On the Estimation of Safe Life When the Underlying Life Distribution Is Weibull

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Abstract
The problem of estimating Y (1), the smallest of a future sample of k observations from the Weibull distribution, based on an observed sample from the same distribution, is considered. A conditional confidence interval solution is proposed for the estimation of Y (1). The results have direct application in reliability theory, where the time until the first failure in a group of k items in service provides a measure of assurance regarding the operation of the items.

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