Abstract
Gertsbakh et al. (Journal of Applied Probability, 49, 416–429, 2012) proposed the concept of bivariate signature for a 3-state system. In this paper, we first give an equivalent definition for the bivariate signature in the sense of order statistics of component lifetimes and establish the formula for computing the bivariate signature of the dual of a 3-state system. A useful method for computing the bivariate signature based on the combinatorial meaning of the bivariate tail signature is presented. By this method, we derive formulas for computing the bivariate signatures of some systems consisting of independent modules. Some examples are also presented to illustrate our main results.
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Acknowledgements
The research is supported by the Fundamental Research Funds for the Central Universities and the NNSF of China (Nos. 11071232,70821001, 71090401).
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Da, G., Hu, T. (2013). On Bivariate Signatures for Systems with Independent Modules. In: Li, H., Li, X. (eds) Stochastic Orders in Reliability and Risk. Lecture Notes in Statistics(), vol 208. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6892-9_7
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DOI: https://doi.org/10.1007/978-1-4614-6892-9_7
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