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In this paper, the influence of a cold standby component on a coherent system is studied. A method for computing the system reliability of coherent systems with a cold standby component based on signature is presented. Numerical examples are presented. Reliability and mean time to failure of different systems are computed.

A system can be classified with respect to the physical arrangement of its components
and the functioning principle. A circular consecutive k-within-m-out-of-n:F system consists
of n circularly ordered components and fails if and only if there are m consecutive
components that include among them at least k failed components. A circular consecutive
k-within-m-out-of-n:F system turns into circular consecutive k-out-of-n:F for
m = k and k-out-of-n:F system for m = n. In this study, signature-based analysis of
circular consecutive k-within-m-out-of-n:F system is performed. A new approximation
to this system is provided based on maximum number of failed components and an
illustrative example is given for different values of n,m, k to compare the approximate
results with simulated and exact results.