Journal of Applied Reliability (한국신뢰성학회지:신뢰성응용연구)

The Korean Reliability Society (한국신뢰성학회)
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Lifetime Performance Index for Weibull Distribution: Estimation and Applications

와이블 분포를 따를 때 수명성능지수의 추정과 활용

  • Seo, Sun-Keun (Dept. of Industrial & Management Systems Engineering, Dong-A University)
  • 서순근 (동아대학교 산업경영공학과)
  • Received : 2013.08.13
  • Accepted : 2013.09.13
  • Published : 2013.09.25
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Abstract

Application areas for Lifetime Performance Index(LPI), a kind of process capability index to be frequently used as a means of measuring process performance are illustrated with examples. Statistical properties for maximum likelihood and unbiased estimators of LPI are evaluated and discussed under Weibull distribution with known shape parameter. Furthermore, guidelines for selecting an estimator of LPI are also presented.

Keywords

References

  1. 서순근(2011), 2단계 신뢰성 실증시험의 통계적 설계, 품질경영학회지, 39권, 2호, 313-319.
  2. Ahmadi, M. V., Doostparast, M., and Ahmadi, J.(2013a), "Estimating the Lifetime Performance Index with Weibull Distribution Based on Progressive First-Failure Censoring Scheme," Journal of Computational and Applied Mathematics, Vol. 239, 93-102. https://doi.org/10.1016/j.cam.2012.09.006
  3. Ahmadi, M. V., Doostparast, M., and Ahmadi, J.(2013b), "Statistical Inference for the Lifetime Performance Index Based on Generalised Order Statistics from Exponential Distribution," International Journal of Systems Science, to appear.
  4. Annis, M. Z.,(2008), "Basic Process Capability Indices: An Expository Review," International Statistical Review, Vol. 76, 347-367. https://doi.org/10.1111/j.1751-5823.2008.00060.x
  5. Hong, C-W., Wu, J-W., and Cheng, C-H.(2007), "Computational Procedure of Performance Assessment of Lifetime Index of Businesses for the Pareto Lifetime Model with the Right Type II Censored Sample," Applied Mathematics and Computation, Vol. 184, 336-350. https://doi.org/10.1016/j.amc.2006.05.199
  6. Hong, C-W., Lee, W-C., and Wu, J-W.(2012), "Computational Procedure of Performance Assessment of Lifetime Index of Products for the Weibull Distribution with the Progressive First-Failure-Censored Sampling Plan," Journal of Applied Mathematics, Vol. 2012, Article ID 717184, 13 pages.
  7. Jiang, R. and Murthy, D. N. P.(2011), "A Study of Weibull Shape Parameter: Properties and Significance," Reliability Engineering and System Safety, Vol. 96, 1619-1626. https://doi.org/10.1016/j.ress.2011.09.003
  8. Kane, V. E.(1986), "Process Capability Indices," Journal of Quality Technology, Vol. 18, 41-52.
  9. Lawless, J. E.(2003), Statistical Models and Methods for Lifetime Data, 2nd ed., John Wiley & Sons Inc., New York(USA).
  10. Lee, H-M., Lee, W-C., Lei, C-L., and Wu, J-W.(2011a), "Computational Procedure of Assessing Lifetime Performance Index of Weibull Lifetime Products with the Upper Record Values," Mathematics and Computers in Simulation, Vol. 81, 1177-1189. https://doi.org/10.1016/j.matcom.2010.11.004
  11. Lee, H-M., Wu, J-W., Lei, C-L., and Hung, W-L.(2011b), "Implementing Lifetime Performance Index of Products with Two-Parameter Exponential Distribution," International Journal of Systems Science, Vol. 42, 1305-1321. https://doi.org/10.1080/00207721.2010.494774
  12. Lee, W-C.(2011), "Inferences on the Lifetime Performance Index for Weibull Distribution Based on Censored Observations Using the Max p-Value Method," International Journal of Systems Science, Vol. 42, 931-937. https://doi.org/10.1080/00207720903260168
  13. Lee, W-C., Wu, J-W., and Hong, C-W.,(2009), "Assessing the Lifetime Performance Index for Exponential Distribution," Journal of Computational and Applied Mathematics, Vol. 231, 648-656. https://doi.org/10.1016/j.cam.2009.04.018
  14. Lee, W-C., Wu, J-W., and Lei, C-L.,(2010), "Evaluating the Lifetime Performance Index with the Exponential Distribution under Progressively Type II Right Censored Samples," Applied mathematical Modelling, Vol. 34, 1217-1224. https://doi.org/10.1016/j.apm.2009.08.013
  15. Tong, L-I., Chen, K. S., and Chen, H. T.(2002), "Statistical Testing for Assessing the Performance of Lifetime Index of Electronic Components with Exponential Distribution", International Journal of Quality & Reliability Management, Vol. 19, 812-824. https://doi.org/10.1108/02656710210434757
  16. Wu, J-W., Lee, H-M., and Lei, C-L.(2007), "Computational Testing Algorithmic Procedure of Assessment for Lifetime Performance Index of Products with Two-Parameter Exponential Distribution," Applied Mathematics and Computation, Vol. 190, 116-125. https://doi.org/10.1016/j.amc.2007.01.010
  17. Yum, B-J. and Kim, K-W.(2010), "A Bibliography of the Literature on Process Capability Indices," Quality and Reliability Engineering International, Vol. 27, 251-268.