On residual lifetimes in sequential (n-k+1)-out-of-n systems

Sequential order statistics is an extension of ordinary order statistics. They model the successive failure times in sequential k-out-of-n systems, where the failures of components possibly affect the residual lifetimes of the remaining ones. In this paper, we consider the residual lifetime of the components after the kth failure in the sequential (n - k + 1)-out-of-n system. We extend some results on the joint distribution of the residual lifetimes of the remaining components in an ordinary (n - k + 1)-out-of-n system presented in Bairamov and Arnold (Stat Probab Lett 78(8):945-952, 2008) to the case of the sequential (n - k + 1)-out-of-n system.