Bayes Estimation of Reliability for the Inverse Gaussian Model

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Abstract
Estimation of the reliability function is considered for the inverse Gaussian distribution. When the mean lifetime μ is known, the Jeffreys vague prior and the natural conjugate prior for λ easily yield Bayes estimators of reliability for squared-error loss. If both μ and λ are unknown, the Bayes solution for reliability in a compact form is extremely difficult. In this case a modified estimator of reliability can be used which is based on the Bayes estimator obtained for μ known. The modified estimator is simpler to calculate than the MVUE. Computer simulations indicate that it is more conservative than either the MVUE or the MLE for small mission times, but performs better than the MLE and MVUE for large times.