Reliability Estimation For The Generalized Gamma Distribution And Robustness Of The Weibull Model
Two test statistics are suggested for discriminating between the exponential model and the more general Weibull or gamma models, and these are compared to some previously used test statistics by Monte Carlo methods. The results of estimating reliability under an exponential assumption when the true model is Weibull is also investigated. These results as well as the tests mentioned above indicate that the exponential model is often not adequate when the more general models hold. In contrast to this result it was found that the Weibull model was quite robust relative to the generalized gamma distribution with regard to reliability estimation. Some general pivotal function properties are presented for the maximum likelihood estimator of reliability for the generalized gamma distribution and similar results also hold for the Weibull procedure under a generalized gamma assumption. These results made a Monte Carlo study of this problem feasible. Since the maximum likelihood estimators are apparently ill-behaved for smaller sample sizes and since the Weibull model is robust it appears little is gained by using the generalized gamma distribution for samples of size less than 200 to 400. © 1971 Taylor and Francis Group, LLC.
H. W. Hager et al., "Reliability Estimation For The Generalized Gamma Distribution And Robustness Of The Weibull Model," Technometrics, vol. 13, no. 3, pp. 547 - 557, Taylor and Francis Group; Taylor and Francis; American Statistical Association, Jan 1971.
The definitive version is available at https://doi.org/10.1080/00401706.1971.10488817
Mathematics and Statistics
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01 Jan 1971