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A New Compromise Design Plan for Accelerated Failure Time Models with Temperature as an Acceleration Factor

Author

Listed:
  • Irene Mariñas-Collado

    (Department of Statistics and Operations Research and Mathematics Didactics, University of Oviedo, 33007 Oviedo, Spain)

  • M. Jesús Rivas-López

    (Department of Statistics, Institute of Fundamental Physics and Mathematics, University of Salamanca, 37008 Salamanca, Spain)

  • Juan M. Rodríguez-Díaz

    (Department of Statistics, Institute of Fundamental Physics and Mathematics, University of Salamanca, 37008 Salamanca, Spain)

  • M. Teresa Santos-Martín

    (Department of Statistics, Institute of Fundamental Physics and Mathematics, University of Salamanca, 37008 Salamanca, Spain)

Abstract

An accelerated life test of a product or material consists of the observation of its failure time when it is subjected to conditions that stress the usual ones. The purpose is to obtain the parameters of the distribution of the time-to-failure for usual conditions through the observed failure times. A widely used method to provoke an early failure in a mechanism is to modify the temperature at which it is used. In this paper, the statistically optimal plan for Accelerated Failure Time (AFT) models, when the accelerated failure process is described making use of Arrhenius or Eyring equations, was calculated. The result was a design that had only two stress levels, as is common in other AFT models and that is not always practical. A new compromise plan was presented as an alternative to the widely used “4:2:1 plan”. The three-point mixture design proposed specified a support point in the interval that was optimal for the estimation of the parameters in AFT models, rather than simply the middle point. It was studied in comparison to different commonly used designs, and it proved to have a higher D-efficiency than the others.

Suggested Citation

  • Irene Mariñas-Collado & M. Jesús Rivas-López & Juan M. Rodríguez-Díaz & M. Teresa Santos-Martín, 2021. "A New Compromise Design Plan for Accelerated Failure Time Models with Temperature as an Acceleration Factor," Mathematics, MDPI, vol. 9(8), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:836-:d:534416
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    References listed on IDEAS

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    1. Engler David & Li Yi, 2009. "Survival Analysis with High-Dimensional Covariates: An Application in Microarray Studies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-24, February.
    2. L. Altstein & G. Li, 2013. "Latent Subgroup Analysis of a Randomized Clinical Trial through a Semiparametric Accelerated Failure Time Mixture Model," Biometrics, The International Biometric Society, vol. 69(1), pages 52-61, March.
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