Journal of Statistical Computation and Simulation Vol. 77, No. 1, January 2007, 19–27 Statistical inference based on progressively censored samples with random removals from the Burr type XII distribution SHUO-JYE WU*,YI-JU CHEN and CHUN-TAO CHANG Department of Statistics, Tamkang University, Tamsui, Taipei, Taiwan 251, Republic of China (Revised 7 July 2004; in final form 7 December 2005) In this article, we study the estimation problems for the Burr type XII distribution based on progressive type II censoring with random removals, where the number of units removed at each failure time has a discrete uniform distribution. We use the method of maximum likelihood to derive the point estimators of the parameters. The main purpose of this article is to construct the exact confidence interval and region for the parameters. Finally, a numerical example is presented to illustrate the methods developed here. Keywords: Confidence interval; Joint confidence region; Maximum likelihood estimator; Pivot; Progressive type II censoring; Random removals 1. Introduction In reliability analysis, experiments must often terminate before all units on test have failed. In such cases, one has complete information only on part of the sample. On all units which have not failed, one has only partial information. Such data are called censored. There are several types of censored tests. One of the most common censored tests is type II censoring. In type II censoring, a total of n units are placed on test, but instead of continuing until all n units have failed, the test is terminated at the time of the mth (1 ≤ m ≤ n) unit failure. In the literature, type II censoring with different failure time distributions has been investigated rather extensively by many authors including Mann et al. [1], Meeker and Escobar [2], and Lawless [3]. If an experimenter desires to remove live units at points other than the final termination point of the life test, the above described scheme will not be of use to the experimenter. Type II censoring does not allow for units to be lost or removed from the test at points other than the final termination point. This allowance will be desirable, as in the case of studies of wear, in which the study of the actual aging process requires units to be fully disassembled at different stages in the experiment. Intermediate removal may also be desirable when a compromise between reduced time of experimentation and the observation of at least some *Corresponding author. Email: shuo@stat.tku.edu.tw Journal of Statistical Computation and Simulation ISSN 0094-9655 print/ISSN 1563-5163 online © 2007 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/10629360600569204