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임의절단 하에서 신뢰성 자료의 평균잔여수명 추정에 대한 연구

The Study on the Mean Residual Life Estimation of Reliability Data under Random Censoring

  • 이미숙 (경북대학교 경영학부 대학원 BK21)
  • Lee, Mi-Sook (BK21, Graduate School of Business Administration, Kyungpook National University)
  • 투고 : 2010.02.15
  • 심사 : 2010.06.18
  • 발행 : 2010.06.30

초록

평균잔여수명은 공학, 의학, 생존분석, 사회과학 등 많은 분야에서 중요한 역할을 하고 있다. 특히 시스템의 신뢰성연구에서 시스템의 갑작스런 중지는 심각한 문제를 초래하기 때문에, 부품에 대한 평균잔여수명 추정은 매우 중요하다. 그래서 많은 상황변수를 고려한 시뮬레이션 연구가 되어왔다. 본 연구에서는 임의절단(random censoring) 에서 가지 평균잔여수명 추정기법을 소개하고 3가지 와이블 수명분포와 6가지 절단분포의 조합에서 시뮬레이션하였다. 또한 이들의 성과를 편의(bias)와 MSE측면에서 비교 분석하였다.

Mean Residual Life (MRL) function plays a very important role in the area of engineering, medical science, survival studies, social sciences, and many other fields. Specially, in the reliability study of technical systems, the MRL estimation of a component is very important because the sudden stop of a system brings a serious problem. So, many simulation studies of MRL estimation have been done considering various situation variables. In this paper, four estimators of MRL are proposed under random censoring and their performances re compared through bias and Mean Square Error (MSE) by Monte Carlo simulation.

키워드

참고문헌

  1. B. Abdous and Berred, A., "Mean residual life estimation", J. Statist. Plann. Inference 132, pp. 3-19, 2005. https://doi.org/10.1016/j.jspi.2004.06.012
  2. D. Oakes and Dasu, T., "A note on residual life", Biometrika, 77, pp. 409-410, 1990. https://doi.org/10.1093/biomet/77.2.409
  3. F. Guess, Zhang, X. Young, T., and Leon, R., "Using mean residual life function for unique insight into strengths of materials data", International Journal of Reliability and Application, 6(2), pp. 79-85, 2005.
  4. G. A. Moon, Shin, I. H., and Chae, H. S., "The estimation of MRL function under left truncation and right censoring model", Journal of statistical Theory and Methods, 6, pp. 65-76, 1995.
  5. J. H. Lim and Park, D. H., "A family of tests for trend change in mean residual life", Statistical Planning and Inference, 29, pp. 99-110, 1998.
  6. J. K. Ghorai, and Rejtwo, L., "Estimation of mean residual life with censored data under the proportional hazard model", Comm. Statist. A-Theory Meth., 16(7), pp. 2097-2114, 1987. https://doi.org/10.1080/03610928708829492
  7. M .H. Na, "A new UDB-MRL test with unknown change point", Korean quality management, 30(3), pp. 195-202, 2002.
  8. M. Asadi and Ebrahimi, N., "Residual entropy and its characterizations in terms of hazard function and mean residual life function", Statistics & Probability Letters, 49(3), pp. 263-269, 2000. https://doi.org/10.1016/S0167-7152(00)00056-0
  9. M. C. Bhattacharjee and Krishnaji, N., "DFR and other heavy tail properties in modelling the distribution of land and some alternative measures of inequality", Proceedings of the Indian Statistical Institute Golden Jubilee International Conference, 1981.
  10. M. H. Na, and Kim, J. J., "A family of tests for trend change in mean residual life using censored data", International Journal of Reliability and Application, 1, pp. 39-47, 2000.
  11. M. Z. Anis, Basu, S. K., and Mitra, M., "Change point detection in mean residual life function", Indian Society for Probability and Statistics, 8, pp. 57-71, 2004.
  12. P. Chaubey and Sen, P. K., "Smooth estimation of mean residual life under random censoring", Institute of Mathematical Statistics, 1, pp. 35-49, 2008.
  13. P. Embrechts, Kluppelberg, C. and Mikosch, T., In: I. Karatzas and M. Yor, Editors, Modelling Extremal Events, Springer, Berlin, 1997.
  14. W. Zhao, and Elsayed, E., "Optimum accelerated life testing plans based on proportional mean residual life", Quality and Reliability Engineering International, 21, pp. 701-713, 2005. https://doi.org/10.1002/qre.709
  15. X. Hu, Kochar, S. C., Mukerjee, H. and Samniego, F., "Estimation of two ordered mean residual life functions", J. Statist. Plann. Inference, 107, pp. 321-341, 2002. https://doi.org/10.1016/S0378-3758(02)00261-6
  16. Y. Kumazawa, "A note on Estimator of Life Expectancy with Random Censoring", Biometrika, 74(3), pp. 655-658, 1987. https://doi.org/10.1093/biomet/74.3.655
  17. Y. P. Chaubey and Kochar, S. C., "Smooth estimation of stochastically ordered survival functions", J. Indian Statist. Assoc. 38, pp. 209-225, 2000.
  18. Y. P. Chaubey and Sen, P. K., "On smooth functional estimation under random censorship", In: A.P. Basu et al., Editors, Frontiers in Reliability, Series on Quality, Reliability and Engineering Statistics 4, World Scientific Publishing Co. Pvt. Ltd., Singapore, pp. 83-97, 1998.