Abstract
This paper considers the problem of choosing between an existing component whose reliability is well established and a new component that has an unknown reliability. In some scenarios, the designer may have some initial beliefs about the new component’s reliability. The designer may also have the opportunity to obtain more information and to update these beliefs. Then, based on these updated beliefs, the designer must make a decision between the two components. This paper examines the statistical approaches for updating reliability assessments and the decision policy that the designer uses. We consider four statistical approaches for modeling the uncertainty about the new component and updating assessments of its reliability: a classical approach, a precise Bayesian approach, a robust Bayesian approach, and an imprecise probability approach. The paper investigates the impact of different approaches on the decision between the components and compares them. In particular, given that the test results are random, the paper considers the likelihood of making a correct decision with each statistical approach under different scenarios of available information and true reliability. In this way, the emphasis is on practical comparisons of the policies rather than on philosophical arguments.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aughenbaugh, J.M., Herrmann, J.W., 2007. Updating uncertainty assessments: A comparison of statistical approaches. In 2007 ASME International Design Engineering Technical Conferences. Las Vegas, NV.
Berger, J.O., 1984. The robust Bayesian viewpoint. In Robustness of Bayesian Analysis, Kadane, J.B. (editor), 63–124. North-Holland, New York.
Berger, J.O., 1985. Statistical Decision Theory and Bayesian Analysis. 2nd edition. Springer.
Berger, J.O., 1993. An overview of robust Bayesian analysis. Technical Report 93-53c, Purdue University.
Brown, L.D., Cai, T.T., DasGupta, A., 2001. Interval estimation for a binomial proportion. Statistical Science, 16(2), 101–133.
Coolen, F.P.A., 1994. On bernoulli experiments with imprecise prior probabilities. The Statistician, 43(1), 155–167.
Coolen, F.P.A., 1998. Low structure imprecise predictive inference for bayes’ problem. Statistics and Probability Letters, 36, 349–357.
Coolen, F.P.A., 2004. On the use of imprecise probabilities in reliability. Quality and Reliability in Engineering International, 20, 193–202.
Coolen-Schrijner, P., Coolen, F.P.A., 2007. Non-parametric predictive comparison of success-failure data in reliability. Proc. IMechE, Part 0: J. Risk and Reliability, 221, 319–327.
Dempster, A.P., 1967. Upper and lower probabilities induced by a multivalued mapping. The Annals of Mathematical Statistics, 38, 325–339.
Dubois, D., Prade, H.M., 1988. Possibility theory: an approach to computerized processing of uncertainty. Plenum Press, New York.
Groen, F.J., Mosleh, A., 2005. Foundations of probabilistic inference with uncertain evidence. International Journal of Approximate Reasoning, 39(1), 49–83.
Insua, D.R., Ruggeri, F., 2000. Robust Bayesian Analysis. Springer, New York.
Lindley, D.V., Phillips, L.D., 1976. Inference for a bernoulli process (a Bayesian view). American Statistician, 30, 112–119.
Rekuc, S.J., Aughenbaugh, J.M., Bruns, M., Paredis, C.J.J., 2006. Eliminating design alternatives based on imprecise information. In Society of Automotive Engineering World Congress. Detroit, MI.
Shafer, G., 1976. A Mathematical Theory of Evidence. Princeton University Press, Princeton.
Utkin, L.V., 2004a. Interval reliability of typical systems with partially known probabilities. European Journal of Operational Research, 153(3 SPEC ISS), 790–802.
Utkin, L.V., 2004b. Reliability models of m-out-of-n systems under incomplete information. Computers and Operations Research, 31(10), 1681–1702.
Walley, P., 1991. Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, New York.
Walley, P., 1996. Inferences from multinomial data: Learning about a bag of marbles. Journal of the Royal Statistical Society. Series B (Methodological), 58(1), 3–57.
Walley, P., Gurrin, L., Burton, P., 1996. Analysis of clinical data using imprecise prior probabilities. The Statistician, 45(4), 457–485.
Weber, M., 1987. Decision making with incomplete information. European Journal of Operational Research, 28(1), 44–57.
Weichselberger, K., 2000. The theory of interval probability as a unifying concept for uncertainty. International Journal of Approximate Reasoning, 24, 149–170.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Aughenbaugh, J.M., Herrmann, J.W. Reliability-Based Decision Making: A Comparison of Statistical Approaches. J Stat Theory Pract 3, 289–303 (2009). https://doi.org/10.1080/15598608.2009.10411926
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1080/15598608.2009.10411926