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Reliability Assessment for Very Few Failure Data and Weibull Distribution

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  • Lulu Zhang
  • Guang Jin
  • Yang You

Abstract

Only very few failure data can be obtained for the time censored test of high-reliability and long-life products. For very few failure data, the current methods fail to obtain both the point estimation and confidence interval of reliability parameters. If the point estimation and confidence interval of reliability parameters are obtained based on different methods, the results tend to be unreliable. In this study, based on the existing research, a Bayesian reliability evaluation method for very few failure data under the Weibull distribution was proposed. First, the range of failure probability was limited based on the convexity and self-features of the Weibull distribution function. Second, based on the background of the sample with very few failure data, the pretest distribution function and parameters were set and solved. The point estimation and confidence interval model of failure probability based on the Bayesian formula was established. The improved match distribution curve method was used to compute both the point estimation and confidence interval of reliability parameters. Furthermore, by comparing the results of numerical examples, the calculation results obtained by the proposed method were verified as being very reasonable. Finally, taking wet friction plates as an example, the results showed the effectiveness of this method in engineering practice.

Suggested Citation

  • Lulu Zhang & Guang Jin & Yang You, 2019. "Reliability Assessment for Very Few Failure Data and Weibull Distribution," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-9, September.
    • Handle: RePEc:hin:jnlmpe:8947905
    DOI: 10.1155/2019/8947905
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    Cited by:

    1. Chang, Ping-Chen, 2022. "MC-based simulation approach for two-terminal multi-state network reliability evaluation without knowing d-MCs," Reliability Engineering and System Safety, Elsevier, vol. 220(C).
    2. Xiaowei Dong & Feng Sun & Fangchao Xu & Qi Zhang & Ran Zhou & Liang Zhang & Zhongwei Liang, 2022. "Three-Parameter Estimation Method of Multiple Hybrid Weibull Distribution Based on the EM Optimization Algorithm," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    3. Somnath Chattopadhyaya & Brajeshkumar Kishorilal Dinkar & Alok Kumar Mukhopadhyay & Shubham Sharma & José Machado, 2021. "Meta-Analysis and Forest Plots for Sustainability of Heavy Load Carrier Equipment Used in the Industrial Mining Environment," Sustainability, MDPI, vol. 13(15), pages 1-15, August.

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