Pathological behaviors of fisher confidence bounds for Weibull distribution

The Weibull distribution is widely used in reliability engineering. To estimate its parameters and associated reliability indices, the maximum likelihood (ML) approach is often employed, and the associated Fisher information matrix is used to obtain the confidence bounds on the reliability indices that are of interest. The estimates and the confidence bounds usually behave similarly in terms of monotonic and asymptotic properties. However, the confidence bounds may behave differently under certain circumstances. As a result, the Fisher matrix approach may not always be preferred in obtaining the desired confidence bounds. This paper provides some properties of Fisher confidence bounds for the Weibull distribution. These properties can be used as guidelines when implementing the ML approach and Fisher information matrix to analyze failure time data and plan life tests.