of operation. Failures, and their consequences, can be tallied against total 'dam years' of operation, giving us a fairly accurate picture of annual probability of dam failure. Natural disasters, as well as accidents involving the structural failure of some man-made objects (like dams), are amenable to this type of statistical determination of probabilities. There exist rather long recorded histories of such events.

When statistical data is limited, we must resort to logical analysis of component processes that may contribute to catastrophic events. This is the approach taken with nuclear power plants, for example. Here, operating experience (reactor years) is fairly limited. We do, however, have some good data on component failures (like valves, piping, pressure vessels and such). These component failure probabilities can be combined with engineering judgement to obtain probabilities for heretofore unexperienced events.

A Compendium of Chances

Based on statistical data and logical analysis, we can estimate the chances of unfavorable occurrences of various magnitudes. The chart below shows the annual probability for some of these events, culled from a variety of official and unofficial sources. We can view these probabilities as the expected number of years between events, or as the number of occurrences expected per year in a sample of given size. For example, a probability 1/10 for automobile collision (property damage only) means that we can expect one such event every 10 years for a single auto, or one event per year for every 10 autos. Events that affect individuals, businesses and geographic regions are included for comparison.

In order to fit the vast scale of probabilities of dangerous events onto a single chart, a logarithmic scale of probabilities was used. That is, the scale of the chart was partitioned into even segments representing decrements by a factor of ten (1, 1/10, 1/100, 1/1,000, and so on). We can in this way compare the probability of relatively 'frequent' events, like an automobile collision involving only property damage, with extremely rare events (a fatal lightning strike, for example).

Note also that the probabilities given for some of these events constitute only a 'best guess'. Data on rare events is, naturally, scarce. Uncertainty as to the causal mechanisms leading to nuclear reactor core melts, for example, suggests a range of possible probability values from 1/1,000,000 to 1/100,000 per reactor year.

Pegging an exact value somewhere in between these two endpoints gives us a useful landmark for comparison to other exposures. In actual decision making situations we would want to be more explicit about the uncertainty involved.

The chart clearly illustrates that the probabilities of disastrous events are often very low. For perspective, the probability of a penny toss landing 'heads' 10 times in a row is 1/1,000. Most of the disastrous events listed in our chart have a lower probability.

Their rarity, however, is counterbalanced by their severe consequences. All distinctly possible disaster scenarios constitute genuine risk. And as our collective experience has shown, risk is something that must be very carefully reckoned with.

Probabilities which we might safely ignore when making relatively trivial decisions become troublesome in the realm of disaster. While being '99 percent' sure that it will not rain tomorrow (implying a 1/100 chance that it will) is certainly enough to convince me to leave my umbrella and galoshes at home, it is of cold comfort in the face of catastrophe. When the lives of human beings or the survival of the enterprise are at stake, even the proverbial 'one chance in a million' may still be sufficient for genuine concern.

The chart also shows that the probabilities of these troublesome events vary considerably. Comparing probabilities in this fashion gives us a better appreciation for this fact. The relativities allow us to categorize events with respect to probabilities. As we will see, categorical representations of disaster probabilities form the basis of important decisions. Distinctions between categories can only be effectively made once we understand that disaster probabilities run the spectrum.

Above all, the chart drives home the point that probabilities are a characteristic of the physical world, and not some abstract mathematical entity. They exist (though how well we are able to determine them is another story!).

As the probabilities of disastrous events are often subject to only very limited manipulation on our part, it behooves us to learn how to live with them. That's what disaster planning is all about.

Probability and
Disaster Planning

Probabilities enter disaster planning in a variety of formal and informal ways. Among the formal methods: Scenario-based risk analysis (DRJ, Oct-Nov-Dec 1995). Scenario-based risk analysis lets us prioritize potential accidents with respect to risk. Chains of events ('scenarios') that may lead to disruption and destruction may be charted by both probability and expected consequences.

Inspection of the resulting risk map (p. 66) can provide valuable insight into the planning process, as well as formal support for planning decisions.

Numerical probability estimates also provide us with a mechanism to compute the combined risk from multiple exposures. Informally, we all recognize the existence of certain events whose chance of occurrence, while not strictly zero, is low enough to be classed as 'virtually impossible'.

The disaster planner may on this basis decide to dispense with preparations for a catastrophic meteor strike, for example.

Contrary to the casual planning philosophy that says 'anything can happen', probabilities suggest that some events are certainly more possible than others.

Rational planning demands that we pay increased attention to these. To exclude only events that we are sure have a zero probability of occurring extends the planning process to infinite, an hence unknowable, variations.
Of course, by using these probability arguments it is a possibility that a disaster recovery specialist may fail to plan for some significant, yet rare, event that may indeed occur.

Probability is tricky that way. At any rate, we could not fault the planner for such oversights, for he or she is only human. We can, however, take comfort in the fact that most scenarios will be planned for when probabilities are taken into consideration.

This discussion suggests that disaster planners can benefit from a better understanding of the probabilities of catastrophic events. Recognizing the probabilities of these events, and their relative magnitudes, is essential to the process.

The benefits of a more rational approach can be obtained even if our probability analysis is only approximate. A little knowledge is, after all, better than none at all.

A basic understanding of rare event probabilities can be obtained by constructing and studying compendiums, like the one that accompanies this article.

Probabilities more specific to the planner's enterprise can be obtained from a variety of sources. These include governmental entities, insurers and industry groups.

Planning for disaster can be enhanced once we are able to answer the question: What are the chances?

Mark Jablonowski, CPCU, ARM, is Risk Manager for the Hamilton Standard Division of United Technologies Corporation in Windsor Locks, Connecticut.

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