Abstract
This article focuses on using E-Bayesian estimation for the Weibull distribution based on adaptive type-I progressive hybrid censored competing risks (AT-I PHCS). The case of Weibull distribution for the underlying lifetimes is considered assuming a cumulative exposure model. The E-Bayesian estimation is discussed by considering three different prior distributions for the hyper-parameters. The E-Bayesian estimators as well as the corresponding E-mean square errors are obtained by using squared and LINEX loss functions. Some properties of the E-Bayesian estimators are also derived. A simulation study to compare the various estimators and real data application is applied to show the applicability of the different estimators are proposed.
Highlights
In life-testing and reliability studies, both type I and type II censoring schemes are widely used.These two types of censoring schemes are described as follows: Consider n identical components are placed in the test, in type I censoring, the experiment continues up to a predetermined time τ.in the type II censoring scheme, the experiment is terminated when a predetermined number of failures m < n occurs
For a mixture of type I and type II censoring schemes, which is called the type I hybrid censoring scheme, is introduced by Epstein [1], and the life test experiment is terminated at a random time τ ∗ = min{ xm:m:n, τ }
To be sure from this condition, we find the first derivative of g(λ j ), j = 1, 2 with respect to λ j, j = 1, 2 as
Summary
In life-testing and reliability studies, both type I and type II censoring schemes are widely used.These two types of censoring schemes are described as follows: Consider n identical components are placed in the test, in type I censoring, the experiment continues up to a predetermined time τ.in the type II censoring scheme, the experiment is terminated when a predetermined number of failures m < n occurs. In life-testing and reliability studies, both type I and type II censoring schemes are widely used These two types of censoring schemes are described as follows: Consider n identical components are placed in the test, in type I censoring, the experiment continues up to a predetermined time τ. Childs et al [2] proposed a new hybrid censoring scheme called a type-II hybrid censoring scheme in which the experiment would terminate at the random time τ ∗ = max{ xm:m:n , τ }. These schemes do not allow for removing the components from the experiment at any time other than the terminal point. A more general censoring scheme called progressive type II censoring is used to deal with this problem
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