Inference for Weibull competing risks model with partially observed failure causes under generalized progressive hybrid censoring

A competing risks model is considered under a generalized progressive hybrid censoring. When the latent failure times are Weibull distributed, maximum-likelihood estimates for the unknown model parameters are established where the associated existence and uniqueness are shown. An asymptotic distribution of the maximum-likelihood estimators is used to construct approximate confidence intervals via the observed fisher information matrix. Moreover, Bayes point estimates and the highest probability density credible intervals of unknown parameters are also presented, and the Gibbs sampling technique is used to approximate corresponding estimates. Simulation studies and real-life example are presented for illustration purpose.

Inference for Weibull Competing Risks Data Under Generalized Progressive Hybrid Censoring

In this paper, inference for a competing risks model is studied when latent failure times follow Kumaraswamy distribution and causes of failure are partially observed. Under generalized progressive...

Inference for partially observed competing risks model for Kumaraswamy distribution under generalized progressive hybrid censoring

Inference for two‐parameter Rayleigh competing risks data under generalized progressive hybrid censoring

Generalized progressive hybrid censoring plan proposed to overcome the limitation of the progressive hybrid censoring scheme is that it cannot be applied when very few failures may occur before pre-specified terminal time T $ T$ . In this paper, the estimating problems of the model parameters, reliability and hazard rate functions of Nadarajah-Haghighi distribution when a sample is available from generalized progressive hybrid censoring have been considered. The maximum likelihood and Bayes estimators have been obtained for any function of the model parameters. Approximate confidence intervals for the unknown parameters and any function of them are constructed. Using independent gamma informative priors, the Bayes estimators of the unknown parameters are derived under the squared-error loss function. Two approximation techniques, namely: Lindley approximation method and Metropolis Hastings algorithm have been used to carry out the Bayes estimates and also to construct the associate highest posterior density credible intervals. The performance of the proposed methods are evaluated through a Monte Carlo simulation study. To select the optimum censoring scheme among different competing censoring plans, different optimality criteria have been considered. A real-life dataset, representing the failure times of electronic devices, is analyzed to demonstrate how the applicability of the proposed methodologies in real phenomenon. 

Statistical reliability analysis of electronic devices using generalized progressively hybrid censoring plan

The progressive Type-II hybrid censoring scheme introduced by Kundu and Joarder (Comput Stat Data Anal 50:2509–2528, 2006), has received some attention in the last few years. One major drawback of this censoring scheme is that very few observations (even no observation at all) may be observed at the end of the experiment. To overcome this problem, Cho et al. (Stat Methodol 23:18–34, 2015) recently introduced generalized progressive censoring which ensures to get a pre specified number of failures. In this paper we analyze generalized progressive censored data in presence of competing risks. For brevity we have considered only two competing causes of failures, and it is assumed that the lifetime of the competing causes follow one parameter exponential distributions with different scale parameters. We obtain the maximum likelihood estimators of the unknown parameters and also provide their exact distributions. Based on the exact distributions of the maximum likelihood estimators exact confidence intervals can be obtained. Asymptotic and bootstrap confidence intervals are also provided for comparison purposes. We further consider the Bayesian analysis of the unknown parameters under a very flexible beta–gamma prior. We provide the Bayes estimates and the associated credible intervals of the unknown parameters based on the above priors. We present extensive simulation results to see the effectiveness of the proposed method and finally one real data set is analyzed for illustrative purpose.

On generalized progressive hybrid censoring in presence of competing risks

Kundu and Gupta [Analysis of hybrid life-tests in presence of competing risks. Metrica. 2007;65:159–170] provided the analysis of Type-I hybrid censored competing risks data, when the lifetime dist...

Analysis of Type-II hybrid censored competing risks data

Analysis of progressive Type-II censoring in presence of competing risk data under step stress modeling

SYNOPTIC ABSTRACTIn this article, we consider the statistical inference of the unknown parameter of an exponential distribution based on the time truncated data. The time truncated data occurs quite often in reliability analysis for type-I or hybrid censoring cases. All results available today are based on the conditional argument that at least one failure occurs during the experiment. In this article, we provide some inferential results based on the unconditional argument. We extend the results for some two-parameter distributions.

Interval Estimation of the Unknown Exponential Parameter Based on Time Truncated Data

In this paper we consider the statistical inference of the unknown parameter of an exponential distribution based on the time truncated data. The time truncated data occurs quite often in the reliability analysis for type-I or hybrid censoring cases. All the results available today are based on the conditional argument that at least one failure occurs during the experiment. In this paper we provide some inferential results based on the unconditional argument. We extend the results for some two-parameter distributions also.

Arnab Koley

Papers

On generalized progressive hybrid censoring in presence of competing risks

Analysis of Type-II hybrid censored competing risks data

Analysis of progressive Type-II censoring in presence of competing risk data under step stress modeling

Interval Estimation of the Unknown Exponential Parameter Based on Time Truncated Data

Interval Estimation of the Unknown Exponential Parameter Based on Time Truncated Data