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TTT-SiZer: A graphic tool for aging trends recognition

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  • Gámiz, Maria Luz
  • Nozal-Cañadas, Rafael
  • Raya-Miranda, Rocío

Abstract

A new graphic tool is presented to test aging trends based on lifetime data. The graphical test is developed by means of scale and space inference about the Total-Time-on-Test transform and its first and second derivatives. The graphic tool TTT-SiZer is defined considering nonparametric local polynomial kernel estimators and constructing the corresponding (simultaneous as well as punctual) confidence intervals around three different curves. The finite sample properties of the method are evaluated by a simulation study and the comparison with other non-graphical tests shows that the graphical test helps localize discrepancies of empirical data concerning a given hypothesized aging property, thus allowing to solve the problem locally.

Suggested Citation

  • Gámiz, Maria Luz & Nozal-Cañadas, Rafael & Raya-Miranda, Rocío, 2020. "TTT-SiZer: A graphic tool for aging trends recognition," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    • Handle: RePEc:eee:reensy:v:202:y:2020:i:c:s0951832020305111
    DOI: 10.1016/j.ress.2020.107010
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    References listed on IDEAS

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    1. Szymkowiak, Magdalena, 2018. "Generalized aging intensity functions," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 198-208.
    2. Hannig, J. & Marron, J.S., 2006. "Advanced Distribution Theory for SiZer," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 484-499, June.
    3. Viertävä, Janne & Vaurio, Jussi K., 2009. "Testing statistical significance of trends in learning, ageing and safety indicators," Reliability Engineering and System Safety, Elsevier, vol. 94(6), pages 1128-1132.
    4. Park, Cheolwoo & Kang, Kee-Hoon, 2008. "SiZer analysis for the comparison of regression curves," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 3954-3970, April.
    5. A. D. Hutson & M. D. Ernst, 2000. "The exact bootstrap mean and variance of an L‐estimator," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 89-94.
    6. Bo H. Lindqvist & Francisco J. Samaniego, 2019. "Some new results on the preservation of the NBUE and NWUE aging classes under the formation of coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(5), pages 430-438, August.
    7. Jorge Navarro & Yolanda del Águila & Miguel A. Sordo & Alfonso Suárez‐Llorens, 2014. "Preservation of reliability classes under the formation of coherent systems," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 30(4), pages 444-454, July.
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    Cited by:

    1. Jiang, Renyan & Qi, Faqun & Cao, Yu, 2023. "Relation between aging intensity function and WPP plot and its application in reliability modelling," Reliability Engineering and System Safety, Elsevier, vol. 229(C).

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