  As a specific proportional hazard rates model, sequential order statistics
can be used to describe the lifetimes of load-sharing systems. Inference for
these systems needs to account for small sample sizes, which are prevalent in
reliability applications. By exploiting the probabilistic structure of
sequential order statistics, we derive exact finite sample inference procedures
to test for the load-sharing parameters and for the nonparametrically specified
baseline distribution, treating the respective other part as a nuisance
quantity. This improves upon previous approaches for the model, which either
assume a fully parametric specification or rely on asymptotic results.
Simulations show that the tests derived are able to detect deviations from the
null hypothesis at small sample sizes. Critical values for a prominent case are
tabulated.
