FEN FAKÜLTESİ FEN DERGİSİ Ekim(2016) 42 (2), 189-224 Geliş (Recieved) :16/06/2016 Kabul (Accepted) :10/09/2016 Research Article İlerleyen Tür Sansürlü Verilere Dayalı Aralık Tahmini Coşkun KUŞ, Nagihan ÇÖKEK, İsmail KINACI, Yunus AKDOĞAN & Kadir KARAKAYA Selcuk University, Science Faculty, Depertmant of Stattistics,42250,Turkey e-mail: kkarakaya@selcuk.edu.tr Öz: Bu çalışmada, literatürde olan bir pivot kullanılarak Weibull, Burr XII ve Gompertz dağılımı için güven aralıkları oluşturulmuştur. İstatistiksel sonuç çıkarımı ilerleyen sansürleme altında tartışılmıştır. Pivot elemanın dağılımı literatürde verilen tablolara göre farklı sansür şemaları için daha da genişletilmiştir. Tam örneklem durumunda, regresyon modelleri pivot elemanının sınır değerlerini elde etmek için tahmin edilmiştir. Ayrıca sayısal bir örnek verilmiştir. Anahtar kelimeler: Burr XII dağılımı, Gompertz dağılımı, güven aralığı, ilerleyen sansürleme, pivot, Weibull dağılımı, Interval Estimation Based on Progressively Censored Data Abstract: In this paper, a pivot in the literarture is used to construct the confidence intervals for Weibull, Burr XII and Gompertz distribution. Statistical inference are discussed under progressive censoring. The tables for the distribution of pivotal quantity are extended according to tables of existing papers with different censoring schemes. Regression models are estimated to get cut off point of pivotal quantity for complete sample. Numerical examples are also provided. Keywords: Progressive censoring, Gompertz distribution, Burr XII distribution, Weibull distribution, pivot, confidence interval 1. Introduction In reliability analysis, life testing with censoring scehemes are performed when the cost of the test items is high or/and test time is restricted. A type II censored sample is one for which: 1. Only the m smallest observations in a sample of size n are observed, 1 . m n ≤ ≤ 2. m is determined before the data are collected. The model of progressive type-II right censoring is also defined as follows: Suppose n identical units are placed on a lifetime test. At the time of i th failure, i r surviving units are randomly withdrawn from the experiment, 1 . m n ≤ ≤ Thus, if m failures are observed then n m − units are progressively censored. 1: : 2: : : : mn mn mmn X X X < < < R R R  describe the progressively censored failure times where ( ) 1 2 , , , m rr r = R  denotes the censoring scheme. Extensive publications can be found in the literature which discuss the statistical inference for progressively censored data 189