Interval Enclosures for Reliability Metrics

Marcilia Andrade Campos, André Feitoza Mendonça

Resumo


The computation of reliability metrics involves real numbers. Therefore, numerical problems are generated due to the limitation of representing and operating with real numbers in computers. This paper proposes interval functions for controlling numeric errors in the computation of reliability metrics values of complex systems, based on interval mathematics and high accuracy arithmetic. The interval functions calculate interval enclosures, using Intlab toolbox, for real values of reliability metrics and the SHARPE software was used to validate the results. Analysis of the numerical results obtained with the proposed functions showed that the intervals really enclose the real numbers calculated by the software SHARPE, indicating that these functions, in fact, are an alternative for auto-validating representation of these reliability values of complex systems.


Palavras-chave


Reliability; Interval mathematics; High accuracy arithmetic; Interval enclosures

Texto completo:

PDF (English)

Referências


M.A. Campos. Interval probability: applications to discrete random variables. TEMA – Trends in Applied and Computational Mathematics, 1(2) (2000), 333–343.

M.A. Campos & M.G. Santos. Interval Probabilities and Enclosures. Computational & Applied Math- ematics, 32(1) (2013), 413–423.

O. Caprani, K. Madsen & H.B. Nielsen. “Introduction to Interval Analysis”. Technical University of Denmark, Copenhagen (2002).

F.P.A. Coolen & M.J. Newby. “Bayesian Reliability Analysis with Imprecise Prior Probabilities”. Eindhoven University of Technology, Eindhoven (1992).

C.E. Ebeling. “An Introduction to Reliability and Maintainability Engineering”. Waveland Press, Illinois (1997).

B.V. Goldberg. What every computer scientist should know about floating-point arithmetic. ACM Computing Surveys, 23(1) (1991), 153–230.

P.S. Grigoletti, G.P. Dimuro & L.V. Barboza. Módulo python para matemática intervalar. TEMA – Trends in Applied and Computational Mathematics, 8(1) (2007), 73–82.

N.J. Higham. Accuracy and stability of numerical algorithms, 2nd edn. SIAM Publications, Philadel- phia (2002).

C. Hirel, X. Sahner, X. Zang & K. Trivedi. “Reliability and Performability Modeling using SHARPE 2000” (2011). (avaliable in: .)

IEEE Standard 754-2008: IEEE Standard for Floating-Point Arithmetic. IEEE Computer Society, New York (2008).

R. Klatte, U. Kulisch, C. Lawo, M. Rauch & A. Wietho. “C-XSC - A C++ class library for extended scientific computing”. Springer, Heidelberg (1993).

U.W. Kulisch & W.L. Miranker. “Computer Arithmetic in Theory and Practice”, Academic Press, New York (1981).

W. Kuo & M.J. Zuo. “Optimal Reliability Modeling: Principles and Applications”. John Wiley & Sons Inc, New Jersey (2003).

G. Levitin, L. Xing, H. Ben-Haim & Y. Dai. Reliability of series-parallel systems with random failure propagation time. IEEE Transactions on Reliability, PP, Issue: 99, 1–11 (2013).

The MathWorks Inc, “MATLAB 7.5” (2007). (available in: http://www.mathworks.com/ products/matlab/.)

A.F. Mendonc ̧a & M.A. Campos. Confiabilidade Autovalidável de Sistemas com Processo Exponencial de Falhas. TEMA – Trends in Applied and Computational Mathematics, 14(3) (2013), 383–398.

P.L. Meyer. “ Probabilidade Aplicações à Estatística”. Livros Técnicos e Científicos, Rio de Janeiro (1983).

R.E. Moore, W. Strother & C.T. Yang. “Interval Integrals”. Technical Report Space Div. Report LMSD703073, Lockheed Missiles and Space Co., (1960).

R.E. Moore. “Interval Analysis”. Englewood Cliffs, New Jersey (1966).

R.E. Moore. “Methods and Applications of Interval Analysis”. Society for Industrial and Applied Mathematics Philadelphia, Philadelphia, (1979).

R.E. Moore, R. B. Kearfott & M.J. Cloud. “Introduction to Interval Analysis”. Society for Industrial and Applied Mathematics Philadelphia, Philadelphia, (2009).

S.M. Rump: INTLAB – INTerval LABoratory. In Tibor Csendes, editor, Developments in Reliable Computing, pages 77-104. Kluwer Academic Publishers, Dordrecht (1999).

R. Sahner, K.S. Trivedi & A. Puliafito. “Performance and Reliability of Computer Systems: An Example-Based Approach Using the SHARPE Software Package”. Kluwer Academic Publishers, Boston (1996).

R. Sahner & K. Trivedi. Reliability Modeling Using SHARPE. Reliability, IEEE Transactions, 36(2) (1987), 186–193.

M. Spivak. “Calculus”. Publish or Perish, Houston (1994).

T. Sunaga. Theory of An Interval Algebra and its Application to Numerical Analysis. RAAG Memoirs, 2 (1958), 29–46.

L.V. Utkin. Imprecise reliability of cold standby systems. International Journal of Quality & Reliability Management, 20 (2003), 722–739.

L.V. Utkin. Interval reliability of typical systems with partially known probabilities. European Journal of Operational Research, 153(3) (2004), 790–802.

Y. Wang. Imprecise probabilities based on generalized intervals for system reliability assessment. International Journal of Reliability & Safety, 1 (2009), 1–23.

J. Yang & H. Sun. Discrete method for structural interval reliability analysis. Chinese Control and Decision Conference, 1 (2008), 2441–2446.




DOI: https://doi.org/10.5540/tema.2016.017.02.0143

Métricas do artigo

Carregando Métricas ...

Metrics powered by PLOS ALM

Apontamentos

  • Não há apontamentos.



Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of  Applied and Computational Mathematics (SBMAC)

Indexed in:

                        

 

Desenvolvido por:

Logomarca da Lepidus Tecnologia