###
3rd International Symposium
on

Imprecise
Probabilities and Their Applications

ISIPTA '03

#####
University of Lugano

Lugano, Switzerland

14-17 July 2003

####
ELECTRONIC PROCEEDINGS

## Lev Utkin

# A Second-Order Uncertainty Model of Independent Random Variables: An Example of the Stress-Strength Reliability

### Abstract

A second-order hierarchical uncertainty model of a system of independent random variables is studied in the paper. It is shown that the complex non-linear optimization problem for reducing the second-order model to the first-order one can be represented as a finite set of simple linear programming problems with a finite number of constraints. The stress-strength reliability analysis by unreliable information about statistical parameters of the stress and strength exemplifies the model. Numerical examples illustrate the proposed algorithm for computing the stress-strength reliability.

** Keywords. ** Stress-Strength Reliability, Imprecise Probabilities, Second-Order Uncertainty, Natural Extension, Previsions, Linear Programming

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** Authors addresses: **

Department of Computer Science,

St. Petersburg Forest Technical Academy

Institutski per. 5,

St. Petersburg, 194021

** E-mail addresses: **

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