Estimation in constant-stress accelerated life tests for extension of the exponential distribution under progressive censoring

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

doi:10.1007/s40300-016-0089-4

Cited by 38 publications

(25 citation statements)

References 16 publications

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“…The posterior density function in (14) for the two parameters ψ and ζ can be formed by the multiplication of Equations (6) with (11) and making some simplification, and its final form is as below:…”

Section: Bayes Estimationmentioning

confidence: 99%

“…This paper aims to make a full study on the Lindley distribution under ALT using progressive Type II censored samples and apply an experimental application to introduce the importance of this distribution in fitting many real data applications in many fields of life. We refer to different recent studies to explain the difference kinds of ALT; for more reading about constant, step, and progressive ALT, see the works of El-din et al [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

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Study on Lindley Distribution Accelerated Life Tests: Application and Numerical Simulation

Hussam¹,

Riad

Mubarak

et al. 2020

Symmetry

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Saving money and time are very important in any research project, so we must find a way to decrease the time of the experiment. This method is called the accelerated life tests (ALT) under censored samples, which is a very efficient method to reduce time, which leads to a decrease in the cost of the experiment. This research project includes inference on Lindley distribution in a simple step-stress ALT for the Type II progressive censored sample. The paper contains two major sections, which are a simulation study and a real-data application on the experimental design of an industry experiment on lamps. These sections are used to conduct results on the study of the distribution. The simulation was done using Mathematica 11 program. To use real data in the censored sample, we fitted them to be compatible with the Lindley distribution using the modified Kolmogorov–Smirnov (KS) goodness of fit test for progressive Type II censored data. We used the tampered random variable (TRV) acceleration model to generate early failures of items under stress. We also found the values of the distribution parameter and the accelerating factor using the maximum likelihood estimation of (MLEs) and Bayes estimates (BEs) using symmetric loss function for both simulated data and real data. Next, we estimated the upper and lower bounds of the parameters using three methods, namely approximate confidence intervals (CIs), Bootstrap CIs, and credible CIs, for both parameters of the distribution, ψ and ζ. Finally, we found the value of the parameter for the real data set under normal use conditions and stress conditions and graphed the reliability functions under normal and accelerated use.

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Section: Bayes Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Study on Lindley Distribution Accelerated Life Tests: Application and Numerical Simulation

Hussam¹,

Riad

Mubarak

et al. 2020

Symmetry

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“…Let t ij∶m i ∶n i = t ij be the observed values of the lifetime T obtained from a progressive type-II censoring under progressive-stress level S i (t), i = 1, 2, … , k and j = 1, 2, … , m i . From the CDF in (6) and the corresponding PDF in (7), the likelihood function of the 3 parameters , a, and b based on the progressive type-II censoring sample is obtained as follows:…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

“…1 In constant-stress ALT, each unit is run at constant high stress until either all units fail or the test terminates. Constant-stress models were studied by several authors; see Kim and Bai, 2 Watkins and John, 3 Jaheen et al, 4 Guan et al, 5 and Mohie El-Din et al 6,7 In step-stress ALT, the stress on every unit is not fixed but is increasing step by step at prespecified times or simultaneous the occurrence of a fixed number of failures. The step-stress models were studied extensively in the literature; see, for instance, Miller and Nelson, 8 Bai et al, 9 Gouno et al, 10 Balakrishnan et al, 11 and Mohie El-Din et al [12][13][14] In progressive-stress ALT, the stress on each test unit is continuously increasing in time.…”

Section: Introductionmentioning

confidence: 99%

Classical and Bayesian inference on progressive‐stress accelerated life testing for the extension of the exponential distribution under progressive type‐II censoring

El-Din

Abu-Youssef

Ali

et al. 2017

Quality & Reliability Eng

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In this paper, a progressive‐stress accelerated life test under progressive type‐II censoring is considered. The cumulative exposure model is assumed when the lifetime of test units follows an extension of the exponential distribution. The maximum likelihood and Bayes estimates of the model parameters are obtained. The approximate and credible confidence intervals of the estimators are derived. Furthermore, a real lifetime data set is analyzed to illustrate the proposed procedures. Finally, the simulation studies are used to compare between 2 different designs of the progressive‐stress test (simple and multiple ramp‐stress tests).

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“…See Nelson (1990) and Mohie El-Din et al (2016) for more details about constant-stress ALT. In step-stress ALT, the stress on every unit is not fixed but is increased step by step at prespecified times or simultaneous the occurrence of a fixed number of failures.…”

Section: Introductionmentioning

confidence: 99%

Parametric inference on step-stress accelerated life testing for the extension of exponential distribution under progressive type-II censoring

El-Din

Abu-Youssef

Ali

et al. 2016

CSAM

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In this paper, a simple step-stress accelerated life test (ALT) under progressive type-II censoring is considered. Progressive type-II censoring and accelerated life testing are provided to decrease the lifetime of testing and lower test expenses. The cumulative exposure model is assumed when the lifetime of test units follows an extension of the exponential distribution. Maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of the model parameters are also obtained. In addition, a real dataset is analyzed to illustrate the proposed procedures. Approximate, bootstrap and credible confidence intervals (CIs) of the estimators are then derived. Finally, the accuracy of the MLEs and BEs for the model parameters is investigated through simulation studies.

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Estimation in constant-stress accelerated life tests for extension of the exponential distribution under progressive censoring

Cited by 38 publications

References 16 publications

Study on Lindley Distribution Accelerated Life Tests: Application and Numerical Simulation

Study on Lindley Distribution Accelerated Life Tests: Application and Numerical Simulation

Classical and Bayesian inference on progressive‐stress accelerated life testing for the extension of the exponential distribution under progressive type‐II censoring

Parametric inference on step-stress accelerated life testing for the extension of exponential distribution under progressive type-II censoring

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