Artificial Intelligence Review

, Volume 7, Issue 1, pp 3–42 | Cite as

Expert system verification and validation: a survey and tutorial

  • Robert M. O'Keefe
  • Daniel E. O'Leary


Assuring the quality of an expert system is critical. A poor quality system may make costly errors resulting in considerable damage to the user or owner of the system, such as financial loss or human suffering. Hence verification and validation, methods and techniques aimed at ensuring quality, are fundamentally important.

This paper surveys the issues, methods and techniques for verifying and validating expert systems. Approaches to defining the quality of a system are discussed, drawing upon work in both computing and the model building disciplines, which leads to definitions of verification and validation and the associated concepts of credibility, assessment and evaluation. An approach to verification based upon the detection of anomalies is presented, and related to the concepts of consistency, completeness, correctness and redundancy. Automated tools for expert system verification are reviewed.

Considerable attention is then given to the issues in structuring the validation process, particularly the establishment of the criteria by which the system is judged, the need to maintain objectivity, and the concept of reliability. This is followed by a review of validation methods for validating both the components of a system and the system as a whole, and includes examples of some useful statistical methods. Management of the verification and validation process is then considered, and it is seen that the location of methods for verification and validation in the development life-cycle is of prime importance.

Key Words

expert systems knowledge-based systems verification validation testing evaluation credibility assessment development life cycle statistics 

ACM Categories and Subject Descriptors

D.2.4 [Software Engineering]

Program Verification — Validation

D.2.5 [Software Engineering]

Testing and Debugging

1.2 [Artificial Intelligence]

Applications and Expert Systems

K.6.1 [Management of Computers and Information System]

Project and People Management — Life Cycle


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Adelman, L. (1991) ‘Experiments, Quasi-experiments, and Case Studies A Review of Empirical Methods for Evaluating Decision Support Systems’,IEEE Transactions on Systems, Man, and Cybernetics 21: 2, 293–301.Google Scholar
  2. Adrion, W., Branstad, M. and Cherniavsky, J. (1982) ‘Validation, Verification and Testing of Computer Software’,ACM Computing Surveys 14: 2, 159–192.Google Scholar
  3. Agarwal, R. and Tanniru, M. (1992) ‘A Petri-net Approach for Verifying the Integrity of Production Systems’,International Journal of Man-Machine Studies 26, 447–468.Google Scholar
  4. Bachant, J. and McDermott, J. (1983) ‘R1 Revisited: Four Years in the Trenches’,AI Magazine 5: 3, 21–32.Google Scholar
  5. Balci, O. (1987) ‘Credibility Assessment’, in Balci, O. (ed.),Proceedings of the 1987 Eastern Simulation Conference, the Society for Computer Simulation, La Jolla, CA.Google Scholar
  6. Balci, O. and Sargent, R. (1981) ‘A Methodology for Cost Risk Analysis in the Statistical Validation of Simulation Models’,Communications of the ACM 24: 4, 190–197.Google Scholar
  7. Balci, O. and Sargent, R. (1984) ‘Validation of Simulation Models Via Simultaneous Confidence Intervals’,American Journal of Mathematics and Management Sciences 4: 3&4, 375–406.Google Scholar
  8. Batarekh, A., Preece, A. D., Bennett, A. and Grogono, P. (1991) ‘Specifying an Expert System’,Expert Systems with Applications 2, 285–303.Google Scholar
  9. Bellman, K. L. (1990) ‘The Modeling Issues Inherent in Testing and Evaluating Knowledge-based Systems’,Expert Systems With Applications 1: 3, 199–216.Google Scholar
  10. Benbasat, I. and Dhaliwal, J. (1989) ‘A Framework for the Validation of Knowledge Acquisition’,Knowledge Acquisition 1, 215–233.Google Scholar
  11. Boehm, B. W. (1981)Software Engineering Economics, Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
  12. Boose, J. and Bradshaw, J. (1987) ‘Expertise Transfer and Complex Problems Using Aquinas as a Knowledge Acquisition Workbench for Expert Systems’,International Journal of Man-Machine Systems 26, 3–28.Google Scholar
  13. Boose, J. H. (1986)Expertise Transfer for Expert System Design, Elsevier, New York.Google Scholar
  14. Bratko, I., Mozetic, I. and Lavrac, N. (1989)KARDIO: A Study in Deep and Qualitative Knowledge for Expert Systems, MIT Press, Cambridge, MA.Google Scholar
  15. Buchanan, B. and Shortliffe, E. (1985)Rule-Based Expert Systems: The MYCIN Experiments of the Stanford Heuristic Project, Addison-Wesley, Reading, MA.Google Scholar
  16. Buchanan, B., Sutherland, G. and Feigenbaum, E. A. (1969) ‘Heuristic DENDRAL: A Program for Generating Explanatory Hypotheses in Organic Chemistry’, in Michie, D. (ed.),Machine Intelligence 4, Elsevier, NY.Google Scholar
  17. Castore, G. (1987) ‘Validation and Verification for Knowledge-based Control Systems’,Proceedings of the First Annual Workshop on Space Operations, Automation and Robotics, NASA, pp. 197–202.Google Scholar
  18. Chandrasekaran, B. (1983) ‘On Evaluating AI Systems for Medical Diagnosis’,AI Magazine 4: 2, 34–37.Google Scholar
  19. Chang, C. L., Combs, J. B. and Stachowitz, R. A. (1990) ‘A Report on the Expert Systems Validation Associate (EVA)’,Expert systems With Applications 1: 3, 217–230.Google Scholar
  20. Cochran, T. and Hutchins, B. (1987) ‘Testing, Verifying and Releasing an Expert System: The Case History of Mentor’,Proceedings of the Third IEEE Conference on AI Applications, pp. 163–167.Google Scholar
  21. Cohen, J. (1960) ‘A Coefficient of Agreement for Nominal Scales’,Educational and Psychological Measurement 20, 37–46.Google Scholar
  22. Cohen, J. (1968) ‘Weighted Kappa: Nominal Scale Agreement with Provision for Scaled Disagreement or Partial Credit’,Psychological Bulletin 70: 4, 213–220.Google Scholar
  23. Cragun, B. and Steudal, H. (1987) ‘A Decision-table-based Processor for Checking Completeness and Consistency in Rule-based Expert Systems’,International Journal of Man-Machine Systems 25: 5, 633–648.Google Scholar
  24. Davis, R. and Lenat, D. B. (1982)Knowledge-based Systems in Artificial Intelligence, McGraw-Hill, New York, NY.Google Scholar
  25. Davis, R. (1984) ‘Reasoning from First Principles in Electronic Troubleshooting’,International Journal of Man-Machine Studies 24, 347–410.Google Scholar
  26. Duchessi, P., Shawky, H. and Seagle, J. P. (1988) ‘A Knowledge-Engineered System for Commercial Loan Decisions’,Financial Management 17: 3, 57–65.Google Scholar
  27. Duda, R., Gaschnig J. and Hart, P. (1979) ‘Model Design in the Prospector Consultant System for Mineral Exploration’, in Michie, D. (ed.),Expert Systems in the Microelectronic Age, Edinburgh University Press, pp. 153–167.Google Scholar
  28. Eglese, R. W. (1986) ‘Heuristics in Operational Research’, in Belton, V. and O'Keefe, R. M. (eds.),Recent Developments in Operational Research, Pergamon Press, Oxford, UK, pp. 49–68.Google Scholar
  29. Enand, R., Kahn, G. S. and Mills, R. A. (1990) ‘A Methodology for Validating Large Knowledge Bases’,International Journal of Man-Machine Studies 33, 361–371.Google Scholar
  30. Ernst, C. J. (ed.) (1988)Management Expert Systems, Addison-Wesley, Reading, MA.Google Scholar
  31. Fleiss, J. L. (1981)Statistical Methods for Rates and Proportions, John Wiley, NY.Google Scholar
  32. Fox, M. S. (1990) ‘AI and Expert System Myths, Legends, and Facts’,IEEE Expert 5: 1, 8–20.Google Scholar
  33. Gains, B. R. (1987) ‘An Overview of Knowledge Acquisition and Transfer’,International Journal of Man-Machine Studies 26, 453–472.Google Scholar
  34. Gaschnig, J., Klahr, P., Pople, H., Shortliffe, E. and Terry, A. (1983) ‘Evaluation of Expert Systems: Issues and Case Studies’, in Hayes-Roth, F., Waterman, D. A. and Lenat, D. B. (eds.),Building Expert Systems, Addison-Wesley, Reading, MA, pp. 241–280.Google Scholar
  35. Ginsberg, A. (1988) ‘Knowledge-based Reduction: A New Approach to Checking Knowledge Bases for Inconsistency and Redundancy’,Proceedings of AAAI'88, AAAI, Menlo Park, CA, pp. 585–589.Google Scholar
  36. Ginsberg, A., Weiss, S. M. and Politakis, P. (1988) ‘Automatic Knowledge Base Refinement for Classification Systems’,Artificial Intelligence 35, 197–226.Google Scholar
  37. Gruhl, J. (1982) ‘Model Credibility and Independent Evaluation: Three Case Studies’,Omega 10: 5, 525–537.Google Scholar
  38. Hall, D. L. and Heinze, D. T. (1989) ‘The Use of Simulation Techniques for Expert System Test and Evaluation’,ISA Transactions 28: 1, 19–22.Google Scholar
  39. Hamilton, D., Kelley, K. and Culbert, C. (1991) ‘State-of-the-practice in Knowledge-based System Verification and Validation’, Technical Report, NASA/Johnson Space Center, Houston, TX.Google Scholar
  40. Hamilton, S. and Chervany, N. L. (1981) ‘Evaluating Information System Effectiveness — Part I: Comparing Evaluation Approaches’,MIS Quarterly 5: 3, 55–69.Google Scholar
  41. Hansen, J. and Messier, W. (1986) ‘A Preliminary Investigation of EDP-XPERT’,Auditing: A Journal of Theory and Practice 6: 1, 109–123.Google Scholar
  42. Harrison, P. R. (1989) ‘Testing and Evaluation of Knowledge-Based Systems’, in Liebowitz, J. and De Salvo, D. A. (eds.),Structuring Expert Systems, Prentice-Hall, Englewood Cliffs, NJ, pp. 303–329.Google Scholar
  43. Harrison, P. R. and Ratcliffe, P. A. (1991) ‘Towards Standards for the Validation of Expert Systems’,Expert Systems With Applications 2, 251–258.Google Scholar
  44. Hickam, D. H., Shortliffe, E. H., Bischoff, M. B., Scott, A. C. and Jacobs, C. D. (1985) ‘The Treatment Advice of a Computer-based Cancer Chemotherapy Protocol Advisor’,Annals of Internal Medicine 103, 928–936.Google Scholar
  45. Hilden, J. and Habbeman, J. D. F. (1990) ‘Evaluation of Clinical Decision Aids — More to Think About’,Medical Informatics 15: 3, 275–284.Google Scholar
  46. Jackson, P. (1986)Introduction to Expert Systems, Addison-Wesley, Reading, MA.Google Scholar
  47. Jacob, R. J. K. and Froscher, J. N. (1990) ‘A Software Engineering Methodology for Rule-based Systems’,IEEE Transactions on Knowledge and Data Engineering 2: 2, 173–189.Google Scholar
  48. Jafar, M. J. and Bahill, A. T. (1990) ‘Validator, A Tool for Verifying and Validating Personal Computer Based Expert Systems’, in Brown, D. E. and White C. C. (eds.),Operations Research and Artificial Intelligence: The Integration of Problem Solving Strategies, Kluwer Academic Press, Boston, MA.Google Scholar
  49. Keen, P. W. (1981) ‘Value Analysis: Justifying Decision Support Systems’,MIS Quarterly 5: 1, 1–15.Google Scholar
  50. Kerlinger, F. (1973)Foundations of Behavioral Research, Holt, Reinhart & Winston, New York.Google Scholar
  51. King, M. and Phythian, G. J. (1992) ‘Validating an Expert Support System for Tender Enquiry Evaluation: A Case Study’,Journal of the Operational Research Society 43, 203–214.Google Scholar
  52. Klinker, G., Bentolila, J., Genetet, S., Grimes, M. and McDermott, J. (1987) ‘KNACK — Report-Driven Knowledge Acquisition’,International Journal of Man-Machine Studies 26, 65–79.Google Scholar
  53. Kulikowski, C. A. and Weiss, S. H. (1982) ‘Representation of Expert Knowledge for Consultation: the Casnet and Expert Projects’, in Szolovits, P. (ed.),Artificial Intelligence in Medicine, Westview Press, Boulder, CO, pp. 21–56.Google Scholar
  54. Laudaner, C. (1990) ‘Correctness Principles for Rule-based Systems’,Expert Systems With Applications 1: 3, 291–316.Google Scholar
  55. Landry, M., Malouin, J.-L. and Oral, M. (1983) ‘Model Validation in Operations Research’,European Journal of Operational Research 14, 207–220.Google Scholar
  56. Langlotz, C. P. and Shortliffe, E. H. (1983) ‘Adapting a Consultation System to Critique User Plans’,International Journal of Man-Machine Studies 19, 479–496.Google Scholar
  57. Langlotz, C. P., Shortliffe, E. H. and Fagan, L. M. (1986) ‘Using Decision Theory to Justify Heuristics’, inProceedings of AAAI'86, AAAI, Menlo Park, CA, pp. 215–219.Google Scholar
  58. Lee, S. and O'Keefe, R. M. ‘Subsumption Anomalies in Hybrid Knowledge-bases’,International Journal of Expert Systems (forthcoming).Google Scholar
  59. Lehner, P. (1989) ‘Toward an Empirical Approach to Evaluating the Knowledge Base of an Expert System’,IEEE Transactions on Systems, Man and Cybernetics 19: 3, 658–662.Google Scholar
  60. Lethan, H. and Jacobsen, H. (1987) ‘ESKORT — An Expert System for Auditing VAT Accounts’,Proceedings of Expert Systems and their Applications, Avignon, France.Google Scholar
  61. Liebowitz, J. (1986) ‘Useful Approach for EvaluatingExpert Systems’,Expert Systems 2: 3, 86–96.Google Scholar
  62. Liu, N. K. and Dillon, T. (1991) ‘An Approach Towards the Verification of Expert Systems Using Numerical Petri Nets’,International Journal of Intelligent Systems 6, 255–276.Google Scholar
  63. Meservy, R., Bailey, A. and Johnson, P. (1986) ‘Internal Control Evaluation: A Computational Model of the Review Process’,Auditing: A Journal of Theory and Practice 6: 1, 44–74.Google Scholar
  64. Messier, W. F. and Hansen, J. V. (1992) ‘A Case Study and Field Evaluation of EDP-XPERT’,International Journal of Intelligent Systems in Accounting, Finance and Management 1: 3, 173–186.Google Scholar
  65. Miller, L. A. (1989) ‘A Comprehensive Approach to the Verification and Validation of Knowledge-Based Systems’, inProceedings of the 1989 AAAI Workshop on Verification, Validation and Testing of Knowledge-Based Systems, AAAI, Menlo Park, CA.Google Scholar
  66. Miller, L. A. (1990) ‘Dynamic Testing of Knowledge Bases Using the Heuristic Testing Approach’,Expert Systems with Applications 1: 3, 249–269.Google Scholar
  67. Moninger, W. R., Stewart, T. R. and McIntosh, P. (1988) ‘Validation of Knowledge-Based Systems for Probabilistic Reasoning’, inProceedings of the 1988 AAAI Workshop on Verification, Validation and Testing of Knowledge-Based Systems, AAAI, Menlo Park, CA.Google Scholar
  68. Mosteller, F. and Rourke, R. E. K. (1973)Sturdy Statistics, Addison Wesley, Reading, MA.Google Scholar
  69. Nazareth, D. (1989) ‘Issues in the Verification of Knowledge in Rule-Based Systems’,International Journal of Man-Machine Studies 30, 255–271.Google Scholar
  70. Nguyen, T., Perkins, W., Laffery, T. and Pecora, D. (1985) ‘Checking an Expert Systems Knowledge Base for Consistency and Completeness’,Proceedings of the International Joint Conference on Artificial Intelligence, pp. 374–378.Google Scholar
  71. Nguyen, T., Perkins, W., Laffery, T. and Pecora, D. (1987) ‘Knowledge Base Verification’,AI Magazine 8: 2, 65–79.Google Scholar
  72. Norman, P. and Naveed, S. (1990) ‘A Comparison of Expert System and Human Operator Performance for Cement Kiln Operation’,Journal of the Operational Research Society 41: 11, 1007–1019.Google Scholar
  73. O'Keefe, R. M. (1989) ‘The Evaluation of Decision-aiding Systems: Guidelines and Methods’,Information and Management 17, 217–226.Google Scholar
  74. O'Keefe, R. M. and Lee, S. (1990) ‘An Integrative Model of Expert System Verification and Validation’,Expert Systems and Their Application 1: 3, 231–236.Google Scholar
  75. O'Keefe, R. M. and O'Leary, D. E. ‘Managing and Performing Expert System Validation’, in Grabowski, M. and Wallace, W. A. (eds.),Advances in Expert Systems and Artificial Intelligence for Management, JAI Press (forthcoming).Google Scholar
  76. O'Keefe, R. M., Balci, O. and Smith, E. (1987) ‘Validating Expert System Performance’,IEEE Expert 2: 4, 81–89.Google Scholar
  77. O'Leary, D. (1987) ‘Validation of Expert Systems’,Decision Sciences 18: 3, 468–486.Google Scholar
  78. O'Leary, D. (1988a) ‘Methods of Validating Expert Systems’,Interfaces 18: 6, 72–79.Google Scholar
  79. O'Leary, D. (1988b) ‘On the Representation and the Impact of Reliability on Expert System Weights’,International Journal of Man-Machine Studies 29: 6, 637–646.Google Scholar
  80. O'Leary, D. (1988c) ‘Expert System Prototyping as a Research Tool’, in Turban, E. and Watkins, P. (eds.),Applied Expert Systems, North-Holland, Amsterdam, pp. 17–32.Google Scholar
  81. O'Leary, D. (1990a) ‘Soliciting Weights or Probabilities from Experts for Rule-Based Systems’,International Journal of Man-Machine Studies 32, 293–301.Google Scholar
  82. O'Leary, D. (1990b) ‘Verification of Frames and Semantic Networks’, in Gaines, B. (ed.),Proceedings of the Fourth Annual Workshop on Knowledge Acquisition, Banff, Canada.Google Scholar
  83. O'Leary, D. (1991) ‘Design, Development and Validation of Expert Systems: A Survey of Developers’, inVerification, Validation and Testing of Expert Systems, John Wiley, New York, NY, pp. 3–19.Google Scholar
  84. O'Leary, D. and Kandelin, N. (1988) ‘Validating the Weights in Rule-based Expert Systems’,International Journal of Expert Systems 1: 3, 253–279.Google Scholar
  85. O'Leary, D. and Watkins, P. (1989)Expert Systems in Internal Auditing, Research Monograph, Institute of Internal Auditors.Google Scholar
  86. O'Leary, T. J., Goul, M., Moffitt, K. E. and Radwan, A. E. (1990) ‘Validating Expert Systems’,IEEE Expert 5: 3, 51–58.Google Scholar
  87. O'Neil, M. and Glowinski, A. (1990) ‘Evaluating and Validating Very Large Knowledge-based Systems’,Medical Informatics 15: 3, 237–252.Google Scholar
  88. Ow, P. and Smith, S. (1987) ‘Two Design Principles for Knowledge-based Systems’,Decision Sciences 18: 3, 430–447.Google Scholar
  89. Pearce, D. A. (1988) ‘The Induction of Fault Diagnosis Systems from Qualitative Models’,Proceedings of AAAI '88, AAAI, Menlo Park, CA, pp. 353–357.Google Scholar
  90. Preece, A. D. (1989) ‘Verification of Rule-based Systems in Wide Domains’, in Shadbolt, N. (ed.),Research and Development in Expert Systems VI, Cambridge University Press, pp. 66–77.Google Scholar
  91. Preece, A. D. (1990) ‘Towards a Methodology for Evaluating Expert Systems’,Expert Systems 7: 4, 215–223.Google Scholar
  92. Preece, A. D., Shinghal, R. and Batarekh, A. (1992) ‘Verifying Expert Systems: A Logical Framework and a Practical Tool’,Expert Systems With Applications 5, 421–436.Google Scholar
  93. Quinlan, J. R. (1979) ‘Discovering Rules by Induction from Large Collections of Samples’, in Michie, D. (ed.),Expert Systems in the Microelectronic Age, Edinburgh Univesity Press, UK, pp. 168–201.Google Scholar
  94. Radwan, A. E., Goul, M., O'Leary, T. J. and Moffitt, K. (1989) ‘A Verification Approach for Knowledge-based Systems’,Transportation Research-A 23A: 4, 287–300.Google Scholar
  95. Rushby, J. (1988)Quality Measures and Assurance for AI Software, NASA Contract Report 4187, Washington DC.Google Scholar
  96. Shatz, H., Strahs, R. and Campbell, L. (1987) ‘ExperTAX: The Issue of Long-Term Maintenance’,Proceedings of the 3rd International Conference on Expert Systems, pp. 291–300.Google Scholar
  97. Shaw, M. and Woodward, J. (1988) ‘Validation in a Knowledge Support System: Construing and Consistency with Multiple Experts’,International Journal of Man-Machine Studies 29: 3, 329–350.Google Scholar
  98. Shpilberg, D. and Graham, L. E. (1989) ‘Developing ExperTAX: An Expert System for Corporate Tax Accrual and Planning’, in Vasarhelyi, M. A. (ed.),Artificial Intelligence in Accounting and Auditing, Markus Weiner, New York, NY, pp. 343–372.Google Scholar
  99. Soloway, E., Bachant, J. and Jensen, K. (1987) ‘Assessing the Maintainability of XCON-in-RIME: Coping with the Problems of a Very Large Rule-base’, inProceedings of AAAI '87, AAAI, Menlo Park, CA.Google Scholar
  100. Suen, C. Y., Grogono, P. D. and Shingahl, R. (1990) ‘Verifying, Validating and Measuring the Performance of Expert Systems’,Expert Systems With Applications 1, pp. 93–102.Google Scholar
  101. Suwa, M., Scott, A. and Shortliffe, E. (1982) ‘Completeness and Consistency in Rule-Based Expert Systems’,AI Magazine 3: 4, 16–21 (see also Buchanan and Shortliffe (1985), Chapter 8).Google Scholar
  102. Turing, A. M. (1950) ‘Computing Machinery and Intelligence’,Mind 59.Google Scholar
  103. Waterman, D. A. (1986)A Guide to Expert Systems, Addison-Wesley, Reading, MA.Google Scholar
  104. Weiss, S. M. and Kulikowski, C. A. (1984)A Practical Guide to Designing Expert Systems, Rowman, and Allenhead.Google Scholar
  105. Weitzel, J. R. and Kershberg, L. (1989) ‘Developing Knowledge-Based Systems: Reorganizing the System Development Life-Cycle’,Communications of the ACM 32, 482–487.Google Scholar
  106. Williams, G. (1976) ‘Comparing the Joint Agreement of Several Raters with Another Rater’,Biometrics 32: 2, 619–627.Google Scholar
  107. Wyatt, J. and Spiegelhalter, D. (1990) ‘Evaluating Medical Expert Systems: What to Test and How?’,Medical Informatics 15: 3, 205–217.Google Scholar
  108. Yager, R. R. and Larsen, H. L. (1991) ‘On Discovering Potential Inconsistencies in Validating Uncertain Knowledge Bases by Reflecting on the Input’,IEEE Transactions on Systems, Man and Cybernetics 21: 4, 790–801.Google Scholar
  109. Yen, J., Neches, R. and MacGregor, R. (1991) ‘CLASP: Integrating Term Subsumption Systems and Production Systems’,IEEE Transactions on Knowledge and Data Engineering 3: 1, 25–31.Google Scholar
  110. Yu., V., Buchanan, B., Shortliffe, E., Wraith, S., Davis, R., Scott, A. and Cohen, S. (1979a) ‘Evaluating the Performance of a Computer-based Consultant’,Computer Programs in Biomedicine 9: 1, 95–102.Google Scholar
  111. Yu., V., Fagan, L., Wraith, S., Clancey, W., Scott, A., Hanigan, J., Blum, R., Buchanan, B. and Cohen S. (1979b) ‘Antimicrobial Selection by Computer’,Journal of the American Medical Association 242: 12, 1279–1282 (see also Buchanan and Shortliffe (1985), Chapter 31).Google Scholar
  112. Zlatareva, N. P. (1992) ‘Truth Maintenance Systems and Their Application for Verifying Expert System Knowledge Bases’,Artificial Intelligence Review 6: 1, 67–108.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Robert M. O'Keefe
    • 1
  • Daniel E. O'Leary
    • 2
  1. 1.Department of Decision Sciences and Engineering SystemsRensselaer Polytechnic InstituteTroyUSA
  2. 2.Graduate School of BusinessUniversity of Southern CaliforniaLos AngelesUSA

Personalised recommendations