Reliability properties of consecutive k-out-of-n systems of arbitrarily dependent components

In this paper, the reliability properties of consecutive k-out-of-n   systems with arbitrarily dependent components are studied. For 2k⩾n2k⩾n we present efficient formulas to compute the reliability characteristics such as meantime to failure, failure rate, and mean residual lifetime. Approximations for the survival functions when 1⩽k⩽n1⩽k⩽n are also provided. The results are illustrated for the multivariate survival distribution generated by a Weibull and Inverse-Gaussian mixture.