Reliability Analysis of Multi-state Two-Dimensional System by Universal Generating Function

  • K. MeenakshiEmail author
  • S. B. Singh
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 302)


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.


Multi-state system Two-dimensional system Reliability Universal generating function Mean time to failure Sensitivity analysis 


\( R_{stm} (t) \)

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


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


ith components of system


Symbol for counting elements of k × l matrix.


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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of Mathematics, Statistics and Computer ScienceG.B. Pant University of Agriculture and TechnologyPantnagarIndia

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