On conditional spacings and their properties under coherent system setting

This paper introduces the concepts of conditional spacings and normalized conditional spacings when an (n−k+1)-out-of-n system or a general coherent system having independent and identically distributed (IID) components just fails at time t. First, we obtain the marginal reliability and joint reliability of conditional spacings, and then conduct some comparisons of conditional spacings. We also investigate the dependent and ISO ∗ properties of the conditional spacings. Finally, the case when the lifetimes of components are IID exponential is discussed in detail.