Constant-partially accelerated life tests for Burr type-XII distribution with progressive type-II censoring

Abdel-Hamid, Alaa H.

doi:10.1016/j.csda.2009.01.018

Cited by 62 publications

(31 citation statements)

References 23 publications

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“…The bootstrap percentile method for obtaining confidence intervals of model parameters has been explained in Section 3.1.1 (See [1] and [8] also). , ' s * [3] ), …”

Section: Confidence Intervals Of Model Parametersmentioning

confidence: 99%

Reliability Prediction During Development Phase of a System

Wanti

Jain

2011

Quality Technology & Quantitative Management

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Reliability Growth analysis is a process of collecting, modeling, analyzing and interpreting data from the reliability development test program to achieve reliability goal. Many mathematical models have been developed for reliability growth in the literature. In general, it is not possible to fix a priori the model to be used in a given situation. A physical motivation of the problem, based on failure or defect causes/mechanisms, can help in such a choice. The Power Law Process (PLP) is vastly used for monitoring reliability growth during the development test phase. However, in the reliability growth context, the intensity function of the PLP model has two unrealistic situations, viz., it tends to infinity as t tends to zero and tends to zero as t tends to infinity. In this paper, we have proposed Modified PLP model to overcome the second drawback and Doubly Bounded PLP model to overcome both the drawbacks. For the proposed models, the estimates of the model parameters and other quantities of interest have been obtained using Maximum Likelihood approach, for both failure truncated and time truncated data. Reliability Prediction is done using system reliability measures of intensity function and mean time between failures (MTBF). Further confidence intervals of the relevant parameters have been obtained. The procedures developed have been illustrated using numerical examples. Keywords: Bootstrap confidence intervals, maximum likelihood estimation, mean time between failures, non-Homogeneous Poisson Process, test-fix-test program. ______________________________________________________________________ Notations , , parameters. ( ) r t failure intensity at time . t time of failure. th i i t total number of failures. n time of truncation. T additional time-units of testing. S predicted failure intensity at . T S 0 r 2 Cramer-von Mises statistic. n C MLE maximum likelihood estimator. MTBF mean time between failures. NHPP non-homogeneous Poisson process.

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“…The bootstrap percentile method for obtaining confidence intervals of model parameters has been explained in Section 3.1.1 (See [1] and [8] also). , ' s * [3] ), …”

Section: Confidence Intervals Of Model Parametersmentioning

confidence: 99%

Reliability Prediction During Development Phase of a System

Wanti

Jain

2011

Quality Technology & Quantitative Management

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“…Soliman (2005) derived maximum likelihood, Bayes and empirical Bayes estimators (BEs) of Burr type XII distribution based on progressive censored samples using various loss functions and Wang and Shi (2010) considered empirical Bayes inference for the Burr model based on record values. Interested readers may refer to AL-Hussaini and Jaheen (1992,1994,1995,1996) and Abdel-Hamid (2009) for more researches in this area.…”

Section: Introductionmentioning

confidence: 98%

On the Construction of Preliminary Test Estimator Based on Record Values for the Burr XII Model

Belaghi

Arashi

Tabatabaey

2014

Communications in Statistics - Theory and Methods

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In this paper some different sorts of estimators are proposed based on record breaking observations in the Burr type XII model. We define Bayes as well as empirical Bayes preliminary test estimators in the same fashion as in the ordinary preliminary test estimator using relevant combinations of uniformly minimum variance unbiased (UMVU) and Bayes estimators. Exact and asymptotic bias and mean square error (MSE) expressions for the proposed estimators are derived under two different conditions of knowing the shape parameters. We compare the MSEs and obtain the confidence interval for the parameter of interest in which the preliminary test type estimators outperform the UMVU, Bayes and empirical Bayes estimators.An application of the ordinary preliminary test estimator is also considered. We conclude this approach by a useful discussion for practical purposes and a summary.

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“…Based on progressively Type-II censored samples, [2] considered constant-stress PALT when the lifetime of units under use condition follows the Burr Type-XII distribution. Bayes and maximum likelihood (ML) methods of estimation are applied on constant-stress ALTs to finite mixtures of distributions by [3,4].…”

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confidence: 99%

Bayesian Estimation of Exponentiated Weibull Distribution Under Partially Acceleration Life Tests

Ahmad

Soliman

Yousef

2015

Bull. Malays. Math. Sci. Soc.

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This paper presents statistical methods for analyzing partially accelerated life test from constant-stress test. The lifetime of items under use condition follows the two-parameter exponentiated Weibull distribution. Based on progressively Type-II censored sample, the classical maximum likelihood method as well as a fully Bayesian method based on Lindley (Trabajos de Estadistica 31:223-237, 1980) approximation form and the Markov chain Monte Carlo technique are developed for inference about model parameters and acceleration factor. Furthermore, approximate confidence intervals and credible intervals are presented. A Monte Carlo simulation is given to study the precision of different estimators.

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Constant-partially accelerated life tests for Burr type-XII distribution with progressive type-II censoring

Cited by 62 publications

References 23 publications

Reliability Prediction During Development Phase of a System

Reliability Prediction During Development Phase of a System

On the Construction of Preliminary Test Estimator Based on Record Values for the Burr XII Model

Bayesian Estimation of Exponentiated Weibull Distribution Under Partially Acceleration Life Tests

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