Abstract
In this paper, the Weibull extension distribution parameters are estimated under a progressive type-II censoring scheme with random removal. The parameters of the model are estimated using the maximum likelihood method, maximum product spacing, and Bayesian estimation methods. In classical estimation (maximum likelihood method and maximum product spacing), we did use the Newton–Raphson algorithm. The Bayesian estimation is done using the Metropolis–Hastings algorithm based on the square error loss function. The proposed estimation methods are compared using Monte Carlo simulations under a progressive type-II censoring scheme. An empirical study using a real data set of transformer insulation and a simulation study is performed to validate the introduced methods of inference. Based on the result of our study, it can be concluded that the Bayesian method outperforms the maximum likelihood and maximum product-spacing methods for estimating the Weibull extension parameters under a progressive type-II censoring scheme in both simulation and empirical studies.
Highlights
Several cases in life-testing and reliability experiments arise when units are withdrawn or lost from the test before failure
Left, interval censoring, single or multiple censoring, and type-I or type-II censoring are all examples of censoring schemes, but conventional type-I and type-II censoring schemes do not allow units to be withdrawn at any stage other than the end of the experiment
The maximum likelihood estimation (MLE), maximum product of spacing (MPS), and Bayesian estimation methods of Weibull extension (WE) distribution parameters based on progressive type-II censored scheme (PTIICS) data with binomial random removal are discussed
Summary
Several cases in life-testing and reliability experiments arise when units are withdrawn or lost from the test before failure. Cheng and Amin (1983) [27] discuss the MPS consistency and asymptotic properties, as well as the fact that when they exit, the MPS is at least as effective as the MLEs. The major objective of this paper is to address the estimation problem of the WE distribution parameters when the data are progressively type-II censored with binomial removals. The major objective of this paper is to address the estimation problem of the oWf 1E6 distribution parameters when the data are progressively type-II censored with binomial removals. The probability mass function for the number of units removed at each failure time, it’s a binomial distribution, is as follows: Pr( 1 = r1) =. The MLE, MPS, and Bayesian estimation methods of WE distribution parameters based on PTIICS data with binomial random removal are discussed
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