In the situation of a multi-sample experiment consisting of differently equipped sequential k-out-of-n systems, scale parameters of underlying distributions from a general location-scale family of distributions are estimated under an order restriction. In each sample, the case of missing the smallest observations is included. Moreover, based on a profile likelihood a homogeneity test against an ordered alternative is proposed and analyzed. This work extends an approach of bhattacharya [2007. Testing for ordered failure rates under general progressive censoring. J. Statist. Plann. Inference 137, 1775–1786] in the progressive type-ii censoring framework.
Beutner, E. A., & Kamps, U. (2009). Order restricted statistical inference for scale parameters based on sequential order statistics. Journal of Statistical Planning and Inference, 139(9), 2963-2969. https://doi.org/10.1016/j.jspi.2009.01.017