Ordered properties on the residual life and inactivity time of -out-of- systems under double monitoring

The Mean Residual Lifetime of (<i>n</i> － <i> k</i> + 1)-out-of-<i>n</i> Systems in Discrete Setting

“…Among the researchers who investigated the reliability and aging properties of the conditional random variable , , r k n t T , under various conditions and for different values of k and r , we can refer to Bairamov et al [1], Asadi and Bairamov [2,3], Asadi and Goliforushani [4], Li and Zhao [5] and Zhang and Yang [6]. The extension to coherent systems has also been considered by several authors; see, among others, Li and Zhang [7], Navarro et al [8], Zhang [9,10], Zhang and Li [11], Asadi and Kelkin Nama [12], and references therein.…”

On system reliability in stress–strength setup

“…Similarly, a k-outof-n: G system is a system consisting of n components such that the system functions if, and only if, at least k components function. Some recent contributions on k-out-of-n systems, among others, are the works of Bairamov and Arnold (2008), Raqab (2009) and Zhang and Yang (2010).The number of path sets of k-out-of-n: F and k-out-of-n: G systems including n − j working components are n j for j < k and n j for j < n − k + 1, respectively. Thus the corresponding coefficients for k-out-of-n: F and k-out-of-n: G systems are given respectively by …”

Some results for repairable systems with minimal repairs

“…In the literature, several authors studied stochastic comparisons of the residual lifetimes of two systems. For recent results, one can see, Li and Lu , Khaledi and Shaked , Li and Zhang , Zhang , Zhang and Yang , Zhang and Li and Kochar and Xu . In the present paper, we consider a repairable system.…”