한국신뢰성학회지:신뢰성응용연구 (Journal of Applied Reliability)

  • 제18권3호
  • /
  • Pages.220-228
  • /
  • 2018
  • /
  • 1738-9895(pISSN)
  • /
  • 2733-8320(eISSN)
한국신뢰성학회 (The Korean Reliability Society)
권호 표지

Stochastic Properties of Life Distribution with Increasing Tail Failure Rate and Nonparametric Testing Procedure

  • Lim, Jae-Hak (Department of Business & Accounting, Hanbat National University) ;
  • Park, Dong Ho (Industry Academic Cooperation Foundation, Hallym University)
  • 투고 : 2018.07.22
  • 심사 : 2018.09.19
  • 발행 : 2018.09.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Purpose: The purpose of this study is to investigate the tail behavior of the life distribution which exhibits an increasing failure rate or other positive aging effects after a certain time point. Methods: We characterize the tail behavior of the life distribution with regard to certain reliability measures such as failure rate, mean residual life and reliability function and derive several stochastic properties regarding such life distributions. Also, utilizing an L-statistic and its asymptotic normality, we propose new nonparametric testing procedures which verify if the life distribution has an increasing tail failure rate. Results: We propose the IFR-Tail (Increasing Failure Rate in Tail), DMRL-Tail (Decreasing Mean Residual Life in Tail) and NBU-Tail (New Better than Used in Tail) classes, all of which represent the tail behavior of the life distribution. And we discuss some stochastic properties of these proposed classes. Also, we develop a new nonparametric test procedure for detecting the IFR-Tail class and discuss its relative efficiency to explore the power of the test. Conclusion: The results of our research could be utilized in the study of wide range of applications including the maintenance and warranty policy of the second-hand system.

키워드

참고문헌

  1. Shafiee, M., Finkelstein, M. and Chukova, S. (2011). "On optimal upgrade level for used products under given cost structures". Reliability Engineering and System Safety, Vol. 96, No. 2, pp. 286-291. https://doi.org/10.1016/j.ress.2010.07.008
  2. Kim, D. K., Lim, J. H. and Park, D. H. (2014). "Optimal maintenance level for second-hand product with periodic inspection schedule". Applied Stochastic Models in Business and Industry, Vol. 31, No. 3, pp. 349-359. https://doi.org/10.1002/asmb.2051
  3. Hollander, M. and Proschan, F. (1972). "Testing whether new is better than used". The Annals of Mathematical Statistic, Vol. 43, No. 4, pp. 1136-1146. https://doi.org/10.1214/aoms/1177692466
  4. Hollander, M., Park, D. H. and Proschan, F. (1986). "A class of life distribution for aging". Journal of American Statistics Association, Vol. 81, No. 393, pp. 91-95. https://doi.org/10.1080/01621459.1986.10478242
  5. Ahmad, I. A. (2005). "Statistical analysis of old age behavior". Journal of Statistical Planning and Inference, Vol. 129, No. 1-2, pp. 239-252. https://doi.org/10.1016/j.jspi.2004.06.050
  6. Alzaid, A. A. (1994). "Aging concepts for items of unknown age". Communications in Statistics-Stochastic Models, Vol. 10, No. 3, pp. 649-659. https://doi.org/10.1080/15326349408807314
  7. Ahmad, I. A. (1999). "Testing whether a life distribution is new better than used in tail". Journal of Nonparametric Statistics, Vol. 11, No. 1-3, pp. 319-335. https://doi.org/10.1080/10485259908832787
  8. Willmot, G. E. and Cai, J. (2000). "On classes of lifetime distributions with unknown age". Probability in the Engineering and Information Sciences, Vol. 14, No. 4, pp. 473-484. https://doi.org/10.1017/S0269964800144067
  9. Ahmad, I. A. (2004). "Some properties of classes of life distributions with unknown age". Statistics and Probability Letters, Vol. 69, No. 3, pp. 333-342. https://doi.org/10.1016/j.spl.2004.06.029
  10. Guess, F., Nam, K. H. and Park, D. H. (1998). "Failure rate and mean residual life with trend changes". Asia-Pacific Journal of Operations Research, Vol. 15, No. 2, pp. 239-244.
  11. Mitra, M. and Anis, M. Z. (2008). "An L-statistic approach to a test of exponentiality against IFR alternatives". Journal of Statistical Planning and Inference, Vol. 138, No. 10, pp. 3144-3148. https://doi.org/10.1016/j.jspi.2007.12.005
  12. Anis, M. Z. (2013). "A family of tests for exponentiality against IFR alternatives". Journal of Statistical Planning and Inference, Vol. 143, No. 8, pp. 1409-1415. https://doi.org/10.1016/j.jspi.2013.03.012
  13. Lim, J. H. and Park, D. (1998). "A family of tests for trend change in mean residual life". Communication in Statistics-Theory and Models, Vol. 27, No. 5, pp. 1163-1179. https://doi.org/10.1080/03610929808832151
  14. Joe, H. and Proschan, F. (1983). "Tests for properties of the percentile residual life function". Communications in Statistics-Theory Methods, Vol. 12, No. 10, pp. 1087-1119. https://doi.org/10.1080/03610928308828518