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More on the mis‐specification of the shape parameter with Weibull‐to‐exponential transformation
Author(s) -
Xie Min,
Yang Zhenlin,
Gaudoin Olivier
Publication year - 2000
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/1099-1638(200007/08)16:4<281::aid-qre338>3.0.co;2-n
Subject(s) - weibull distribution , exponential function , transformation (genetics) , shape parameter , exponential distribution , reliability (semiconductor) , percentile , scale parameter , mathematics , statistics , weibull modulus , exponentiated weibull distribution , gamma distribution , power transform , reliability engineering , power (physics) , engineering , mathematical analysis , physics , discrete mathematics , biochemistry , chemistry , quantum mechanics , gene , consistency (knowledge bases)
When lifetimes follow Weibull distribution with known shape parameter, a simple power transformation could be used to transform the data to the case of exponential distribution, which is much easier to analyze. Usually, the shape parameter cannot be known exactly and it is important to investigate the effect of mis‐specification of this parameter. In a recent article, it was suggested that the Weibull‐to‐exponential transformation approach should not be used as the confidence interval for the scale parameter has very poor statistical property. However, it would be of interest to study the use of Weibull‐to‐exponential transformation when the mean time to failure or reliability is to be estimated, which is a more common question. In this paper, the effect of mis‐specification of Weibull shape parameters on these quantities is investigated. For reliability‐related quantities such as mean time to failure, percentile lifetime and mission reliability, the Weibull‐to‐exponential transformation approach is generally acceptable. For the cases when the data are highly censored or when small tail probability is concerned, further studies are needed, but these are known to be difficult statistical problems for which there are no standard solutions. Copyright © 2000 John Wiley & Sons, Ltd.