Sequential order statistics have been introduced to model sequential kk-out-of-nn systems which, as an extension of kk-out-of-nn systems, allow the failure of some components of the system to influence the remaining ones. Based on an independent sample of vectors of sequential order statistics, the maximum likelihood estimators of the model parameters of a sequential kk-out-of-nn system are derived under order restrictions. Special attention is paid to the simultaneous maximum likelihood estimation of the model parameters and the distribution parameters for a flexible location-scale family. Furthermore, order restricted hypothesis tests are considered for making the decision whether the usual kk-out-of-nn model or the general sequential kk-out-of-nn model is appropriate for a given data.
Balakrishnan, N., Beutner, E. A., & Kamps, U. (2008). Order restricted inference for sequential k-out-of-n stystems. Journal of Multivariate Analysis, 99(7), 1489-1502. https://doi.org/10.1016/j.jmva.2008.04.014