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Estimating the parameters of the Weibull distribution under generalized type II hybrid censoring
Journal of the Korean Data & Information Science Society 2021;32:905-15
Published online July 31, 2021;  https://doi.org/10.7465/jkdi.2021.32.4.905
© 2021 Korean Data and Information Science Society.

Kyeongjun Lee1

1Division of Mathematics and Big Data Science, Daegu University
Correspondence to: 1 Assistant professor, Division of Mathematics and Big Data Science, Daegu University, Gyeongsan 38453, Korea. E-mail: indra_74@naver.com
Received June 30, 2021; Revised July 12, 2021; Accepted July 14, 2021.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In hybrid censoring both the time and the number of failures are considered for the life testing of the product. The combination of type I and type II censoring is called the hybrid censoring. Though the type II hybrid censored scheme guarantees a pre-fixed number of failures, it might take a long time to complete the test. In order to provide a guarantee in terms of the time to complete the test, generalized type II hybrid censoring scheme was introduced. In this paper, we consider the MLEs of the parameters and reliability when the data are generalized type II hybrid censoredWeibull data. However, the MLEs cannot be obtained in a closed form. We use the approximate MLEs using Taylor series expansion. Also, we consider the Bayes estimation for the parameters and reliability when the data are generalized type II hybrid censored Weibull data. In Bayes estimation, Lindley's approximation is used to obtain the Bayes estimators. Simulation experiments are performed to see the effectiveness of the different estimators. Finally, a real data set has been analysed for illustrative purposes.
Keywords : Bayes estimation, generalized type II hybrid censoring, Linex loss, squared error loss, Weibull distribution.