It is shown how various exact nonparametric inferences based on an ordinary right or progressively type-ii right censored sample can be generalized to situations where two independent samples are combined. We derive the relevant formulas for the combined ordered samples to construct confidence intervals for a given quantile, prediction intervals, and tolerance intervals. The results are valid for every continuous distribution function. The key results are the derivations of the marginal distribution functions in the combined ordered samples. In the case of ordinary type-ii right censored order statistics, it is shown that the combined ordered sample is no longer distributed as order statistics. Instead, the distribution in the combined ordered sample is closely related to progressively type-ii censored order statistics.
Balakrishnan, N., Beutner, E. A., & Cramer, E. (2010). Exact two-sample non-parametric confidence, prediction, and tolerance intervals based on ordinary and progressively Type-II right censored data. Test, 19(1), 68-91. https://doi.org/10.1007/s11749-008-0133-7