In this article, we consider a particular type of coherent systems, in which, when the coherent system fails, either no active component remains or the remaining active components are connected in parallel. This work studies two coherent systems of such type with two components, four coherent systems with three components, and seven coherent systems with four components as examples. Lifetime as well as system signature of each of these coherent systems is given. We investigate the restart of such a coherent system using a single cold standby component. The reliability of a system is studied through the (reliability) characteristics such as reliability function, mean time to failure, mean residual life functions of the system. We compute signature-based exact expression for the reliability function of the considered coherent system, which is equipped with a cold standby component. Also, we obtain three different mean residual life functions of the system. So far, no attempt has been made to study such coherent systems in cold standby sparing; therefore, we have provided some new results. We illustrate the theoretical results by considering three particular coherent systems as examples.

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