Data Analysis of Step-Stress Accelerated Life Test with Random Group Effects under Weibull Distribution

Juan, Wang

doi:10.1155/2020/4898123

Cited by 4 publications

(6 citation statements)

References 20 publications

(29 reference statements)

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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%

“…The importance of the Lindley distribution in this paper is that it provides more fit than its traditional competitor, the two-parameter Weibull distribution, as we checked for the p-value for both distributions for fitting the real data application and found that the Lindley distribution has p-value greater than 0.05 for both levels of stress in the experiment, while in case of the Weibull distribution it makes a poor-fitting for the real data set because the p-value of the first level of acceleration is less than 0.05, while it provides good fitting for the second level, so we can deduce that the Lindley distribution makes better fitting than the Weibull distribution for both levels of experiment so we can use it instead of the Weibull distribution by fitting the two levels of the Lindley distribution which has a merit over the two parameters Weibull distribution in fitting this kind of experiment. For more information about the reliability of engineering data, please see references [12][13][14].…”

Section: Comparison With Competitive Distributionmentioning

confidence: 99%

“…We introduce three different types of intervals, namely asymptotic, bootstrap, and credible confidence intervals (CIs), for the parameters of the model in Section 5. In Section 6, a real data example for reliability engineering data is fitted and studied to apply the proposed methods (for more reading about reliability engineering modelling and applications, see [12][13][14]). Section 6 also includes the graphs of the reliability function and some elaboration about these graphs.…”

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: Comparison With Competitive Distributionmentioning

confidence: 99%

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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“…Abdelmonem and Jaheen (2017) considered a SSALT study assuming that the lifetime follows a generalized exponential distribution based on Type-II censored data and applying MLE and Bayesian approaches. Samanta et al (2018) provide the order-restricted Bayesian inference of a simple step-stress test and more recently, Wang (2020).…”

Section: Introductionmentioning

confidence: 99%

Bayesian analysis for multiple step-stress accelerated life test model under gamma lifetime distribution and type-II censoring

Moala

Chagas²

2022

IJQRM

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PurposeThe step-stress accelerated test is the most appropriate statistical method to obtain information about the reliability of new products faster than would be possible if the product was left to fail in normal use. This paper presents the multiple step-stress accelerated life test using type-II censored data and assuming a cumulative exposure model. The authors propose a Bayesian inference with the lifetimes of test item under gamma distribution. The choice of the loss function is an essential part in the Bayesian estimation problems. Therefore, the Bayesian estimators for the parameters are obtained based on different loss functions and a comparison with the usual maximum likelihood (MLE) approach is carried out. Finally, an example is presented to illustrate the proposed procedure in this paper.Design/methodology/approachA Bayesian inference is performed and the parameter estimators are obtained under symmetric and asymmetric loss functions. A sensitivity analysis of these Bayes and MLE estimators are presented by Monte Carlo simulation to verify if the Bayesian analysis is performed better.FindingsThe authors demonstrated that Bayesian estimators give better results than MLE with respect to MSE and bias. The authors also consider three types of loss functions and they show that the most dominant estimator that had the smallest MSE and bias is the Bayesian under general entropy loss function followed closely by the Linex loss function. In this case, the use of a symmetric loss function as the SELF is inappropriate for the SSALT mainly with small data.Originality/valueMost of papers proposed in the literature present the estimation of SSALT through the MLE. In this paper, the authors developed a Bayesian analysis for the SSALT and discuss the procedures to obtain the Bayes estimators under symmetric and asymmetric loss functions. The choice of the loss function is an essential part in the Bayesian estimation problems.

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“…Sha and Pan (2014) presented a Bayesian approach for the Weibull proportional hazard model used in SSALT. Wang (2020) built a non-linear mixed model with the assumption of the Weibull distribution for lifetime data analysis from SSALT to consider the random effects from the group-to-group variation.…”

mentioning

confidence: 99%

Comparison between continuous and periodic inspections in step‐stress tests

Hakamipour

2021

Stat

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Accelerated life test is currently the main method of assessing product reliability rapidly, and the design of efficient test plans is a critical step to ensure that accelerated life tests can assess the product reliability accurately, quickly and economically. In these tests, the samples are tested at stress levels higher than normal. Then, the product life at the normal stress level can be estimated by extrapolating the life information of samples at high stress levels to the normal level based on the stress–life relationship. In this paper, optimal k‐level step‐stress accelerated life tests are considered for the Weibull failure data under progressive Type‐I censoring. There are two strategies for performance inspection of the test unit, which include continuous inspection and periodic inspection. These two strategies generate the life data and group data, respectively. In this paper, these two inspection modes are compared and the efficiencies of these are obtained. This paper investigates the optimal design based on five optimality criteria under the constraint that the total experimental cost does not exceed a pre‐specified budget. Finally, based on the simulation study and a real data set, the advantages of using the continuous inspection relative to periodic inspection are investigated.

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Data Analysis of Step-Stress Accelerated Life Test with Random Group Effects under Weibull Distribution

Cited by 4 publications

References 20 publications

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

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

Bayesian analysis for multiple step-stress accelerated life test model under gamma lifetime distribution and type-II censoring

Comparison between continuous and periodic inspections in step‐stress tests

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