Iranian Statistical Society Journal of the Iranian Statistical Society 1726-4057 23 1 2024 11 04 Analysis of the Three-parameter Weibull Distributed Lifetime Data based on Progressive Type-II Right Censoring: a New Approach to Determine the Random Removals 1 31 717740 10.22034/jirss.2024.1999725.1020 EN Maryam Sharafi Department of Statistics, Faculty of Science, Razi University Reza Hashemi Department of Statistics, Faculty of Science, Razi University Masumeh Ghahramani Department of Statistics, Science and Research Branch, Islamic Azad University, Iran Journal Article 2023 04 09 An important challenge in using progressive Type-II right censoring is to determine a removal scheme. It can be predetermined or randomly chosen per discrete distributions. This paper considers the random removal problem and proposes two scenarios for determining the removal vector without introducing any parameter to a model when progressively Type-II censored samples are available from the three-parameter Weibull distribution. The proposed scenarios are based on the normalized spacings with random and fixed coefficients according to progressively Type-II censored order statistics from an exponential distribution. The joint probability mass functions of removal vectors are provided as well as expected experimental time under the proposed two methods. Moreover, the maximum likelihood estimators (MLEs) and corrected maximum likelihood estimators (corrected MLEs) of parameters are obtained. The new approaches are compared with the patterns of removal derived from the discrete uniform and binomial distributions using a Monte Carlo simulation study. This comparison is based on their estimated biases, estimated mean squared errors and expected total time on the experiment. Finally, a real data example is given to show the practical applications of the paper. https://jirss.irstat.ir/article_717740_adb87251577b9ace90608605f597868f.pdf