In this paper, by considering two multi-state semi-coherent systems sharing some components, we define the multi-state joint signature. Then, some properties of this multi-state joint signature are discussed in detail, and some preservation results are established in terms of stochastic ordering. A south-east shift order for comparing the multi-state joint signature matrices is then discussed. Finally, some numerical examples are presented for illustrating all the theoretical results established here.
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This work has been supported by the National Natural Science Foundation of China (No.72001016 and No.71631001). Our thanks also go to the anonymous reviewers and the Editor-in-Chief for their useful comments and suggestions on the earlier version of this manuscript which led to this improved version.
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Yi, H., Balakrishnan, N. & Cui, L. On Dependent Multi-State Semi-Coherent Systems Based on Multi-State Joint Signature. Methodol Comput Appl Probab (2021). https://doi.org/10.1007/s11009-021-09877-3
- Joint signature
- Stochastic ordering
- Preservation property
- South-east shift order
Mathematics Subject Classification (2010)
- Primary 60E15
- Secondary 62H10