Comparison of Reliability Systems Based Uncertainty

Authors: A. Aissani, H. Benaoudia

Abstract:

Stochastic comparison has been an important direction of research in various area. This can be done by the use of the notion of stochastic ordering which gives qualitatitive rather than purely quantitative estimation of the system under study. In this paper we present applications of comparison based uncertainty related to entropy in Reliability analysis, for example to design better systems. These results can be used as a priori information in simulation studies.

Keywords: Uncertainty, Stochastic comparison, Reliability, serie's system, imperfect repair.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1334900

References:

[1] A. Aissani,, Modèles Stochastiques de la Théorie de Fiabilité. Algiers, OPU, 1992 (in french).
[2] R.E. Barlow, F. Proshan, Statistical Theory of Reliability and Life Testing, Probability Models, New York, Holt, Rinehart and Winston, 1975.
[3] M. Brown, F. Proshan, "Imperfect Repair", J. Applied Probability 20, 851-859, 1983.
[4] N. Ebrahimi, F. Pellery, "New Partial Ordering of Survival Function Based on the Notion of Uncertainty," J. Appl. Probability 32, 202-211.
[5] N. Ebrahimi, "How to measure uncertainty in the residual Life Time Distribution", Sankhya, The Indian Journal of Statistics 58 (A), 48-56.
[6] M. Shaked, J.G. Shanthikumar, Stochastic Orders and their Applications, Boston, Academic Press, 1994.
[7] Terje Aven, "Reliability Analysi as a tool for expressing and communicating uncertainty," in: Recent Advances in Reliability Theory, Methodologies, Practice and Inference, Series Statistic for Industry and Technology, eds: Limnios N., M. Nikulin, Birkhauser, Boston, 2000.