Statistical Methodology 10 (2013) 58–71 Contents lists available at SciVerse ScienceDirect Statistical Methodology journal homepage: www.elsevier.com/locate/stamet On properties of progressively Type-II censored order statistics arising from dependent and non-identical random variables M. Rezapour a , M.H. Alamatsaz b , N. Balakrishnan c , E. Cramer d,∗ a Department of Statistics, Shahid Bahonar University, Kerman, Iran b Department of Statistics, University of Isfahan, Isfahan, 81746-73441, Iran c Department of Mathematics and Statistics, McMaster University, Ontario L8S 4K1, Canada d Institute of Statistics, RWTH Aachen University, Aachen, Germany article info Article history: Received 9 March 2012 Received in revised form 5 June 2012 Accepted 16 June 2012 Keywords: Archimedean copula Order statistics Progressive censoring Progressively Type-II censored order statistics Reliability systems abstract In this paper, we study progressively Type-II censored order statis- tics arising from identical as well as non-identical units under test which are jointly distributed according to an Archimedean cop- ula with completely monotone generator (PCOSDNARCM-II). Den- sity, distribution and joint density functions of PCOSDNARCM-II are all derived. For certain special cases, more explicit expres- sions are presented. Some interesting recurrence relations and transformational properties are also established. Results estab- lished here contain the results by Balakrishnan and Cramer [5] as particular cases. Finally, some examples of PCOSDNARCM-II are also provided. © 2012 Elsevier B.V. All rights reserved. 1. Introduction An efficient way of collecting lifetime data that results in a saving in experimental time and cost is progressive Type-II censoring. When the units under test are dependent, we should use a model that takes this dependency into account. Let us consider a dependent progressively Type-II censored sample. Under this scheme, N dependent units (with some joint distribution) are placed on a life-test; after the i-th failure, R i (i = 1,..., m ≤ N ) surviving units are removed at random from the test. ∗ Corresponding author. E-mail addresses: mohsenrzp@gmail.com (M. Rezapour), alamatho@sci.ui.ac.ir (M.H. Alamatsaz), bala@mcmaster.ca (N. Balakrishnan), erhard.cramer@rwth-aachen.de (E. Cramer). 1572-3127/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.stamet.2012.06.001