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On the meaning of probability in the context of probabilistic safety assessment
Reliability Engineering and System Safety 23 (1988) 305-308
Technical Note On the Meaning of Probability in the Context of Probabilistic Safety Assessment
ABSTRACT Assessments of reliability and safety in technology require the application not only offrequentistic statistics but also of subjective estimates of probabilities. This is true in particular for decision-making about complex systems made up of both 'hard' and 'soft' elements. Problems occur when objective and subjective considerations have to be integrated and accommodated to the decision-makers' mental models.
The following comments on the editor's questions about the meaning of probability in the context of probabilistic safety assessment are based on an evaluation of the writer's impressions derived from a number of studies related to nuclear safety and the reliability of building materials, In these studies the writer has in principle participated as a materials engineer in cooperation with specialists on philosophy, statistics and psychology. Classical statistics is by definition the basis of any analysis of the probability of events assumed to be stochastic in nature. In many cases such analyses may lead to reliable predictions. Experience tells us, however, that strict orthodox statistics should not always be used as the sole basis for safety assessments. There may be conditions when other than 'objective', frequentistic arguments can be more important and decisive. So-called 'subjective' estimates not only serve as a complement to classical assessments when data are lacking, but may sometimes be preferred on epistemological grounds. In recent years, theoretical philosophers also interested in the psychological aspects of assessments of probability have advanced ideas about 305 Reliability Engineering and System Safety 0951-8320/88/$03.50 © 1988 Elsevier Science Publishers Ltd, England. Printed in Great Britain
306
Gustq[ Ostberg
epistemic or second-order probabilities in order to deal with such cases as court decisions when an 'objective', statistical treatment alone might not appear satisfactory. For the sake of brevity, the reader is referred to the literature for examples showing that arguments based on other than frequentistic analyses may be quite respectable and convincing from a logical and epistemological point of view. 1 -8 The application of approaches that are complementary and alternative to classical statistics has an appeal not only on philosophical grounds. There is enough experience of failures of systems, in particular complex systems, that cannot primarily be related to causes accounted for as stochastic in a regular probabilistic assessment. On the contrary, numerous failures have occurred unexpectedly with respect to their causes; sometimes these cases are labelled 'inconceivable'ft' 1o This is true even when the utmost care has been taken to ensure that the system in question was analysed and described as completely as possible using conventional techniques, for instance in nuclear and aerospace technologies. With hindsight, some of these unforeseen failures can in principle be explained and remedied with reference to causes which were in fact known beforehand. Nevertheless, their mere occurrence in contrast to predictions about their unlikelihood, based on classical probabilistic assessments, calls for openness towards complementary and alternative perspectives. From treatments made by theoretical philosophers that also involve psychological considerations it appears that mental aspects need to be taken into account. Observations made by psychologists support the idea that the mental models used by those assigned to decide on probabilities may make it possible to extend safety assessment beyond the bounds of classical statistics.9- 12 Again it should be stressed that caution has to be taken to avoid 'subjectivity' that is not warranted by the deficiencies of more 'positivistic' analyses, but rather used only for convenience. (The term 'positivistic' is used here reluctantly in view of its ambiguity, for lack of a better alternative.) 'Subjective' assumptions are not meant to be a substitute for data which can eventually be acquired, at least approximately, in some way or other. Furthermore, epistemic or second order probabilities should not be considered as a means of falsification of classical assessments but as complementary or alternative inferences, the values of which should be estimated with respect to the aim of the assessment in question. Many risk assessors educated and trained according to a 'positivistic' paradigm will find it difficult to accept and respect an approach based on other than so-called 'objective' data to be dealt with using mathematics only. One way of overcoming the reluctance to consider other evidence may be to recognize the fact that most classical probabilistic analyses of complex systems involve some estimates and evaluations of data by processes that are
On the meaning of probability in the context of PSA
307
influenced by attitudes and mentalities based on values. Even issues which by description appear quite 'factual' and straightforward can be found to contain elements based on values. 13 If properly applied according to the guide-lines just indicated, so-called 'subjective' assessments should be a means of resolving a dilemma in risk assessments during decision-making that has become more evident lately in cases of societal importance. High-level decision-makers who are inclined towards holistic views are not content with classical, frequentistic, 'objective' assessments alone for at least two reasons. As mentioned above and elaborated in a paper recently, 12 the mental models of risks differ from the strict statistical models. The mental models also have to consider values that are not evident or elicited in conventional accounts of probabilities. The introduction of arguments based on 'subjective' estimates, therefore, makes the ultimate decision-makers more comfortable. As a consequence, their judgements are more likely to become trustworthy and defensible in the long run. Until recently classical, frequentistic probabilistics has dominated risk assessments made in organized and formalised ways, in particular in public reviews. On the other hand, many risk assessments are made more or less intuitively with little or no statistical basis, but rather against the background of tacit knowledge about risks associated with the type of event in question. In such cases the decision-maker is left without the assistance of any competence related to the application of the philosophy and psychology of epistemological or subjective assessments. Both of these extremes-frequentistic probabilities excluding other than exact numbers and epistemological, subjective estimates respectively--may lead to less satisfactory decisions about risks. Disadvantages and deficiencies of any of these methods should not, however, be used as categorically negative arguments against them. Both methods should rather be regarded as complements or alternatives to be used to an extent considered proper with respect to the values and aims of the decision-making. Finally, to respond to the editor's question about cases of 'wrong' decisions, it is difficult to find examples that are indisputably of one type of approach or the other. The case of the probability of the catastrophic failure of a nuclear pressure vessel referred to above ~3 might possibly serve as an illustration. REFERENCES 1. G/irdenfors, P., Forecasts, decisions and uncertain probabilities. Erkennmis, 14 0979), 159-81. 2. G~irdenfors, P. & Sahlin, N.-E., Unreliable probabilities, risk taking and decision making. Synthese, 53 (1982), 361-86.
308
Gustat Ostber~
3. GS,rdenfors, P. & Sahlin, N.-E., Decision making with unreliable probabilities. British Journal of Mathematical and Statistical Psychology, 36 (1983), 240-51. 4. Sahlin, N.-E., Preference among preferences as a method for obtaining a higher order metric scale. British Journal of Mathematical and Statistical Psychology, 34 (1981), 62 75. 5. Sahlin, N.-E., On second order probabilities and the notion ofepistemic risk. In Foundations ~1FUtility and Risk Theory with Applications, ed. B. P. Stigum & F. D. Wenstop, D. Reidel, Dordrecht, 1983, pp. 95-104. 6. Sahlin, N.-E., Level of aspiration and risk. Philosophical Studies, No. 24, Department of Philosophy, University of Lund, 1984. 7. Sahlin, N.-E., How to be 100% certain 99.5 % of the time. Journal of Philosophy (1986), 91--111. 8. Goldsmith, R. W. & Sahlin, N.-E., The role of second-order probabilities in decision making. In Analysing and Aiding Decision Processes, ed. P. C. Humphreys, O. Svensson & A. Vari. North-Holland, Amsterdam, 1983, pp. 456 67. 9. Ostberg, G., Hoffstedt, H., Holm, G., Klingenstierna, B., Rydnert, B., Samonsonowitz, V., Sj6berg, L., Inconceivable events in handling material in a heavy mechanical engineering industry. FTL A-report A16: 71E, 1977. 10. Ostberg, G., Evaluation of a design for inconceivable event occurrence. Materials & Design, 5 (1984), 88-93. 11. Brehmer, B., Development of mental models for decision in technological systems. In New Technology and Human Error, ed. J. Rasmussen, K. Duncan & J. Leplat. John Wiley, 1987, pp. 111-20. 12. Ostberg, G., Rydnert, B. & Ofverbeck, P., How decision makers deal with low probabilities. Report to the Swedish Energy Research Commission, Sweden, Project No. AES 13132, 1987. 13. ()stberg, G., Some reflections on attitudes and mind-sets concerning pressure vessel failure in nuclear reactors. In Assuring Structural Integrity of Steel Reactor Pressure Bounda O, Compounds, ed. K. E. Stahlkopf & L. E. Steele. Elsevier Applied Science, London (in press).
Gustaf ()stberg Engineering Materials, University o[ Lund, Box 118, S-221 O0 Lund, Sweden
Technical Note On the Meaning of Probability in the Context of Probabilistic Safety Assessment
ABSTRACT Assessments of reliability and safety in technology require the application not only offrequentistic statistics but also of subjective estimates of probabilities. This is true in particular for decision-making about complex systems made up of both 'hard' and 'soft' elements. Problems occur when objective and subjective considerations have to be integrated and accommodated to the decision-makers' mental models.
The following comments on the editor's questions about the meaning of probability in the context of probabilistic safety assessment are based on an evaluation of the writer's impressions derived from a number of studies related to nuclear safety and the reliability of building materials, In these studies the writer has in principle participated as a materials engineer in cooperation with specialists on philosophy, statistics and psychology. Classical statistics is by definition the basis of any analysis of the probability of events assumed to be stochastic in nature. In many cases such analyses may lead to reliable predictions. Experience tells us, however, that strict orthodox statistics should not always be used as the sole basis for safety assessments. There may be conditions when other than 'objective', frequentistic arguments can be more important and decisive. So-called 'subjective' estimates not only serve as a complement to classical assessments when data are lacking, but may sometimes be preferred on epistemological grounds. In recent years, theoretical philosophers also interested in the psychological aspects of assessments of probability have advanced ideas about 305 Reliability Engineering and System Safety 0951-8320/88/$03.50 © 1988 Elsevier Science Publishers Ltd, England. Printed in Great Britain
306
Gustq[ Ostberg
epistemic or second-order probabilities in order to deal with such cases as court decisions when an 'objective', statistical treatment alone might not appear satisfactory. For the sake of brevity, the reader is referred to the literature for examples showing that arguments based on other than frequentistic analyses may be quite respectable and convincing from a logical and epistemological point of view. 1 -8 The application of approaches that are complementary and alternative to classical statistics has an appeal not only on philosophical grounds. There is enough experience of failures of systems, in particular complex systems, that cannot primarily be related to causes accounted for as stochastic in a regular probabilistic assessment. On the contrary, numerous failures have occurred unexpectedly with respect to their causes; sometimes these cases are labelled 'inconceivable'ft' 1o This is true even when the utmost care has been taken to ensure that the system in question was analysed and described as completely as possible using conventional techniques, for instance in nuclear and aerospace technologies. With hindsight, some of these unforeseen failures can in principle be explained and remedied with reference to causes which were in fact known beforehand. Nevertheless, their mere occurrence in contrast to predictions about their unlikelihood, based on classical probabilistic assessments, calls for openness towards complementary and alternative perspectives. From treatments made by theoretical philosophers that also involve psychological considerations it appears that mental aspects need to be taken into account. Observations made by psychologists support the idea that the mental models used by those assigned to decide on probabilities may make it possible to extend safety assessment beyond the bounds of classical statistics.9- 12 Again it should be stressed that caution has to be taken to avoid 'subjectivity' that is not warranted by the deficiencies of more 'positivistic' analyses, but rather used only for convenience. (The term 'positivistic' is used here reluctantly in view of its ambiguity, for lack of a better alternative.) 'Subjective' assumptions are not meant to be a substitute for data which can eventually be acquired, at least approximately, in some way or other. Furthermore, epistemic or second order probabilities should not be considered as a means of falsification of classical assessments but as complementary or alternative inferences, the values of which should be estimated with respect to the aim of the assessment in question. Many risk assessors educated and trained according to a 'positivistic' paradigm will find it difficult to accept and respect an approach based on other than so-called 'objective' data to be dealt with using mathematics only. One way of overcoming the reluctance to consider other evidence may be to recognize the fact that most classical probabilistic analyses of complex systems involve some estimates and evaluations of data by processes that are
On the meaning of probability in the context of PSA
307
influenced by attitudes and mentalities based on values. Even issues which by description appear quite 'factual' and straightforward can be found to contain elements based on values. 13 If properly applied according to the guide-lines just indicated, so-called 'subjective' assessments should be a means of resolving a dilemma in risk assessments during decision-making that has become more evident lately in cases of societal importance. High-level decision-makers who are inclined towards holistic views are not content with classical, frequentistic, 'objective' assessments alone for at least two reasons. As mentioned above and elaborated in a paper recently, 12 the mental models of risks differ from the strict statistical models. The mental models also have to consider values that are not evident or elicited in conventional accounts of probabilities. The introduction of arguments based on 'subjective' estimates, therefore, makes the ultimate decision-makers more comfortable. As a consequence, their judgements are more likely to become trustworthy and defensible in the long run. Until recently classical, frequentistic probabilistics has dominated risk assessments made in organized and formalised ways, in particular in public reviews. On the other hand, many risk assessments are made more or less intuitively with little or no statistical basis, but rather against the background of tacit knowledge about risks associated with the type of event in question. In such cases the decision-maker is left without the assistance of any competence related to the application of the philosophy and psychology of epistemological or subjective assessments. Both of these extremes-frequentistic probabilities excluding other than exact numbers and epistemological, subjective estimates respectively--may lead to less satisfactory decisions about risks. Disadvantages and deficiencies of any of these methods should not, however, be used as categorically negative arguments against them. Both methods should rather be regarded as complements or alternatives to be used to an extent considered proper with respect to the values and aims of the decision-making. Finally, to respond to the editor's question about cases of 'wrong' decisions, it is difficult to find examples that are indisputably of one type of approach or the other. The case of the probability of the catastrophic failure of a nuclear pressure vessel referred to above ~3 might possibly serve as an illustration. REFERENCES 1. G/irdenfors, P., Forecasts, decisions and uncertain probabilities. Erkennmis, 14 0979), 159-81. 2. G~irdenfors, P. & Sahlin, N.-E., Unreliable probabilities, risk taking and decision making. Synthese, 53 (1982), 361-86.
308
Gustat Ostber~
3. GS,rdenfors, P. & Sahlin, N.-E., Decision making with unreliable probabilities. British Journal of Mathematical and Statistical Psychology, 36 (1983), 240-51. 4. Sahlin, N.-E., Preference among preferences as a method for obtaining a higher order metric scale. British Journal of Mathematical and Statistical Psychology, 34 (1981), 62 75. 5. Sahlin, N.-E., On second order probabilities and the notion ofepistemic risk. In Foundations ~1FUtility and Risk Theory with Applications, ed. B. P. Stigum & F. D. Wenstop, D. Reidel, Dordrecht, 1983, pp. 95-104. 6. Sahlin, N.-E., Level of aspiration and risk. Philosophical Studies, No. 24, Department of Philosophy, University of Lund, 1984. 7. Sahlin, N.-E., How to be 100% certain 99.5 % of the time. Journal of Philosophy (1986), 91--111. 8. Goldsmith, R. W. & Sahlin, N.-E., The role of second-order probabilities in decision making. In Analysing and Aiding Decision Processes, ed. P. C. Humphreys, O. Svensson & A. Vari. North-Holland, Amsterdam, 1983, pp. 456 67. 9. Ostberg, G., Hoffstedt, H., Holm, G., Klingenstierna, B., Rydnert, B., Samonsonowitz, V., Sj6berg, L., Inconceivable events in handling material in a heavy mechanical engineering industry. FTL A-report A16: 71E, 1977. 10. Ostberg, G., Evaluation of a design for inconceivable event occurrence. Materials & Design, 5 (1984), 88-93. 11. Brehmer, B., Development of mental models for decision in technological systems. In New Technology and Human Error, ed. J. Rasmussen, K. Duncan & J. Leplat. John Wiley, 1987, pp. 111-20. 12. Ostberg, G., Rydnert, B. & Ofverbeck, P., How decision makers deal with low probabilities. Report to the Swedish Energy Research Commission, Sweden, Project No. AES 13132, 1987. 13. ()stberg, G., Some reflections on attitudes and mind-sets concerning pressure vessel failure in nuclear reactors. In Assuring Structural Integrity of Steel Reactor Pressure Bounda O, Compounds, ed. K. E. Stahlkopf & L. E. Steele. Elsevier Applied Science, London (in press).
Gustaf ()stberg Engineering Materials, University o[ Lund, Box 118, S-221 O0 Lund, Sweden