In the study of the reliability of technical systems in reliability engineering, coherent systems play a key role. In this paper we consider a coherent system consisting of n components with independent and identically distributed components and propose two time-dependent criteria. The first criterion is a measure of the residual lifetime of live components of a coherent system having some of the components alive when the system fails at time t. The second criterion is a time-dependent measure which enables us to investigate the inactivity times of the failed components of a coherent system still functioning though some of its components have failed. Several ageing and stochastic properties of the proposed measures are then established.
S. Goliforushani. M. Asadi. N. Balakrishnan. "On the residual and inactivity times of the components of used coherent systems." J. Appl. Probab. 49 (2) 385 - 404, June 2012. https://doi.org/10.1239/jap/1339878793