Methods for computing the reliability of complex systems described in the current paper are grounded on partial information on system components. A tool for inferring the interval-valued models is the natural extension and the upper and lower bounds of the characteristics to be interpreted as coherent upper and lower previsions. A generic algorithm to find a solution of the natural extension in a practically affordable way braking down the general problem into problems that are much easier to solve is described. In general this can be made at the cost of a lesser precision in the previsions of interest. It is also shown that for some particular cases the genuine, minimally coherent, solutions can be found through the algorithm developed. The second part of the paper is devoted to those cases when the reliability of components constituting a system is represented by identical interval-valued reliability characteristics. That is, all the components are characterized, for example, by probabilities to failure in the same time interval, or by mean times to failure or some others. Often namely these particular cases take place in reliability analysis practice. In this respect, based on the previous works by the authors of the current paper some new findings have been disclosed and new results obtained on particular practical cases.
Keywords. Imprecise probability theory, imprecise reliability, natural extension, previsions.
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Authors addresses:
Igor Kozine
Systems Analysis Department
Building 100
P.O. Box 49, 4000 Roskilde
Denmark
Lev Utkin
Department of Computer Science
Institutski per. 5
Saint Petersburg
194021, Russia
E-mail addresses:
| Igor Kozine | igor.kozine@risoe.dk |
| Lev Utkin | lvu@utkin.usr.etu.spb.ru |