Journal of Applied Reliability (한국신뢰성학회지:신뢰성응용연구)

The Korean Reliability Society (한국신뢰성학회)
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Estimation and Demonstration Test Plan for Availability with Weibull Lifetime and Lognormal Repair Time

와이블 수명분포와 대수정규 수리시간분포 하에서 가용도의 추정과 실증시험계획

  • Seo, Sun-Keun (Dept. of Industrial & Management Systems Engineering, Dong-A University)
  • 서순근 (동아대학교 산업경영공학과)
  • Received : 2013.11.18
  • Accepted : 2014.03.14
  • Published : 2014.03.25
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Abstract

One important measure of performance for a repairable system is steady-state availability. In this paper, a method to estimate and establish confidence interval for the steady-state availability under Weibull lifetime and lognormal repair time distributions is proposed. Also, bias and mean squared error of a point estimator for an availability are investigated. In addition, a procedure to derive the sample size and critical value for availability demonstration test is presented and illustrated with a numerical example.

Keywords

References

  1. Ananda, M. M. A. (2003), "Confidence Intervals for Steady State Availability of a System with Exponential Operating Time and Lognormal Repair Time, Applied Mathematics and Computation, Vol. 137, 499-509. https://doi.org/10.1016/S0096-3003(02)00155-8
  2. Ananda, M. M. A. and Gamage, J. (2004), "On Steady State Availability of a System with Lognormal Repair Time," Applied Mathematics and Computation, Vol. 150, 409-416. https://doi.org/10.1016/S0096-3003(03)00281-9
  3. Cabuk, S. (1986), "Simple Test of Hypotheses on System Availability and Mean Time to Repair," IEEE Transactions Reliability, Vol. 35, 581-583. https://doi.org/10.1109/TR.1986.4335552
  4. Chandrasekhar P. R. and Natarajan, R. (1996), "Confidence Limits for Steady-State Availability of Systems with a Mixture of exponential and Gamma Operating Time and Lognormal Repair Time," Microelectronics Reliability, Vol. 36, 1303-1304. https://doi.org/10.1016/0026-2714(95)00165-4
  5. Chandrasekhar, P. and Natarajan, R. (1997), "Confidence Limits for Steady State Availability of Systems with Lognormal Operating Time and Inverse Gaussian Repair Time," Microelectronics Reliability, Vol. 37, 969-971. https://doi.org/10.1016/S0026-2714(96)00116-3
  6. Chandrasekhar, P., Natarajan, R. and Sujatha (1994), "Confidence Limits for Steady State Availability of Systems," Microelectronics Reliability, Vol. 34, 1365-1367. https://doi.org/10.1016/0026-2714(94)90151-1
  7. Ebeling C. E. (2005), An Introduction to Reliability and Maintainability Engineering, 2nd ed., Waveland Press, USA.
  8. Gray, H. and Lewis, T. (1967), "A Confidence Interval for the Availability Ratio," Technometrics, Vol. 9, 465-471. https://doi.org/10.1080/00401706.1967.10490489
  9. Gray, H. and Schucany, W. (1969), "Lower Confidence Limits for Availability Assuming Lognormally Distributed Repair Times," IEEE Transactions Reliability, Vol. 18, 157-162.
  10. Guo, H., Liao, H., Gerokostopoulos, A., and Mettas, A. (2011), "Design of Reliability Demonstration Testing for Repairable Systems," 2011 Proceedings of the Reliability and Maintainability Symposium, 1-6.
  11. Krishna, H. and Sharma, K. K. (1995), "Inferences on Availability Ratio," Microelectronics Reliability, Vol. 35, 105-108. https://doi.org/10.1016/0026-2714(94)00050-X
  12. Lu, M. and Mi, J. (2011), "Statistical Inference about Availability of System with Gamma Lifetime and Repair Time," International Journal of Reliability, Quality and Safety Engineering, Vol. 18, 1-24. https://doi.org/10.1142/S0218539311004007
  13. Maplesoft (2011), $Maple^{TM}$ 15, Maplesoft, Waterloo, Canada.
  14. Masters, B. and Lewis, T. (1987), "A Note on the Confidence Interval for the Availability Ratio," Microelectronics Reliability, Vol. 27, 487-492. https://doi.org/10.1016/0026-2714(87)90467-7
  15. Masters, B., Lewis, T. and Kolarik, W. (1992), "A Confidence Interval for the Availability Ratio for the Systems with Weibull Operating Time and Lognormal Repair Time," Microelectronics Reliability, Vol. 32, 89-99. https://doi.org/10.1016/0026-2714(92)90089-4
  16. Singh, V. P. and Swaminathan, S. (2002), "Sample Sizes for System Availability," 2002 Proceedings of the Reliability and Maintainability Symposium, 51-55.
  17. Thompson, M .(1966), "Lower Confidence Limits and a Test of Hypotheses for System Availability," IEEE Transactions Reliability, Vol. 15, 32-36.
  18. Wang, W., and Kececioglu, D. B. (2000), "Confidence limits on the Inherent Availability of Equipment." 2000 Proceedings of the Reliability and Maintainability Symposium, 162-167.
  19. Usher, J. H., and Taylor, G. D. (2006), "Availability Demonstration Testing," Quality and Reliability Engineering International, Vol. 22, 473-479. https://doi.org/10.1002/qre.722
  20. Weerahandi, S. (1993), "Generalized Confidence Intervals," Journal of the American Statistical Association, Vol. 88, 899-905. https://doi.org/10.1080/01621459.1993.10476355