Exact Nonparametric Inference for Component and System Lifetime Distributions Based on Joint Signatures

Based on the observed lifetimes of two systems with shared components, we construct exact nonparametric confidence intervals for quantiles of component and system lifetimes using the minimum and maximum lifetimes, as well as by using all component lifetimes. The coverage probabilities and expected widths of these confidence intervals are then compared for several signature matrices and sample sizes.