Abstract
Stability of various systems’ characteristics with respect to changes in initial states or external factors are the key problems in all natural sciences. For stochastic systems stability often means insensitivity or low sensitivity of their output characteristics subject to changes in the shapes of some input distributions. In Kozyev et al. (2018) the reliability function for a two-components standby renewable system operating under the Marshall-Olkin failure model has been found and its asymptotic insensitivity to the shapes of its component times’ distributions has been proved. In the recent paper the problem of asymptotic insensitivity of stationary and quasi-stationary probabilities for the same model are considered.
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Notes
- 1.
The assumption about absolute continuity of c.d.f. is used only for convenient representation of the hazard rate functions \(\beta _k(x)\) and can be omitted.
- 2.
Note that the maximal root of the function \(\tilde{\pi }_3(s)\) is zero.
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Acknowledgments
The publication has been prepared with the support of the “RUDN University Program 5-100” (recipient V.V. Rykov, supervision). The reported study was funded by RFBR, project No. 17-01-00633 (recipient V.V. Rykov, formal analysis) and No. 17-07-00142 (recipient V.V. Rykov, mathematical model development).
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Rykov, V., Dimitrov, B. (2019). Renewal Redundant Systems Under the Marshall-Olkin Failure Model. Sensitivity Analysis. In: Vishnevskiy, V., Samouylov, K., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2019. Lecture Notes in Computer Science(), vol 11965. Springer, Cham. https://doi.org/10.1007/978-3-030-36614-8_18
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