Properties of progressively censored order statistics and inferential procedures based on progressively censored samples have recently attracted considerable attention in the literature. In this paper, I provide an overview of various developments that have taken place in this direction and also suggest some potential problems of interest for further research.

Progressive censoring methodology: an appraisal

This article deals with the Bayesian inference of unknown parameters of the progressively censored Weibull distribution. It is well known that for a Weibull distribution, while computing the Bayes estimates, the continuous conjugate joint prior distribution of the shape and scale parameters does not exist. In this article it is assumed that the shape parameter has a log-concave prior density function, and for the given shape parameter, the scale parameter has a conjugate prior distribution. As expected, when the shape parameter is unknown, the closed-form expressions of the Bayes estimators cannot be obtained. We use Lindley's approximation to compute the Bayes estimates and the Gibbs sampling procedure to calculate the credible intervals. For given priors, we also provide a methodology to compare two different censoring schemes and thus find the optimal Bayesian censoring scheme. Monte Carlo simulations are performed to observe the behavior of the proposed methods, and a data analysis is onducted for ill...

Bayesian Inference and Life Testing Plan for the Weibull Distribution in Presence of Progressive Censoring

Hybrid censoring

In this article, a mixture of Type-I censoring and Type-II progressive censoring schemes, called an adaptive Type-II progressive censoring scheme, is introduced for life testing or reliability experiments. For this censoring scheme, the effective sample size m is fixed in advance, and the progressive censoring scheme is provided but the number of items progressively removed from the experiment upon failure may change during the experiment. If the experimental time exceeds a prefixed time T but the number of observed failures does not reach m, we terminate the experiment as soon as possible by adjusting the number of items progressively removed from the experiment upon failure. Computational formulae for the expected total test time are provided. Point and interval estimation of the failure rate for exponentially distributed failure times are discussed for this censoring scheme. The various methods are compared using Monte Carlo simulation. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009

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Statistical analysis of exponential lifetimes under an adaptive Type-II progressive censoring scheme

Exact likelihood inference for an exponential parameter under generalized progressive hybrid censoring scheme

Analysis of Type-II progressively hybrid censored data

Inferences on Weibull parameters with conventional type-I censoring

In medical studies or in reliability analysis, it is quite common that the failure of any individual or any item may be attributable to more than one cause. Moreover, the observed data are often censored. Hybrid censoring scheme which is the mixture of conventional Type-I and Type-II censoring schemes is quite useful in life-testing or reliability experiments. Recently Type-II progressive censoring scheme becomes quite popular for analyzing highly reliable data. But in that case the length of the experiment can be quite large. Hence, in this paper we introduce a Type-II progressively hybrid censoring scheme for competing risks data, where the experiment terminates at a pre-specified time. We derive the likelihood inference of the unknown parameters under the assumptions that the lifetime distributions of the different causes are independent and exponentially distributed. We obtain the maximum likelihood estimators of the unknown parameters in exact forms. Asymptotic confidence intervals and two bootstrap confidence intervals are also proposed. Bayes estimates and credible intervals of the unknown parameters are obtained under the assumption of gamma priors on the unknown parameters. Different methods have been compared using Monte Carlo simulations. One real data set has been analyzed for illustrative purposes.

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Analysis Of Type-II Progressively Hybrid Censored Competing Risks Data

Progressive Type-II censoring scheme has become quite popular for the last few years. One of the major drawbacks of the progressive censoring scheme is that the length of the experiment can be very large if the items are highly reliable. Because of that, recently Kundu and Joarder (Computational Statistics and Data Analysis, 50, 2509-2528, 2006) introduced the Type-II progressively hybrid censored scheme and analyzed the data assuming that the lifetimes of the items are exponentially distributed. This article presents the analysis of the Type-II progressively hybrid censored data when the lifetime distributions of the items follow Weibull distributions. Maximum likelihood estimators and approximate maximum likelihood estimators are developed for estimating the unknown parameters. Asymptotic confidence intervals based on maximum likelihood estimators and approximate maximum likelihood estimators are proposed. Different methods have been compared using Monte Carlo simulations. One real data set has been analyzed for illustrative purposes.

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Avijit Joarder

Papers

Analysis of Type-II progressively hybrid censored data

Inferences on Weibull parameters with conventional type-I censoring

Analysis Of Type-II Progressively Hybrid Censored Competing Risks Data

On Type-II Progressively Hybrid Censoring