On the mean residual life of a k-out-of-n:G system with a single cold standby component

Nonparametric predictive inference for system reliability using the survival signature

“…For systems with only one type of component, the signature has been derived for some specific system structures [26,27,28,36]. Deriving the survival signature for specific system structures in the case of multiple component types is an interesting topic for research.…”

Stochastic comparisons of residual lifetimes and inactivity times of coherent systems with dependent identically distributed components

“…The residual life time at a age/time t P 0 is denoted by X t ¼ X À tjX > t ð Þ , and the inactivity time of X at time t P 0 is denoted by X ðtÞ ¼ t À XjX 6 t ð Þ . The aging properties and the stochastic comparison results of the residual life time and the inactivity time are extensively studied in the literature, see for example Block, Savits, and Singh (1998), Chandra and Roy (2001), Ross (1996), Li and Lu (2003), Li and Zuo (2004), Misra, Gupta, and Dhariyal (2008), Pellerey and Petakos (2002), Zhang and Li (2003), Eryilmaz (2012) and Si, Wang, Hu, and Zhou (2011). Also for the study of the eta functions one may refer to Glaser (2001).…”

Dynamic network reliability modeling under nonhomogeneous Poisson processes

“…Recently, there has been much interest and focus on the lifetime network and system reliability based on the concept of signatures; see, for example, Boland, Samaniego, and Vestrup (2003), Samaniego (2008, 2010), Rychlik (2007, 2010), Zhang (2010), Gertsbakh and Shpungin (2009, 2012, Levitin, Gertsbakh, and Shpungin (2011), Eryilmaz (2011, 2012 and Balakrishnan and Asadi (2012). The developments on the reliability and lifetime properties of coherent systems, however, are mainly based on the assumption that the system has n independent identically distributed (i.i.d.)…”