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Optimal design of accelerated life tests for an extension of the exponential distribution

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  • Haghighi, Firoozeh

Abstract

Accelerated life tests provide information quickly on the lifetime distribution of the products by testing them at higher than usual levels of stress. In this paper, the lifetime of a product at any level of stress is assumed to have an extension of the exponential distribution. This new family has been recently introduced by Nadarajah and Haghighi (2011 [1]); it can be used as an alternative to the gamma, Weibull and exponentiated exponential distributions. The scale parameter of lifetime distribution at constant stress levels is assumed to be a log-linear function of the stress levels and a cumulative exposure model holds. For this model, the maximum likelihood estimates (MLEs) of the parameters, as well as the Fisher information matrix, are derived. The asymptotic variance of the scale parameter at a design stress is adopted as an optimization objective and its expression formula is provided using the maximum likelihood method. A Monte Carlo simulation study is carried out to examine the performance of these methods. The asymptotic confidence intervals for the parameters and hypothesis test for the parameter of interest are constructed.

Suggested Citation

  • Haghighi, Firoozeh, 2014. "Optimal design of accelerated life tests for an extension of the exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 251-256.
    • Handle: RePEc:eee:reensy:v:131:y:2014:i:c:p:251-256
    DOI: 10.1016/j.ress.2014.04.017
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    References listed on IDEAS

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    1. Mikhail Nikulin & Firoozeh Haghighi, 2009. "On the power generalizedWeibull family: model for cancer censored data," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 75-86.
    2. Elsayed, E.A. & Zhang, Hao, 2007. "Design of PH-based accelerated life testing plans under multiple-stress-type," Reliability Engineering and System Safety, Elsevier, vol. 92(3), pages 286-292.
    3. Nadarajah, Saralees & Kotz, Samuel, 2006. "The beta exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 689-697.
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    1. Wu, Shuo-Jye & Huang, Syuan-Rong, 2017. "Planning two or more level constant-stress accelerated life tests with competing risks," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 1-8.
    2. Mugnaini, Marco & Addabbo, Tommaso & Fort, Ada & Elmi, Alessandro & Landi, Elia & Vignoli, Valerio, 2020. "Magnetic brakes material characterization under accelerated testing conditions," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    3. Peña-Ramírez, Fernando A. & Guerra, Renata Rojas & Canterle, Diego Ramos & Cordeiro, Gauss M., 2020. "The logistic Nadarajah–Haghighi distribution and its associated regression model for reliability applications," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    4. Negreiros, Ana Cláudia Souza Vidal de & Lins, Isis Didier & Moura, Márcio José das Chagas & Droguett, Enrique López, 2020. "Reliability data analysis of systems in the wear-out phase using a (corrected) q-Exponential likelihood," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    5. Abd El-Raheem M. Abd El-Raheem & Mona Hosny & Mahmoud H. Abu-Moussa, 2021. "On Progressive Censored Competing Risks Data: Real Data Application and Simulation Study," Mathematics, MDPI, vol. 9(15), pages 1-17, July.
    6. Cai, Xia & Tian, Yubin & Ning, Wei, 2019. "Change-point analysis of the failure mechanisms based on accelerated life tests," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 515-522.
    7. Ibrahim Elbatal & Naif Alotaibi & Salem A. Alyami & Mohammed Elgarhy & Ahmed R. El-Saeed, 2022. "Bayesian and Non-Bayesian Estimation of the Nadaraj ah–Haghighi Distribution: Using Progressive Type-1 Censoring Scheme," Mathematics, MDPI, vol. 10(5), pages 1-16, February.
    8. Moustafa, Kassem & Hu, Zhen & Mourelatos, Zissimos P. & Baseski, Igor & Majcher, Monica, 2021. "System reliability analysis using component-level and system-level accelerated life testing," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    9. Nasir, Ehab A. & Pan, Rong, 2015. "Simulation-based Bayesian optimal ALT designs for model discrimination," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 1-9.

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