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Regression analysis of the structure function for reliability evaluation of continuous-state system

Author

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  • Gámiz, M.L.
  • Martínez Miranda, M.D.

Abstract

Technical systems are designed to perform an intended task with an admissible range of efficiency. According to this idea, it is permissible that the system runs among different levels of performance, in addition to complete failure and the perfect functioning one. As a consequence, reliability theory has evolved from binary-state systems to the most general case of continuous-state system, in which the state of the system changes over time through some interval on the real number line. In this context, obtaining an expression for the structure function becomes difficult, compared to the discrete case, with difficulty increasing as the number of components of the system increases. In this work, we propose a method to build a structure function for a continuum system by using multivariate nonparametric regression techniques, in which certain analytical restrictions on the variable of interest must be taken into account. Once the structure function is obtained, some reliability indices of the system are estimated. We illustrate our method via several numerical examples.

Suggested Citation

  • Gámiz, M.L. & Martínez Miranda, M.D., 2010. "Regression analysis of the structure function for reliability evaluation of continuous-state system," Reliability Engineering and System Safety, Elsevier, vol. 95(2), pages 134-142.
    • Handle: RePEc:eee:reensy:v:95:y:2010:i:2:p:134-142
    DOI: 10.1016/j.ress.2009.09.004
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    References listed on IDEAS

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    1. Gonzalez Manteiga, W. & Martinez Miranda, M. D. & Perez Gonzalez, A., 2004. "The choice of smoothing parameter in nonparametric regression through Wild Bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 487-515, October.
    2. Gregory Levitin, 2005. "The Universal Generating Function in Reliability Analysis and Optimization," Springer Series in Reliability Engineering, Springer, number 978-1-84628-245-4, April.
    3. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
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