고장 보고율을 이용한 현장 수명자료 분포의 모수추정

Estimating Parameters of Field Lifetime Data Distribution Using the Failure Reporting Probability

  • Kim, Young Bok (Department of Industrial Engineering, Seoul National University) ;
  • Lie, Chang Hoon (Department of Industrial Engineering, Seoul National University)
  • 발행 : 2007.03.31

초록

Estimating parameters of the lifetime distribution is investigated when field failure data are not completelyreported. To take into account the reality and the accuracy of the estimates in such a case, the failure reportingprobability is incorporated in estimating parameters, Firstly, method of maximum likelihood estimate (MLE) isused to estimate parameters of the lifetime distribution when failure reporting probability is known, Secondly,Expectation and Maximization (EM) algorithm is used to estimate the failure reporting probability and parame-ters of the lifetime distribution simultaneously when failure reporting probability is unknown. For both cases,procedures of estimation are illustrated for single Weibull distribution and mixed Weibull distribution. Simula-tion results show that MLE obtained by the proposed method is more accurate than the conventional MLE.

키워드

참고문헌

  1. Abernethy, R. B. (1988), The New Weibull Handbook 3rd ed, Reliability Analysis Center, Florida
  2. Barlow, R. E. and Proschan, F. (1979), Inference and Data Analysis for Reliability and Life Testing, California
  3. Bucar, T., Nagode, M. and Fajdiga, M. (2004), Reliability approximation using finite Weibull mixture distribution, Reliability Engineering and System Safety, 84, 241-251 https://doi.org/10.1016/j.ress.2003.11.008
  4. Coit, D. W. and Dey, K. A. (1988), Analysis of grouped data from field failure reporting systems, Reliability Engineering and System Safety, 65,95-101 https://doi.org/10.1016/S0951-8320(98)00089-1
  5. Coit, D. W. and Jin, T. (2000), Gamma distribution parameter estimation for field reliability data with missing failure times, lIE Transactions, 32, 1161-1166
  6. Hale, P. S. and Arno, R. G. (2001), Survey of Reliability and Availability Information for Power Distribution, Power Generation, and HV AC components for Commercial, Industrial and Utility Installations, IEEE Transaction on Industry Applications, 37(1), 191-196 https://doi.org/10.1109/28.903146
  7. Jiang, S. and Kececioglu, D. (1992), Maximum Likelihood Estimates, from Censored Data, for Mixed- W eibull Distributions, IEEE Transactions on Reliability, 41(2), 248-255 https://doi.org/10.1109/24.257791
  8. Jiang, R. and Murthy, D. N. P. (1995), Modeling Failure-Data by Mixture of 2 Weibull Distribution: A Graphical Approach, IEEE Transactions on Reliability, 44(3), 477-488 https://doi.org/10.1109/24.406588
  9. Jiang, R. and Murthy, D. N. P. (1995), Reliability modeling involving two Weibull distributions, Reliability Engineering and System Safety, 47, 187-198 https://doi.org/10.1016/0951-8320(94)00045-P
  10. Jiang, R. and Murthy, D. N. P. (1988), Mixture of weibull distributionsparametric characterization of failure rate function, Applied Stochastic Models and Data Analysis, 14,47-65 https://doi.org/10.1002/(SICI)1099-0747(199803)14:1<47::AID-ASM306>3.0.CO;2-E
  11. Lim, T. J. (2002). Estimation of Product Reliability with Incomplete Field Warranty Data, Journal of the Korean Institute of Industrial Engineers, 28(4), 368-378
  12. Oh, Y. S. and Bai, D. S. (2001), Field data analyses with additional after warranty failure data, Reliability Engineering and System Safety, 72, 1-8 https://doi.org/10.1016/S0951-8320(00)00056-9