**byEdwin B. Dean**

Risk means many things to many people. The dictionary (Anon., 1989) defines risk as "exposure to the chance of injury or loss." In terms of insurance it defines risk as "the hazard or chance of loss."

Rowe (1994) provides excellent insights into uncertainty and risk. Uncertainty is portrayed from four fundamental dimensions: temporal, structural, metrical, and translational. Risk is defined as the downside of a gamble which is described in terms of probability.

Kaplan and Garrick (1981) provide an excellent introduction to risk, both as a personal thing and a mathematical entity. They note that risk is "relative to the observer" and has to do with both uncertainty and damage. They provide a first level mathematical definition of risk as a "the set of triplets: R = {(si,pi,xi)} ... where si is a senario identification or description, pi is the probability of that scenario, and xi is the consequence or evaluation measure of that scenario, i.e., the measure of damage." They further note that risk is multidimensional, i.e. there are many possible damage measures. Finally, they extend the definition of risk to a probabilistic family of multidimensional curves, which include the first level definition of risk. For the mathematically inclined, very interesting concepts are to be found here.

To measure probabilistic risk requires an understanding of subjective probability (Kyburg and Smokler, 1964) and methodology for applying numbers to subjective probability (Keeney and von Winterfeldt, 1991).

I would like to propose my own simplified definition: Risk is the perceived extent of possible loss.

Risk is individual to a person or organization because what is perceived by one as a major risk may be perceived by another as a minor risk. Perception is very much a factor. To some, risk is defined as the chance of loss. But in reality it is more. Risk also concerns how much could be lost. Probabilistic risk analysis can define risk as the expected loss, or even as a family of probability curves. This has to do not just with the chance of loss, but more specifically with the extent of loss. But expectation has a very well defined meaning in probability which I feel is still inadequate. Similarly for a family of probabilistic curves. Because loss can come in many dimensions, I use extent to cover the many dimensions of possible loss. Kaplan and Garrick (1981) have defined that extent as a spatial surface. Many have rejected possibility in the definition of risk because it was ambiguous and substituted probablility which is crisp. With the growing knowledge base in fuzzy logic and fuzzy systems (Kosko, 1993), we need to readdress the use of possibility, a more general concept which seems to be more closely related to thought and perception than probability. Hence my proposed definition. The challenge, here, is to refine this more general definition into operational mathematics.

But what does risk have to do with competitiveness? Everything! Each decision has the possibility of resulting in loss. Each decision to introduce a new product into the marketplace can result in varying degrees of loss or gain. To be entreprenual is to accept risk, that is, the possibility of loss. A good entreprenuers forte, however, is to make decisions which maximize possible gain, and hence minimize possible loss. This has to do with risk management. Risk analysis has to do with the analytical process used to estimate the extent of possible loss. So does risk assessment which provides rationale for the decision maker.

Timson (1968) demonstrates that technical performance can be used to parameterize system uncertainty. Dean et. al. (1986) note that, in the case of engineering projects, uncertainty is parameterized by process and product characteristics which result from engineering and political choices as the product is brought forth. Uncertainty, relative to project targets, defines measures (projections) of project risk such as cost risk and schedule risk. Project risk may be minimized by designing the project and the product to a set of project and product parameters which are as close to the vector minimum (Takayama, 1974) of the combined set of project success measures as possible. To become and remain competitive requires the use of risk methodology as a guide for decisions which could ultimately mean survival or demise. The Japanese have recognized this for years and have adopted the PDPC diagram as an everyday management tool to deal specifically with risk. The High Speed Research Program at NASA Langley Research Center has begun down the path of using project and product risk to drive programmatic decisions (Dean 1994b).

Decomposing the risk of designing for competitive advantage into the primary components of value ,which are cost, quality, and timeliness, then risk can be estimated by the extent by which final cost is expected to exceed planned cost, by the extent by which expected quality will fall short of planned quality, and by the extent by which expected market introduction will fall short of the planned introduction date. Note that risk as estimated here can be both positive and negative, is a dynamic measure over the life of a project, and is multidimensional. It can be turned into a unidimensional measure by weighting the cost risk, the quality risk and the timeliness risk and summing. Risk is a cumulative effect of those things which went better than planned and those things which went worse than planned. The {expected value - planned value} is a projection of risk onto the basic dimensions of competitive advantage.

Savvides (1994) provides a concise and elementary, yet reasonably complete, introduction to project risk analysis from the perspective of net present value. Slovic (1987) and Slovic (1993) address important psychological and social issues which affect the perception of risk. If you are really serious about understanding risk, Morgan and Henrion (1990) provides a rather comprehensive review of the state-of-the-art. An understanding of the loss function approach in chapter 12 is very important.

Please note that risk is a subject which cannot be adequately understood unless you have a basic understanding of the language of probability and statistics. Wampole and Myers (1993) is an excellent choice to obtain this understanding.

Ock (1996) provides an example of the application of possibility to risk.

- Anon. (1989). Webster's Encyclopedic Unabridged Dictionary of the English Language, Gramercy Books, New York, NY.
- Dean, E. B. (1994b). "Proposed Metrics for the High Speed Research Program," presented at the 1994 NASA Cost Estimating Symposium, Houston TX, USA, 7-10 November.
- Dean, E. B. , D. A. Wood, A. A. Moore, and E. H. Bogart (1986). "Cost Risk Analysis Based on Perception of the Engineering Process," presented at the 1986 Annual Conference of the International Society of Parametric Analysts, Kansas City MO, USA, 12-16 May.
- Kaplan, S. and B. J. Garrick (1981). "On the Quantitative Definition of Risk," Risk Analysis, Vol. 1, No. 1, pp. 11- 27.
- Keeney, R. L. and D. von Winterfeldt (1991). "Eliciting Probabilities from Experts in Complex Technical Problems," IEEE Transactions on Engineering Management, Vol. 38, No. 3, August, pp. 191-201.
- Kosko, B. (1993). Fuzzy Thinking: The New Science of Fuzzy Logic, Hyperion, New York, NY, USA.
- Kyburg, H. E. Jr. and H. E. Smokler (1964). Studies in Subjective Probability, John Wiley & Sons, New York, NY, USA.
- Morgan, M. G. and M. Henrion (1990). Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis<, Cambridge University Press, Cambridge, UK.
- Ock, J. H. (1996). "Activity Duration Quantification Under Uncertainty: Fuzzy Set Theory Application." Cost Engineering, Vol. 38, No. 1, pp. 26-30.
- Rowe, W. D. (1994). "Understanding Uncertainty," Risk Analysis, Vol. 14, No. 5, pp. 743-750.
- Savvides, S. (1994). "Risk Analysis in Investment Appraisal," Project Appraisal, Vol. 9, No. 1, March, pp. 3-18.
- Slovic, P. (1987). "Perception of Risk," Science, Vol. 236, pp. 281- 285.
- Slovic, P. (1993). "Perceived Risk, Trust, and Democracy," Risk Analysis, Vol. 13, No. 6, pp. 675- 682.
- Takayama, A. (1974). Mathematical Economics, The Dryden Press, Hinsdale, IL, USA.
- Timson, F. S. (1968). Measurement of Technical Performance in Weapon System Development Programs: A Subjective Probability Approach, The Rand Corporation, Memorandum RM-5207-ARPA.
- Wampole, R. E. and R. H. Myers (1993). Probability and Statistics for Engineers and Scientists, 5 th. ed., Macmillan Publishing Company, New York, NY, USA.

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