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The Exponentiated Weibull Family: A Reanalysis of the Bus-Motor-Failure Data

Govind S. Mudholkar, Deo Kumar Srivastava and Marshall Freimer
Technometrics
Vol. 37, No. 4 (Nov., 1995), pp. 436-445
DOI: 10.2307/1269735
Stable URL: http://www.jstor.org/stable/1269735
Page Count: 10
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The Exponentiated Weibull Family: A Reanalysis of the Bus-Motor-Failure Data
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Abstract

The Weibull family with survival function exp{-(y/σ)α}, for α > 0 and y ≥ 0, is generalized by introducing an additional shape parameter θ. The space of shape parameters α > 0 and θ > 0 can be divided by boundary line α = 1 and curve αθ = 1 into four regions over which the hazard function is, respectively, increasing, bathtub-shaped, decreasing, and unimodal. The new family is suitable for modeling data that indicate nonmonotone hazard rates and can be adopted for testing goodness of fit of Weibull as a submodel. The usefulness and flexibility of the family is illustrated by reanalyzing five classical data sets on bus-motor failures from Davis that are typical of data in repair-reuse situations and Efron's data pertaining to a head-and-neck-cancer clinical trial. These illustrative data involve censoring and indicate bathtub, unimodal, and increasing but possibly non-Weibull hazard-shape models.

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