Decision-Based Approach for Reliability Design

[+] Author and Article Information
Efstratios Nikolaidis

Mechanical, Industrial and Manufacturing Engineering Department,  The University of Toledo, Toledo, OH 43606enikolai@eng.utoledo.edu

In the rest of the paper, epistemic uncertainty will be called “uncertainty.”

J. Mech. Des 129(5), 466-475 (May 03, 2006) (10 pages) doi:10.1115/1.2712213 History: Received February 04, 2006; Revised May 03, 2006

We propose a decision-based approach for reliability design when there is insufficient information for constructing probabilistic models. The approach enables a designer to perform reliability-cost trade-offs and to assess the importance of variability and epistemic uncertainty. A method for decision under epistemic uncertainty is first presented and justified by presenting axioms on a decision maker’s (DM’s) preferences and by assuming that the DM’s goal is to find the most immune act (in terms of having undesirable consequences) to deviations of the state of the world from an expected state. Thus, the philosophy of the method is similar to that of robust reliability (Ben Haim, Y., 1996, Robust Reliability in the Mechanical Sciences, Springer-Verlag, Berlin). A new formulation of reliability design problems is proposed based on the above decision method and is compared to two reliability-based design optimization formulations that minimize cost given a maximum acceptable failure probability or maximize expected utility. The method is demonstrated on a decision where a designer has to choose between two materials for a structure.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 5

Counterpart of Fig. 4 for the diesel car. The numbers next to the ellipses decrease as the meanings “unacceptable return” and “possible return” are stretched.

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Figure 6

Possibility of a fuzzy event

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Figure 7

Reliability design viewed as a decision

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Figure 8

Conditional utility functions of probability of failure for risk seeking (left panel) and risk averse (right panel) DMs as a function of the relative frequency of failure

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Figure 1

Example of a decision problem under uncertainty: the return rate of the decision depends on the price of gas

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Figure 2

Explanation of axioms about value difference function

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Figure 3

Eliciting possibility of state s by considering certain amount that is equivalent to a gamble. Superscript “C” in SC denotes complement of S.

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Figure 4

Degree to which each gas price is possible and degree to which the resulting return over investment is unacceptable for the hybrid car. The numbers next to the ellipses decrease as the meanings “unacceptable return” and “possible return” are stretched.



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