Communications for Statistical Applications and Methods

  • 제18권2호
  • /
  • Pages.201-211
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  • 2011
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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A Note on the Efficiency Based Reliability Measures for Heterogeneous Populations

  • Cha, Ji-Hwan (Department of Statistics, Ewha Womans University)
  • Received : 20101000
  • Accepted : 20110200
  • Published : 2011.03.31
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Abstract

In many cases, populations in the real world are composed of different subpopulations. Furthermore, in addition to the heterogeneity in the lifetimes of items, there also could be the heterogeneity in the efficiency or performance of items. In this case, the reliability measures should be defined in a different way. In this article, we consider the mixture of stochastically ordered subpopulations. Efficiency based reliability measures are defined when the performance of items in the subpopulations has different levels. Discrete and continuous mixing models are studied. The concept of the association between the lifetime and the performance of items in subpopulations is defined. It is shown that the consideration of efficiency can change the shape of the mixture failure rate dramatically especially when the lifetime and the performance of items in subpopulations are negatively associated. Furthermore, the modelling method proposed in this paper is applied to the case when the stress levels of the operating environment of items are different.

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References

  1. Block, H.W., Savits, T. H. andWondmagegnehu, E. T. (2003). Mixtures of distributions with increasing linear failure rates, Journal of Applied Probability, 40, 485–504.
  2. Finkelstein, M. S. (2008). Failure Rate Modelling for Reliability and Risk, Springer, London.
  3. Gupta, R. C. and Warren, R. (2001). Determination of change points of nonmonotonic failure rates, Communications in Statistics-Theory and Methods, 30, 1903–1920. https://doi.org/10.1081/STA-100105704
  4. Jensen, F. and Petersen, N. E. (1982). Burn-in, John Wiley, New York.
  5. Jiang, R. and Murthy, D. N. P. (1995). Modelling failure rate by mixture of two Weibull distributions. IEEE Transactions on Reliability, 44, 477-488. https://doi.org/10.1109/24.406588
  6. Meeker,W. Q. and Escobar, L. A. (1993). A review of recent research and current issues of accelerated testing, International Statistical Review, 61, 147–168.
  7. Navarro, J. and Hernandez, P. J. (2004). How to obtain bathtub-shaped failure rate models from normal mixtures, Probability in the Engineering and Informational Sciences, 18, 511–531.
  8. Nelson, W. (1990). Accelerated Testing: Statistical Models, Test Plans, and Data Analysis, John Wiley & Sons Inc, New York.