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Tolerance limits under normal mixtures: Application to the evaluation of nuclear power plant safety and to the assessment of circular error probable

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  • Zimmer, Zachary
  • Park, DoHwan
  • Mathew, Thomas

Abstract

Upper tolerance limits are derived for (i) a normal mixture distribution, and (ii) for the distribution of the Euclidean norm of a bivariate normal mixture random variable, using asymptotic normality of the MLE and bootstrap calibration. Scenario (i) is used to model the peak cladding temperature (PCT) of nuclear power plants, to assess if the PCT distribution is below a safety threshold of 2200 °F. Scenario (ii) is used to model impact location data on projectiles launched from different locations or systems, and the problem is inference concerning the circular error probable (CEP). Simulation studies show the accuracy of the proposed methodology.

Suggested Citation

  • Zimmer, Zachary & Park, DoHwan & Mathew, Thomas, 2016. "Tolerance limits under normal mixtures: Application to the evaluation of nuclear power plant safety and to the assessment of circular error probable," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 304-315.
    • Handle: RePEc:eee:csdana:v:103:y:2016:i:c:p:304-315
    DOI: 10.1016/j.csda.2016.05.015
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    References listed on IDEAS

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    1. Boldea, Otilia & Magnus, Jan R., 2009. "Maximum Likelihood Estimation of the Multivariate Normal Mixture Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1539-1549.
    2. Liu, Huan & Tang, Yongqiang & Zhang, Hao Helen, 2009. "A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 853-856, February.
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    Cited by:

    1. Ruijie Guan & Yaohua Rong & Weihu Cheng & Zhenyu Xin, 2025. "A Novel Finite Mixture Model Based on the Generalized t Distributions with Two-Sided Censored Data," Annals of Data Science, Springer, vol. 12(1), pages 341-379, February.
    2. Hany Abdel-Khalik & Dongli Huang & Ugur Mertyurek & William Marshall & William Wieselquist, 2021. "Overview of the Tolerance Limit Calculations with Application to TSURFER," Energies, MDPI, vol. 14(21), pages 1-37, October.
    3. Shin‐Fu Tsai, 2020. "Approximate two‐sided tolerance intervals for normal mixture distributions," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 62(3), pages 367-382, September.

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