CAUTIOUS RELIABILITY ANALYSIS OF MULTI-STATE AND CONTINUUM-STATE SYSTEMS BASED ON THE IMPRECISE DIRICHLET MODEL

2006 ◽  
Vol 13 (05) ◽  
pp. 433-453 ◽  
Author(s):  
LEV V. UTKIN
Keyword(s):  
Set Theory ◽  
System Reliability ◽  
Random Set ◽  
Continuum State ◽  
Random Set Theory ◽  
Reliability Estimates ◽  
Proposed Model ◽  
Imprecise Dirichlet Model ◽  
Dirichlet Model ◽  
Interval Valued

Cautious reliability estimates of multi-state and continuum-state systems are studied in the paper under condition that initial data about reliability of components are given in the form of interval-valued observations, measurements or expert judgments. The interval-valued information is processed by means of a set of the imprecise Dirichlet model which can be regarded as a set of Dirichlet distributions. The developed model of reliability provides cautious reliability measures when the number of observations or measurements is rather small. It can be viewed as an extension of models based on random set theory and robust statistical models. A numerical example illustrates the proposed model and an algorithm for computing the system reliability.

CAUTIOUS ANALYSIS OF PROJECT RISKS BY INTERVAL-VALUED INITIAL DATA

2006 ◽  
Vol 14 (06) ◽  
pp. 663-685 ◽  
Author(s):  
LEV V. UTKIN
Keyword(s):  
Initial Data ◽  
Net Present Value ◽  
Cash Flows ◽  
Random Set ◽  
Present Value ◽  
Random Set Theory ◽  
Imprecise Dirichlet Model ◽  
Project Risks ◽  
Dirichlet Model ◽  
Interval Valued

One of the most common performance measures in selection and management of projects is the Net Present Value (NPV). In the paper, we study a case when initial data about the NPV parameters (cash flows and the discount rate) are represented in the form of intervals supplied by experts. A method for computing the NPV based on using random set theory is proposed and three conditions of independence of the parameters are taken into account. Moreover, the imprecise Dirichlet model for obtaining more cautious bounds for the NPV is considered. Numerical examples illustrate the proposed approach for computing the NPV.

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