On adaptive progressively Type-II censored competing risks data

Hemmati, Fariba; Khorram, Esmaile

doi:10.1080/03610918.2015.1129408

Cited by 27 publications

(13 citation statements)

References 26 publications

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“…To illustrate the proposed methods, a real data is selected from Ebrahimi [25], of which the accelerated stress is voltage, the stress levels are S 1 � 10V, S 2 � 15V, and S 3 � 20V, and the normal stress level is S 0 � 5V. Furthermore, for each stress level, the life tests are allowed to run over the time (τ 1 , τ 2 , τ 3 ) � (2, 1.5, 1), the numbers under the test were (n 1 , n 2 , n 3 ) � (15,15,15), the expected failure number are (m 1 , m 2 , m 3 ) � (11,12,13), and the progressive censoring scheme is R and 3.…”

Section: Real Data Analysismentioning

confidence: 99%

“…Presently, some scholars discussed the AT-II PHCS, i.e., Cramer and Iliopoulos [12] derived some distributional results and showed that maximum likelihood estimators coincide with those in deterministic progressive type-II censoring. Hemmati and Khorram [13] discussed the AT-II PHCS in the presence of the competing risk. Nassar and Abo-Kasem [14] adopted the frequents and Bayse methods to obtain the estimations of the unknown parameters for inverse Weibull distribution under AT-II PHCS.…”

Section: Introductionmentioning

confidence: 99%

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A Nonconstant Shape Parameter-Dependent Competing Risks’ Model in Accelerate Life Test Based on Adaptive Type-II Progressive Hybrid Censoring

Wang

Shi

2021

Mathematical Problems in Engineering

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In this paper, the dependent competing risks’ model is considered in the constant-stress accelerated life test under the adaptive type-II progressive hybrid-censored scheme. The dependency between failure causes is modeled by Marshall–Olkin bivariate Gompertz distribution. The scale and shape parameters in the model both change with the stress levels, and the failure causes of some test units are unknown. Then, the maximum likelihood estimations and approximation confidence intervals of the unknown parameters are considered. And, the necessary and sufficient condition is established for the existence and uniqueness of the maximum likelihood estimations for unknown parameters. The Bayes approach is also employed to estimate the unknown parameters under suitable prior distributions. The Bayes estimations and highest posterior credible intervals of the unknown parameters are obtained. Finally, a simulation experiment has been performed to illustrate the methods proposed in this paper.

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Section: Real Data Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Nonconstant Shape Parameter-Dependent Competing Risks’ Model in Accelerate Life Test Based on Adaptive Type-II Progressive Hybrid Censoring

Wang

Shi

2021

Mathematical Problems in Engineering

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“…Many works have been performed based on the APT-II HC scheme. Hemmati and Khorram [14] addressed the estimation of the competing risks model for the exponential distribution. Al Sobhi and Soliman [15] investigated the estimation issues of the exponentiated Weibull distribution.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with Applications

et al. 2022

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In life testing and reliability studies, obtaining whole data always takes a long time and lots of monetary and human resources. In this case, the experimenters prefer to gather data using censoring schemes that make a balance between the length of the test, the desired sample size, and the cost. Lately, an adaptive progressive type-II hybrid censoring scheme is suggested to enhance the efficiency of the statistical inference. By utilizing this scheme, this paper seeks to investigate classical and Bayesian estimations of the Dagum distribution. The maximum likelihood and Bayesian estimation methods are considered to estimate the distribution parameters and some reliability indices. The Bayesian estimation is developed under the assumption of independent gamma priors and by employing symmetric and asymmetric loss functions. Due to the tough form of the joint posterior distribution, the Markov chain Monte Carlo technique is implemented to gather samples from the full conditional distributions and in turn obtain the Bayes estimates. The approximate confidence intervals and the highest posterior density credible intervals are also obtained. The effectiveness of the various suggested methods is compared through a simulated study. The optimal progressive censoring plans are also shown, and number of optimality criteria are explored. To demonstrate the applicability of the suggested point and interval estimators, two real data sets are also examined. The outcomes of the simulation study and data analysis demonstrated that the proposed scheme is adaptable and very helpful in ending the experiment when the experimenter’s primary concern is the number of failures.

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“…Moreover, if T � 0, this variant reduces to the usual type II censoring scheme. Several investigations based on the APCS-TII have been conducted; readers can refer to the works of Hemmati and Khorram [6], Amein [7], Nassar and Abo-Kasem [8], Ateya and Mohammed [9], and Nassar et al [10], among many others.…”

Section: Introductionmentioning

confidence: 99%

Estimation Based on Adaptive Progressively Censored under Competing Risks Model with Engineering Applications

Nassar

Alotaibi

Dey³

2022

Mathematical Problems in Engineering

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This paper has investigated the estimation problem for the competing risks model where the data are adaptive progressively type-II censored and follow the Rayleigh distribution. Maximum likelihood and Bayesian methods are used to estimate the unknown parameters. To generate the interval estimates of the model parameters, approximate confidence intervals and two bootstrap confidence intervals are also considered based on the classical setup. Bayes estimates are obtained using independent gamma priors based on various loss functions including squared error, LINEX, general entropy, weighted SE, and precautionary loss functions. Moreover, Bayes credible intervals and the highest posterior density intervals of the model parameters are obtained. A numerical investigation has been carried out to assess the performance of the classical and Bayes estimates as well as the associated confidence and credible intervals. Finally, one simulated and two real data sets, one for breaking strengths of wire connections and the other for times to failure of small electrical appliances, have been analyzed for illustrative purposes. The results showed that the Bayes estimates using the LINEX loss function provide more reasonable estimates than the classical and Bayes estimates using squared error, general entropy, and precautionary loss functions.

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On adaptive progressively Type-II censored competing risks data

Cited by 27 publications

References 26 publications

A Nonconstant Shape Parameter-Dependent Competing Risks’ Model in Accelerate Life Test Based on Adaptive Type-II Progressive Hybrid Censoring

A Nonconstant Shape Parameter-Dependent Competing Risks’ Model in Accelerate Life Test Based on Adaptive Type-II Progressive Hybrid Censoring

Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with Applications

Estimation Based on Adaptive Progressively Censored under Competing Risks Model with Engineering Applications

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