Confidence intervals for the threshold parameter

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Abstract
Confidence intervals for the threshold parameter (guarantee-life ) are considered. The first k failure-times from a sample of size n are observed. Under the assumption that as n →∞ the first failure-time is attracted to the Weibull distribution, confidence intervals based on the observed range are constructed. It is shown that as k(k ≥ 2) increases the expected length of the confidence interval is substantially reduced. However, when k = 10 (or 20 in some cases) the expected length is near its minimum value.