Abstract
Bayesian and non-Bayesian estimators are obtained for the unknown parameters of Weibull distribution based on the generalized Type-II progressive hybrid censoring scheme and different special cases are obtained. The asymptotic variance covariance matrix and approximate confidence intervals based on the asymptotic normality of the maximum likelihood estimators are obtained. Bayes estimates and Bayes risks have been developed under a squared error loss function using informative and non-informative priors for the unknown Weibull parameters. It is observed that the estimators obtained are not available in closed forms, although they can be easily evaluated for a given sample by using suitable numerical methods. Therefore, a numerical example is considered to illustrate the proposed estimators.
Highlights
In reliability studies and life-testing experiments, the failure time data of experimental items are often not completely available
We propose a confidence intervals for the unknown Weibull parameters and under generalized Type-II progressive hybrid censoring scheme (PHCS) based on the asymptotic distribution of the MLEsand (10) and (11), respectively, 100 1 % approximate confidence intervals for and can be obtained using the asymptotic normality of the MLEsandas followsz 2
We get to corresponding new results based on Rayleigh distribution as a special case, i.e., for 2 and using the probability density function (PDF) and the cumulative distribution function (CDF) of Rayleigh distribution (4) and (5), respectively, the maximum likelihood estimators (MLEs) will be the solution of the following log likelihood function:
Summary
In reliability studies and life-testing experiments, the failure time data of experimental items are often not completely available. The drawback of the Type-II PHCS is that far fewer than m failures may be observed and it might take a very long time to observe m -th failures and complete the life test. For this motivation, Lee et al (2015) proposed a generalized Type-II PHCS, which the experiment is guaranteed to terminate at a prefixed time.
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