Abstract
In this article, based on the generalized Type-II progressive hybrid censoring sample from the Burr Type-XII distribution, maximum likelihood and Bayesian inference are discussed. Point and interval estimates of unknown parameters, reliability, and hazard functions are developed. We employed several loss functions, such as squared error, LINEX, and general entropy, as symmetric and asymmetric loss functions and various prior distributions as informative and non-informative priors for Bayesian inference of unknown parameters. Under a generalized Type-II progressive hybrid censoring sample, we also propose a Bayesian one-sample prediction for unobserved failures. We conduct simulation study using the MCMC algorithm for the Bayesian approach based on several prior distributions. Finally, we apply the results of the theoretical research to real data.
Highlights
In reliability and survival analysis, the progressive Type-II censoring scheme is the most commonly used scheme
We investigate three forms of loss functions for Bayesian estimation. e first is the squared error loss function (SELF), a symmetric function that in parameter estimation assigns equal weight to overestimates and underestimates. e second is the LINEX loss function (LLF), which is asymmetric and provides overestimation and underestimation distinct weights. e generalization of the entropy loss function is the third loss function (GELF)
LINEX, and general entropy loss functions based on Prior1 and Prior2 distributions are considered in the Bayesian method. e parameters, as well as the survival and hazard functions, are given asymptotic and credible confidence intervals (CIs) of 90% and 95%
Summary
In reliability and survival analysis, the progressive Type-II censoring scheme is the most commonly used scheme. Progressive censoring is beneficial in various real-life applications such as industry, life research, and clinical applications It allows the removal of surviving experimental units until the end of the test. E disadvantages of the Type-II progressive censoring method are that the experiment time can be quite long if the units are highly reliable. E experiment of lifetime test would save time and cost of failures based on this censoring scheme. E Burr Type-XII distribution has been extensively investigated by numerous researchers due to its applications in various disciplines such as biological, industrial, reliability and life testing, clinical studies, and so on (see [15, 16]).
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