Analysis of the Three-parameter Weibull Distributed Lifetime Data based on Progressive Type-II Right Censoring: a New Approach to Determine the Random Removals

Document Type : Original Article

Authors
Maryam Sharafi 1
Reza Hashemi 1
Masumeh Ghahramani 2
1 Department of Statistics, Faculty of Science, Razi University
2 Department of Statistics, Science and Research Branch, Islamic Azad University, Iran
10.22034/jirss.2024.1999725.1020
Abstract
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.
Keywords
Corrected maximum likelihood estimator
Expected test time
Monte Carlo simulation
Progressive censoring
Random removals
Weibull distribution
Subjects
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Journal of the Iranian Statistical Society
Volume 23, Issue 1
June 2024
Pages 1-31

  • Receive Date 09 April 2023
  • Revise Date 26 August 2024
  • Accept Date 13 September 2024