Engineering Risks: Evaluation and Valuation. by Ulrich Hauptmanns; Wolfgang WernerReview by: Matti RuohonenSIAM Review, Vol. 34, No. 2 (Jun., 1992), pp. 345-346Published by: Society for Industrial and Applied MathematicsStable URL: http://www.jstor.org/stable/2132873 .

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BOOK REVIEWS 345

highlight of the chapter is the proof of the exis- tence of at least two geometrically distinct pe- riodic solutions on each energy surface; gener- ically it is shown that there are infinitely many, except in the case of one degree of freedom. The chapter ends with a list of open problems.

This book is a very valuable addition to the literature on Hamiltonian systems. It presents in a well written and coherent form material that is scattered in a lot of papers and famil- iarizes the reader with one of the great success stories in modem Hamiltonian dynamics. The author has gone to great pains to make the material accessible to a wide audience by in- cluding almost all necessary background. The book succeeds as both a reference work and a source of information for an advanced course. It should be on the bookshelf of all those inter- ested in mechanics and symplectic geometry.

TUDOR RATIU University of California at Santa Cruz

Engineering Risks: Evaluation and Valua- tion. By Ulrich Hauptmanns and Wolfgang Wemer. Springer-Verlag, Berlin, 1991. xii + 246 pp. $89.00. ISBN 0-387-52195-X.

The book Engineering Risks: Evaluation and Valuation by Hauptmanns and Werner is an English translation and a thoroughly re- vised edition of the German original that ap- peared in 1987.

This monograph considers the risks related to complex industrial plants. Special attention is paid to energy production and the chem- ical industry. As the subtitle indicates, the book evaluates other risk studies in addition to giving valuations of risks related to dif- ferent energy production technologies. The book also gives a rather comprehensive review on recent safety studies performed in nuclear power plants in the United States and Ger- many.

In the introduction the authors define the fundamental concepts needed in the rest of the book. In mathematical terms there is one particularly interesting definition. Risk is de- fined as the triplet

Ri = (si, hi, Xi)

where si is the event sequence leading to damage, hi is the corresponding expected fre-

quency of occurrence, and Xi represents the consequences. The identification of the event sequence reflects the pragmatic approach of the book. It is vital in risk engineering to iden- tify the sequences that lead to damage in or- der to be able to prevent accidents and to take restrictive measures after an accident. Simi- larly, it is necessary to know the sequence in order to assess the probabilities. In the ab- sence of sufficient statistics it is not possible to calculate or estimate the probabilities based on historical data only. It is necessary to know the physical and chemical processes effective in the event sequences.

In the second chapter different methods of risk analysis are presented. Many aspects of the processes are difficult to model, and hence, subjective expert opinions must be used. One of the most difficult factors to es- timate is the human element in the process. Some methods are described for the analysis and prediction of human error rates.

The descriptions in this chapter are rather superficial from the mathematical point of view. The presentation serves more practi- cal purposes. The text is directed to users of risk analyses who are usually nonmathemati- cians. In order to acquaint oneself more thor- oughly with the mathematics or the methods, the reader is referred to the references men- tioned at the end of the chapter.

The third chapter describes the risk anal- yses that have been performed in nuclear in- stallations. The emphasis is on the conse- quences on employees and population of ac- cidents in nuclear power plants. These analy- ses are extremely important and difficult. One has to handle very complicated processes and very rare incidents with severe consequences. The (fortunately) scarce data on accidents in different nuclear installations and short run- ning history of these installations together with very small probabilities (mainly of the or- der 10-6 or 10-7) renders the estimated prob- abilities very uncertain with wide confidence intervals. The assessing of these probabilities and their confidence intervals requires deep knowledge of the processes that take place in nuclear power plants. Methods from math- ematics, statistics, and reliability theory can only play an assisting role. The task, however, is so important that all the help that mathe- matics and statistics can give in estimating fre- quencies of rare events is welcomed.

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346 BOOK REVIEWS

The fourth chapter concentrates on risk studies for process plants. There are two spe- cific studies that are evaluated. The one per- formed in the U.K. examines the risks related to a whole industrial complex. The other (per- formed in the Netherlands) deals with differ- ent chemical plants. Impacts from other in- stallations were not included. As a conclusion it is worth mentioning that the risk studies in chemical installations are far behind those of nuclear installations. This reflects the worry that is felt towards the unknown risks of nu- clear power compared with those more famil- iar of process plants. These risks, however, can be very fatal. We only have to remem- ber Seveso and Bhopal to convince ourselves about this. The authors give the following list of requirements to be satisfied in order that risk analysis for process plants reach the level of the nuclear installations:

* Systematic collection of reliability data for components in process plants under adequate quality assurance.

* Systematic evaluation of operating expe- rience in order to obtain reliable infor- mation on accident-initiating events and their frequencies of occurrence.

* Development and validation of models for physical and chemical processes like the discharge of multi-phase and multi- component mixtures and for vapour cloud explosions.

* Development of models for the at- mospheric dispersion of explosible and toxic substances, accounting for surface roughness and buildings in the vicinity of the location of release.

* Determination of dose-effect relation- ships for important toxic substances.

The fifth chapter deals with risk compar- isons for nuclear and conventional energy conversion systems. The authors again refer to numerous earlier studies made on different energy production technologies. The studies are not limited to production plants. Also the construction of the plants, mining of the raw materials as well as all transportation and han- dling of waste are treated. Methodologies like input-output analysis also attempt to take into account the other segments in the economy in order to calculate the comprehensive effect of each technology to produce energy.

The sixth chapter considers the prevail- ing practices of appraisal of safety in nuclear

power plants. The probabilistic approach is visible in the definition of different safety lev- els. The ideology behind this is that an event sequence that leads to severe consequences must not have a high probability of occur- rence. This gives a natural scale for assess- ing the decreasing allowed probability with in- creasing severity of consequences.

The book reveals a huge need for further research on methods to be used in risk and re- liability analysis in both nuclear and process plants. Systematic gathering and analysis of data on events that do not lead to a catas- trophe are also needed. The book gives us a rather comprehensive picture of the present state of art and of the deficiencies therein. The importance of strict scientific approach is all the more important when we take into ac- count the fact that these results are used in po- litical decision-making when future guidelines for energy production are being made. This is not a book on applied mathematics, but it deals with one field where the need for applied mathematics is apparent.

MATH RUOHONEN The Sampo Group Turku, Finland

Nonlinear Elliptic and Evolution Problems and Their Finite Element Approximations. By A. Zenisek. Translation editor J. R. White- man. Academic Press Ltd., UK, 1990. xix + 422 pp. $94.50. ISBN 0-12-779560-X. Com- putational Mathematics and Applications.

As a summary of frustrating experiences, the First Law of Applied Mathematics an- nounces: "Nothing Fits." Thus, if you want to quote a result about convergence of finite element approximations, you are likely to find it for a basic polygonal domain, whereas your domain has a curved boundary; or, having fi- nally found a paper dealing with your type of nonlinearity, the initial data are there as- sumed smoother than allowed in your appli- cation, and so on.

Attempting partially to defy the First Law, the present treatise by Professor Zenisek is a synthesis of many investigations devoted to isolating and conquering specific difficul- ties. Let me briefly describe a culminat- ing Super Theorem of the book in the time- dependent situation. (There is a correspond-

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