More on the mis-specification of the shape parameter with Weibull-to-exponential transformation

When lifetimes follow Weibull distribution with known shape parameter, a si mple power transformation could be used to transform the data to the case o f exponential distribution, which is much easier to analyze. Usually the sh ape parameter cannot be known exactly and it is important to investigate th e effect of mis-specification of this parameter. In a recent article, it wa s suggested that the Weibull-to-exponential transformation approach should not be used as the confidence interval for the scale parameter has very poo r statistical property. However, it would be of interest to study the use o f Weibull-to-exponential transformation when the mean time to failure or re liability is to be estimated, which is a more common question. In this pape r, the effect of mis-specification of Weibull shape parameters on these qua ntities is investigated. For reliability-related quantities such as mean ti me 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 concern ed, further studies are needed, but these are known to be difficult statist ical problems for which there are no standard solutions. Copyright (C) 2000 John Wiley & Sons, Ltd.