Abstract
In this paper, two dimensional multi-state non-repairable systems having m rows and n columns have been studied. Markov stochastic process has been applied for obtaining probabilities of the components. Reliability metrics such as reliability, mean time to failure and sensitivity analysis of the target system with the application of universal generating function are evaluated. Finally, the developed model is demonstrated with the help of a numerical example.
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Abbreviations
- \( R_{stm} (t) \) :
-
Reliability of system at time t
- \( \lambda_{{s^{ * } \omega }}^{i} \) :
-
Failure rate of component i from state s* to \( \omega \)
- \( p_{ie} (t) \) :
-
Probability of component i in state e
- D :
-
Demands of system performance
- \( U_{stm} (z) \) :
-
UGF of system
- \( \varphi (U_{stm} (z),D) \) :
-
Function contain only those terms which have sum of the performances ≥D
- E i :
-
ith components of system
- I :
-
Symbol for counting elements of k × l matrix.
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Meenakshi, K., Singh, S.B. (2020). Reliability Analysis of Multi-state Two-Dimensional System by Universal Generating Function. In: Roy, P., Cao, X., Li, XZ., Das, P., Deo, S. (eds) Mathematical Analysis and Applications in Modeling. ICMAAM 2018. Springer Proceedings in Mathematics & Statistics, vol 302. Springer, Singapore. https://doi.org/10.1007/978-981-15-0422-8_7
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