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Parameters Estimation for Wear-out Failure Period of Three-Parameter Weibull Distribution

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  • Takatoshi Sugiyama
  • Toru Ogura
Abstract
The shape parameter estimation using the minimum-variance linear estimator with hyperparameter (MVLE-H) method is believed to be effective for a wear-out failure period in a small sample. In the process of the estimation, our method uses the hyperparameter and estimate shape parameters of the MVLE-H method. To obtain the optimal hyperparameter c, it takes a long time, even in the case of the small sample. The main purpose of this paper is to remove the restriction of small samples. We observed that if we set the shape parameters, for sample size n and c, we can use the regression equation to infer the optimal c from n. So we searched in five increments and complemented the hyperparameter for the remaining sample sizes with a linear regression line. We used Monte Carlo simulations (MCSs) to determine the optimal hyperparameter for various sample sizes and shape parameters of the MVLE-H method. Intrinsically, we showed that the MVLE-H method performs well by determining the hyperparameter. Further, we showed that the location and scale parameter estimations are improved using the shape parameter estimated by the MVLE-H method. We verified the validity of the MVLE-H method using MCSs and a numerical example.

Suggested Citation

  • Takatoshi Sugiyama & Toru Ogura, 2022. "Parameters Estimation for Wear-out Failure Period of Three-Parameter Weibull Distribution," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(1), pages 1-40, March.
    • Handle: RePEc:ibn:ijspjl:v:11:y:2022:i:1:p:40
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    References listed on IDEAS

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    1. Huang, Wen-Tao & Huang, Hui-Hsin, 2006. "Empirical Bayes estimation of the guarantee lifetime in a two-parameter exponential distribution," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1821-1829, October.
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    More about this item

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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