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Reliability Bounds of Dependent Circular Consecutive \(\boldsymbol{k}\)-out-of-\(\boldsymbol{n:G}\) Systems

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Computation of reliability function of a coherent system is a difficult task especially when the system’s configuration is complex. Hence, sometimes, we should simply work with some approximations, as bounds reliability. The computation of these bounds has been widely studied in the case of coherent systems with independent and identically distributed (i.i.d) components. However, few results have been obtained in the case of heterogeneous (non i.d) dependent components. In this paper, we derive sharp bounds for the reliability of circular consecutive \(k\)-out-of-\(n:G\) systems consisting by dependent components with identical or arbitrary distribution functions. Also some stochastic comparisons are made. Illustrative examples are included.

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Correspondence to Megraoui Fatima Zohra or Belaloui Soheir.

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Zohra, M.F., Soheir, B. Reliability Bounds of Dependent Circular Consecutive \(\boldsymbol{k}\)-out-of-\(\boldsymbol{n:G}\) Systems. Math. Meth. Stat. 32, 81–87 (2023).

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