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

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

doi:10.1002/qre.2212

Cited by 29 publications

(2 citation statements)

References 23 publications

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“…Assuming that the scale parameter of NH distribution has a log-linear relation with stress, [ 55 ] obtained MLEs of the parameters under CSALT and SSALT models. Under CSALT and PSALT for type-II PC data, [ 56 , 57 ] considered the MLE and BE techniques to obtain the estimates of model parameters. Reference [ 59 ] explored optimum plans for k -level CSALT plans under complete data for NH distribution using D and C optimality.…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation in Step Stress Partially Accelerated Life Testing under Different Types of Censored Data

Kamal

Siddiqui

Rahman

et al. 2022

Computational Intelligence and Neuroscience

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A long testing period is usually required for the life testing of high-reliability products or materials. It is possible to shorten the testing process by using ALTs (accelerated life tests). Due to the fact that ALTs test products in harsher settings than are typical use conditions, the life expectancy of the objects they evaluate is reduced. Censored data in which the specific failure timings of all units assigned to test are not known, or all units assigned to test have not failed, may arise in ALTs for a variety of reasons, including operational failure, device malfunction, expense, and time restrictions. In this paper, we have considered the step stress partially accelerated life test (SSPALT) under two different censoring schemes, namely the type-I progressive hybrid censoring scheme (type-I PHCS) and the type-II progressive censorship scheme (type-II PCS). The failure times of the items are assumed to follow NH distribution, while the tampered random variable (TRV) model is used to explain the effect of stress change. In order to obtain the estimates of the unknown parameters, the maximum likelihood estimation (MLE) approach is adopted. Furthermore, based on the asymptotic theory of MLEs, the approximate confidence intervals (ACIs) are also constructed. The point estimates under two censoring schemes are compared in terms of root mean squared errors (RMSEs) and relative absolute biases (RABs), while ACIs are compared in terms of their lengths and coverage probabilities (CPs). The performance of the estimators has been evaluated and compared under two censoring schemes with various sample sizes through a simulation study. Simulation results show that estimates with type-I PHCS outperform estimates with type-II PCS in terms of RMSEs, RABs, lengths, and CPs. Finally, a real-world numerical example of insulating fluid failure times is presented to show how the approaches will work in reality.

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Section: Introductionmentioning

confidence: 99%

Parameter Estimation in Step Stress Partially Accelerated Life Testing under Different Types of Censored Data

Kamal

Siddiqui

Rahman

et al. 2022

Computational Intelligence and Neuroscience

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“…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. For more reading about progressive-stress ALT, see Yin and Sheng [18], Mohie El-Din et al [19], Bai et al [20], as well as Ronghua and Heliang [21] and Abdel-Hamid and AL-Hussaini [22] who also studied the progressive-stress ALT based on progressive censoring in case of Weibull distribution in [23]. Bayesian prediction intervals under progressively type-II censoring for the half-logistic distribution under progressive-stress model have been discussed by AL-Hussaini et al [24].…”

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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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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Optimal design of a simple step‐stress accelerated life test under progressive type I censoring with nonuniform durations for exponential lifetimes

Han

2019

Quality & Reliability Eng

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Thanks to continuously advancing technology and manufacturing processes, the products and devices are becoming highly reliable. However, performing the life tests of these products at normal operating conditions becomes extremely difficult, if not impossible, due to their long life spans. This can result in missed opportunities to introduce the products to the market in a timely manner and eventually loss of the market share. This problem is solved by accelerated life tests where the test units are subjected to higher stress levels than the normal usage level so that information on the lifetime parameters can be obtained more quickly. The lifetime at the design condition is then estimated through extrapolation using a regression model. In this work, the design optimization of a simple step-stress accelerated life test under progressive type I censoring is studied with nonuniform step durations for assessing the reliability characteristics of a solar lighting device. Allowing the intermediate censoring to take place at the stress change time point, the nature of the optimal stress duration is demonstrated under various design criteria including D-optimality, C-optimality, A-optimality, and E-optimality. The existence of these optimal designs is investigated in detail for exponential lifetimes with a single stress variable, and the effect of the intermediate censoring proportion is assessed on the design efficiency. KEYWORDS accelerated life tests, design of experiment, exponential distribution, Fisher information, progressive type I censoring, step-stress loading Qual Reliab Engng Int. 2019;35:1297-1312.wileyonlinelibrary.com/journal/qre

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

Cited by 29 publications

References 23 publications

Parameter Estimation in Step Stress Partially Accelerated Life Testing under Different Types of Censored Data

Parameter Estimation in Step Stress Partially Accelerated Life Testing under Different Types of Censored Data

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

Optimal design of a simple step‐stress accelerated life test under progressive type I censoring with nonuniform durations for exponential lifetimes

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