Estimation in Step-Stress Accelerated Life Tests for Power Generalized Weibull Distribution with Progressive Censoring

El-Din, M. M. Mohie; Abu-Youssef, S. E.; Ali, Nahed S. A.; El-Raheem, A. M. Abd

doi:10.1155/2015/319051

Cited by 22 publications

(5 citation statements)

References 9 publications

(10 reference statements)

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“…In this part, we use the important sampling method for estimating the unknown parameters. The posterior distribution presented in (15) can be rewritten as…”

Section: Important Sampling Techniquementioning

confidence: 99%

“…In this kind of stress, we raise the stress level step by step at pre-specified times to get early failures. Many authors have discussed the step-stress ALTs; see for example Bai et al [10], Gouno et al [11], Miller and Nelson [12], Balakrishnan et al [13], and Mohie El-Din et al [14][15][16][17]. On the other hand, in progressive-stress ALT, all of the test units are exposed to stress, which is continuously at an increasing rate with time.…”

Section: Introductionmentioning

confidence: 99%

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Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study

et al. 2020

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In this article, a progressive-stress accelerated life test (ALT) that is based on progressive type-II censoring is studied. The cumulative exposure model is used when the lifetime of test units follows Pareto-IV distribution. Different estimates as the maximum likelihood estimates (MLEs) and Bayes estimates (BEs) for the model parameters are discussed. Bayesian estimates are derived while using the Tierney and Kadane (TK) approximation method and the importance sampling method. The asymptotic and bootstrap confidence intervals (CIs) of the parameters are constructed. A real data set is analyzed in order to clarify the methods proposed through this paper. Two types of the progressive-stress tests, the simple ramp-stress test and multiple ramp-stress test, are compared through the simulation study. Finally, some interesting conclusions are drawn.

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“…In this part, we use the important sampling method for estimating the unknown parameters. The posterior distribution presented in (15) can be rewritten as…”

Section: Important Sampling Techniquementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study

et al. 2020

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“…The acceleration model is then used to extrapolate the reliability performance to the normal use conditions. Where these different types of methods met a lot of researchers and for more details, you can look at the researches [4][5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Analysis Simple Step Stress Model under Competing Extension Weibull Failure Distribution Based on Progressive Type-II Censoring

Abdelfattah¹,

El-Sherpieny²,

Khalil³

2023

MMEP

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Accelerated life testing (ALT), a procedure utilized in reliability analysis, allows testing units to be subject to increasingly elevated grades of stress during an experiment.Stepstress tests are a subclass of accelerated tests in which the stress levels rise consecutively at prearranged cycles, consequently, the researcher might find out results more swiftly than in ordinary working settings about the parameter of the lifetime distribution. Moreover, there are frequently multiple fatal causes for a test element's failure, for instance, technical or electric. These causes are recognized as "competing risks". The purpose of the analysis is to assess simple step stress accelerated life testing (SS-ALT) with competing Risks originating from the extension of Weibull distribution by applying a progressive Type-II censoring scheme. In this case, under the assumption of a cumulative exposure model, the authors successfully obtained the Bayes estimates (BEs) and maximum likelihood estimators (MLEs) of the undetermined average parameters of the various causes. For Bayesian computations, the squared error loss functions are considered. Additionally, the estimators' asymptotic variance-covariance matrix was created. Additionally, credible intervals and asymptotic confidence intervals (CIs) are provided. For a large sample size, the CIs of the unidentified parameters are developed. A numerical study is also involved to exhibit the accuracy and variability of various estimators for several sample sizes. An example is being used to exemplify the inference method that's also considered here. This study concludes that the mean lengths of credible intervals and asymptotic confidence intervals get shorter as the number of failures rises. The credible interval technique is suggested, nevertheless.

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“…Balakrishnan et al [14] estimated the point and interval estimation for the distribution parameters under type-II censoring. e authors in [15][16][17][18][19][20][21] used Bayesian and classical methods to estimate the parameters for the Weibull, the power generalized Weibull distribution, and the extension of the exponentiated exponential distribution, respectively, under SSALT using different kinds of censoring plans.…”

Section: Introductionmentioning

confidence: 99%

Single and Multiple Ramp Progressive Stress with Binomial Removal: Practical Application for Industry

Hussam

Alharbi

Almetwally

et al. 2022

Mathematical Problems in Engineering

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The objective of this article is to conduct a full study on the failure times of items when subjected to a progressive-stress accelerated life test. These failure times follow the Modified Kies exponential distribution. We performed the experiments under a type-II censoring scheme with binomial removal. The stress design has two ways to be applied either the simple ramp-stress test or the multiple ramp-stress level design of acceleration. We made a comparison between these two designs to decide which design is better. When the lifetime of test units follows the Modified Kies distributions, the cumulative exposure model has been used to apply the acceleration on the failure times to produce early failures. The simulation study was done to compare two types of progressive-stress designs. Different estimation techniques such as maximum likelihood estimation and Bayes estimation are employed to estimate the model parameters. The Metropolis Hasting method is used to derive the Bayesian estimates under symmetric and asymmetric loss functions. We also developed interval estimation as well as point estimation, and we estimated the asymptotic confidence intervals, bootstrap, and credible for the distribution parameters. We made a comparison between different estimation methods. We used real data from a practical experiment as a real data set example to assess the performance of the estimations methods. These data are analyzed to demonstrate the adequacy and superiority of the distribution to fit accelerated failure times. Also, we studied the existence and uniqueness of the roots and we used graphs to assure that the estimates used are unique and global maximum. Finally, some noteworthy conclusions are reached.

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Estimation in Step-Stress Accelerated Life Tests for Power Generalized Weibull Distribution with Progressive Censoring

Cited by 22 publications

References 9 publications

Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study

Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study

Analysis Simple Step Stress Model under Competing Extension Weibull Failure Distribution Based on Progressive Type-II Censoring

Single and Multiple Ramp Progressive Stress with Binomial Removal: Practical Application for Industry

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