Estimation from Burr type XII distribution using progressive first-failure censored data

Soliman, Ahmed A.; Abdellah, Ahmed H.; Abou-Elheggag, N. A.; Modhesh, A. A.

doi:10.1080/00949655.2012.690157

Cited by 33 publications

(15 citation statements)

References 29 publications

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“…Tadikamalla (1980) discovered its connections to numerous useful lifetime distributions and concluded that it could be useful in modelling almost all data sets. The Burr(θ, δ) was well-known for its potential applications in reliability studies (Wingo (1983(Wingo ( , 1993, Ali Mousa (1995), Gupta et al (1996), Zimmer et al (1998), Ali Mousa and Jaheen (2002), Upadhyay et al (2004), Wu and Yu (2005), Wu et al (2007), Wu et al (2010), Lio and Tsai (2012), Aslam et al (2013), and Soliman et al (2014)). The probability density function (PDF) and cumulative distribution function of Burr(θ, δ) are, respectively, defined by…”

Section: Truncated Life Testing and Lifetime Distributionmentioning

confidence: 97%

Economical sampling plans with warranty based on truncated data from Burr type XII distribution

Tsai

Lio

Jiang

et al. 2015

Journal of the Operational Research Society

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Economical sampling plans to ensure the qualities of Burr type XII distributed lifetimes were established using a truncated life test. The Bayesian inference method was used to address the lot-to-lot variation of products. The sampling plan was characterized by the sample size and the acceptance number to minimize the expected total cost. A simple empirical Bayesian estimation method was provided to estimate the hyperparameters of prior distribution, and simulation studies were conducted to validate the proposed empirical Bayesian estimation method. Lastly, the application of this proposed method was illustrated using two examples.

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Section: Truncated Life Testing and Lifetime Distributionmentioning

confidence: 97%

Economical sampling plans with warranty based on truncated data from Burr type XII distribution

Tsai

Lio

Jiang

et al. 2015

Journal of the Operational Research Society

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“…A complete sample from a clinical trial describes a relief time (in hours) for 50 arthritic patients given by Wingo [35] and used recently by Ahmed et al [36,37] and Wu et al [38]. Wingo [35], and Ahmed et al [36,37] showed that the Burr type XII model was acceptable for these data. Ahmed et al [37] obtained the estimation of the parameters as b α = 5:115 and b θ = 7:0651.…”

Section: Monte Carlo Simulation and Comparisonsmentioning

confidence: 99%

E-Bayesian Prediction for the Burr XII Model Based on Type-II Censored Data with Two Samples

Okasha

Wang

2020

Advances in Mathematical Physics

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Type-II censored data is an important scheme of data in lifetime studies. The purpose of this paper is to obtain E-Bayesian predictive functions which are based on observed order statistics with two samples from two parameter Burr XII model. Predictive functions are developed to derive both point prediction and interval prediction based on type-II censored data, where the median Bayesian estimation is a novel formulation to get Bayesian sample prediction, as the integral for calculating the Bayesian prediction directly does not exist. All kinds of predictions are obtained with symmetric and asymmetric loss functions. Two sample techniques are considered, and gamma conjugate prior density is assumed. Illustrative examples are provided for all the scenarios considered in this article. Both illustrative examples with real data and the Monte Carlo simulation are carried out to show the new method is acceptable. The results show that Bayesian and E-Bayesian predictions with the two kinds of loss functions have little difference for the point prediction, and E-Bayesian confidence interval (CI) with the two kinds of loss functions are almost similar and they are more accurate for the interval prediction.

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“…For more applications about progressive-first-failure censoring data the readers may refer to Soliman et al [13] Soliman et al ( [14], [15] ), Soliman et al [16] and Ahmadi et al [17].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Progressive First-Failure-Censoring for Non-normal Model Using Competing Risks Data

Modhesh¹

2015

AJTAS

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Competing risks data usually arises in studies in which the death or failure of an individual or an item may be classified into one of T≥2 mutually exclusive causes. In this paper, we will study the competing risks model when the data is progressively first-failure-censored. Based on this type of censoring, we derive the maximum likelihood estimators (MLE's) for the unknown parameters. Approximate confidence intervals and two bootstrap confidence intervals are also proposed. The results in the cases of first-failure censoring, progressive Type II censoring, Type II censoring and complete sample are special cases. A real data set has been analyzed for illustrative purposes. Different methods have been compared using Monte Carlo simulations.

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Estimation from Burr type XII distribution using progressive first-failure censored data

Cited by 33 publications

References 29 publications

Economical sampling plans with warranty based on truncated data from Burr type XII distribution

Economical sampling plans with warranty based on truncated data from Burr type XII distribution

E-Bayesian Prediction for the Burr XII Model Based on Type-II Censored Data with Two Samples

Analysis of Progressive First-Failure-Censoring for Non-normal Model Using Competing Risks Data

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