Nature of probability in safety assessments and application to earthquakes

Nuclear Engineering and Design 60 (1980) 73-77 © North-Holland Publishing Company

NATURE OF PROBABILITY IN SAFETY ASSESSMENTS AND APPLICATION TO EARTHQUAKES * D. COSTES D~partement de St2retdNucldaire, Commissariat ~ l'Energie Atomique, F-92260 Fontenay-aux-Roses, France

Received 15 February 1980

The protection of nuclear installations against earthquakes requires as a first step a realistic description of seismic ground motions which are likely to occur, with their corresponding probabilities. However, large discrepancies in probability evaluations appear between the opinions of the experts for a given site. This paper addresses the concept of confidence intervals, which should not be used when bayesian estimations are concerned, and recommends to use questionnaires which allow weighting elements to be identified.

Probability studies of accidents on nuclear installations allow, on the one hand, the assessment of the corresponding risks for the public, on the other hand, the identification o f the way systems and components contribute to accident prevention and mitigation. The bulk of safety precautions could then be optimized by taking into account the individual reliabilities o f the components, within a cost-benefit framework. As a matter o f fact, if the failure probabilities of elementary compofients in normal operation can be evaluated through statistics, the probabilistic study of initiation and development of accidents requires also probability assessments through experts' judgements. The experts select physical models for the concerned phenomena, taking into account the results of calculations and experiments, and describing by numerical probabilities the likelihood they finally attach to each process considered as possible. This probabilistic wording makes it possible to integrate their judgements into the global probabilistic rationale concerning the safety of the concerned installation. One must wonder what is the most correct expres-

sion these judgements should take in terms o f probabilities, and how to deal with discrepancies between experts. It is first necessary to know whether the probability can be stated as an approximate figure o f a real, physical probability, which could be analyzed as finely as desired, at the price of supplementary studies. In the field of standardized components, one can make the assumption that such real probabilities for given behaviours do exist. It is then possible, using recorded frequencies on a limited sampling, to express such probabilities by best estimate values and confidence intervals at a given ratio: for instance, there are 95 chances out o f 100 that this probability stands between 0.17 and 0.20. In most cases, probabilistic assessments cannot be stated in this way by the experts. The required probabilities represent then only the expert's opinion on a physical process which is imperfectly known although i't is entirely determined by its premisses. The expert cannot generally perform a statistical evaluation o f all. relevant premisses because they are much too complex, and expresses only his opinion in a probabilistic wording on these premisses. Let us take as an example the assessment of the seismic intensity which could potentially occur on a given site. It is understood that not only the macroseismic intensity, but all characteristics o f a seismic motion can be considered as o f random nature ; the

* Panel Contribution presented at the 2nd International Seminar on Structural Reliability of Mechnical Components and Subassemblies of Nuclear Power Plants, Berlin (West), Fed. Rep. Germany, August 20 and 21, 1979. 73

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probabilistic description of the earthquake should then integrate many parameters. Let us suppose however than a unique, continuous level parameter can represent this intensity. If the expert uses several different methods or assumptions conducting to several curves of the exceedence probabifity versus intensity for the given site, he can first weight the values of these methods or assumptions and indicate a best estimate curve, together with confidence intervals. This simulates the evaluation of a real probability curve but has not the same meaning. In fact, the expert can consider a given event (the experienced intensity is between two given levels) and weight the several attached probabilities related to the weighted several assumptions; he then obtains a unique figure of probability which represents his assessment for this event. Finally, he should indicate a unique weighted curve, without confidence intervals, representing his assessment of the exceedence probability for all intensity levels. This curve should however be related to the information he has been able to collect. More generally, when the expert proposes his probability curve, he should include explanations and comments related to uncertainties, which allow for the curve to be examined by the decision-makers, or which will enable comparisons with the curves submitted by other experts, and finally will lead to the choice of a modified curve. These comments take then logically the place of a quantitative confidence interval. The above considerations may be illustrated by the survey made by D. Okrent [1] of the opinions of seven experts for the seismicity of eleven sites in the United States. These opinions are expressed in terms of intensity or of maximum acceleration. It is not clear, however, whether each expert has considered the true maximum acceleration, which has a weak correlation with the destructiveness of a ground motion, or the equivalent acceleration, that is a conventional level to be used with standardized accelerograms or spectra. The questionnaire which has been used is presented in Annex. Fig. 1 shows the exceedence probability versus acceleration curves for all the sites and for each expert, together with average distributions given by Hsieh et al. [2]. Fig. 2 shows the exceedence probability versus intensity curves. Fig. 3 is a compendium given by the author in a paper for OECD [3] for the

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exceedence probability curves in several regions. Fig. 4(a) and 4(b) allow to compare the estimates of the various experts, for the exceedence probabilities of 10-3/yr and 10-6/yr. These figures show that, even taking into account the relatively broad confidence intervals indicated by the experts, the assessments are quite different, and the general tendencies for extrapolating the high level, low probability motions from the low level, high probability ones are not clear. D. Okrent collects in [1] the comments of the experts on each site, without proposing overall conclusions. It has been generally estimated that this paper has put into evidence very large differences between the probabilistic assessments of several experts, and then a lack of credibility for such assessments. We would like, on the contrary, to consider this Okrent-paper as a starting point to facilitate the reaching of a consensus. We consider that a more directive questionnaire would have provided clearer and more useful assessments. As such investigations will certainly be carried out for other sites, we propose below, as a first draft, the following questionnaire. (1) What intensity-prob ability relationship, based on statistics, at least for low and medium levels,

D. Costes / Nature o f probability in safety assessments

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would you propose for a mean undefined site within a large region containing the site? (2) For this mean site, what are the parts of probabilities to be applied, for each intensity level: (a) to local effects of distant earthquakes, at a focal distance of more than 100 km? (b) to effects of nearer earthquakes, between

20 km and 100 km? (c) to effects of nearby earthquakes, less than 20 km? (3) What are the corresponding characteristics of these three types of earthquakes, when physical parameters of the motion are concerned: maximum ground acceleration, maximum velocity, shape and

78

D. Costes / Nature o f probability in safety assessments

duration of accelerogram, shape of spectrum? What is the effect of the ground nature? (4) By what features does the given site differ from the above mean site? (5) To what seismogenic structures do you correlate the earthquakes which are likely to be experienced on the site? (6) Do you use a 'direct method' for assessing the seismic probability, which relies upon probabilitydensities of the source event and upon attenuation-distance relationship? Which method? Do you use a different method? How do you cope with uncertainties? (7) Have you used your method for the mean site considered above? Did you correlate it with statistics? (8) What are your results for the given site, in com-

parison with the results for tile mean site (No. (1)and (2))7 (9) What are the principal difficulties which have been met in these evaluations, and what are your recommendations for better evaluation? We hope that this draft will help to work out questionnaires allowing the experts to present step by step probabilistic assessments, subject to easy comparisons and backfitting.

References [1] D. Okrent, UCLA-ENG-7515 (February 1975). [2] T. ttsieh, D. Okrent and Apostolakis, UCLA-ENG-7516 (March 1975). [3] D. Costes, CSNI Report No. 26, OECD (1978).