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Reliability properties of generalized mixtures of Weibull distributions with a common shape parameter |
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| Authors: | M Franco JM Vivo |
| Institution: | a Department of Statistics and Operations Research, University of Murcia, 30100 Murcia, Spain b Department of Quantitative Methods for Economy, University of Murcia, 30100 Murcia, Spain c Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1 |
| Abstract: | Weibull mixtures have been considered in many applied problems, and they have also been generalized by allowing negative mixing weights. In this paper, we study the classification of the aging properties of generalized mixtures of two or three Weibull distributions in terms of the mixing weights, scale parameters and a common shape parameter, which extends the cases of exponential or Rayleigh distributions. We apply these general results to classify the aging properties of the minimum and maximum lifetimes of two-component systems whose component lifetimes follow one of the known bivariate Weibull distributions. |
| Keywords: | Generalized mixtures Bivariate Weibull distributions Failure rate Log-concavity Series systems Parallel systems Aging properties |
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