Journal of the Korean Society for Aeronautical & Space Sciences (한국항공우주학회지)

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
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Parameter Estimation of Reliability Growth Model with Incomplete Data Using Bayesian Method

베이지안 기법을 적용한 Incomplete data 기반 신뢰성 성장 모델의 모수 추정

  • Park, Cheongeon (School of Aerospace and Mechanical Engineering, Korea Aerospace University) ;
  • Lim, Jisung (School of Aerospace and Mechanical Engineering, Korea Aerospace University) ;
  • Lee, Sangchul (School of Aerospace and Mechanical Engineering, Korea Aerospace University)
  • Received : 2019.05.31
  • Accepted : 2019.08.21
  • Published : 2019.10.01
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Abstract

By using the failure information and the cumulative test execution time obtained by performing the reliability growth test, it is possible to estimate the parameter of the reliability growth model, and the Mean Time Between Failure (MTBF) of the product can be predicted through the parameter estimation. However the failure information could be acquired periodically or the number of sample data of the obtained failure information could be small. Because there are various constraints such as the cost and time of test or the characteristics of the product. This may cause the error of the parameter estimation of the reliability growth model to increase. In this study, the Bayesian method is applied to estimating the parameters of the reliability growth model when the number of sample data for the fault information is small. Simulation results show that the estimation accuracy of Bayesian method is more accurate than that of Maximum Likelihood Estimation (MLE) respectively in estimation the parameters of the reliability growth model.

신뢰성 성장 시험을 수행하며 획득하게 되는 고장 정보와 누적 시험수행시간을 이용하면 신뢰성 성장 모델의 모수 추정이 가능하며, 모수 추정을 통해 해당 제품의 MTBF를 예측할 수 있다. 그러나 시험에 대한 비용, 시간 혹은 제품의 특성 등의 여러 제약으로 인해 고장 정보가 구간적으로 획득되거나, 획득한 고장 정보의 샘플 데이터(Sample Data)의 수가 작을 수 있다. 이는 신뢰성 성장 모델의 모수 추정의 오차를 커지게 하는 원인이 될 수 있다. 본 논문에서는 샘플 데이터의 수가 작을 경우 신뢰성 성장 모델의 모수 추정 시 베이지안 기법 기반의 모수 추정 방법의 적용에 대해 연구를 수행하였다. 시뮬레이션 결과 신뢰성 성장 모델의 모수를 추정할 때, MLE를 적용하여 추정하는 방법보다 베이지안 기법을 적용하는 방법이 추정 정확도가 높음을 확인하였다.

Keywords

References

  1. Duane, T. J., "Learning Curve Approach to Reliability Monitoring," IEEE Transactions on Aerospace, Vol. 2, No. 2, 1964, pp. 563-566. https://doi.org/10.1109/TA.1964.4319640
  2. Lee, Y. E., Kim, G. Y., Lee, G. H., Kim, Y. H., and Jung, Y. M., "Reliability growth analysis for KA-1 Aircraft-Based on Duane and Crow-AMSAA Model," The Korean Society for Aeronautical and Space Science, 2010, pp. 871-874.
  3. Ahmed, A. O. M., Al-Kutubi, H. S., and Ibrahim, N. A., "Comparison of the Bayesian and maximum likelihood estimation for Weibull distribution," Journal of mathematics and statistics 6.2, 2010, pp. 100-104. https://doi.org/10.3844/jmssp.2010.100.104
  4. Zhao, M., and Xie, M., "A model of storage reliability with possible initial failures," Reliability Engineering & System Safety 43.3, 1994, pp. 269-273. https://doi.org/10.1016/0951-8320(94)90031-0
  5. Berger, J. O., Statistical decision theory and Bayesian analysis, Springer Science & Business Media, 2013.
  6. Lee, H. N., Moon, S. I., and Jang, S. G., "Reliability Estimation for One-Shot Items by Empirical Bayes," Proceeding of The Korean Society for Aeronautical and Space Sciences Fall Conference, 2017, pp. 1042-1043.
  7. Mun, B, M., Sun, E, J., and Bae, S, J., "Bayesian Reliability Estimation for Small Sample-Sized One-shot Devices," Journal of Applied Reliability, Vol. 13, No. 2, 2013, pp. 99-107.
  8. Won, D. Y., Lim, J. H., Sim, H. S., Sung, S. I., Lim, H. S., and Kim, Y. S., "A Review on the Analysis of Life Data Based on Bayesian Method: 2000-2016," Journal of Applied Reliability, Vol. 17, No. 3, 2017, pp. 213-223.
  9. Seo, S. K., Minitab Reliability Analysis: Completion of minitab practice centered on case studies, 2nd Ed., Eretech, 2015.
  10. Tang, Z., and et al. "Comparison of the Weibull and the crow-AMSAA model in prediction of early cable joint failures," IEEE Transactions on Power Delivery 30.6, 2015, pp. 2410-2418. https://doi.org/10.1109/TPWRD.2015.2404926
  11. Crow, L. H., and Basu, A. P., "Reliability growth estimation with missing data II," Annual Reliability and Maintainability Symposium(IEEE), 1988, pp. 248-253.
  12. Cho, H. J., Lim, J. H., and Kim, Y. S., "A Comparison of the Reliability Estimation Accuracy between Bayesian Methods and Classical Methods Based on Weibull Distribution," Journal of the Korean Institute of Industrial Engineers, Vol. 42, No. 4, 2016, pp. 256-262. https://doi.org/10.7232/JKIIE.2016.42.4.256
  13. Mohammed A, A. O., Ibrahim, N. A., Adam, M. B., and Arasan, J., "Bayesian survival and hazard estimate for Weibull censored time distribution," Journal of Applied Sciences, Vol. 12, Issue 12, 2012, pp. 1313-1317. https://doi.org/10.3923/jas.2012.1313.1317
  14. Bergomi, M., and Pedrazzoli, C., "Bayesian Statistics: Computational Aspects," Seminar on Statistics, FS 2008, 2008.