Reliability Estimation in Life Testing in the Presence of an Outlier Observation

The behavior of R̂_t, the uniformly minimum variance unbiased estimator (umvne) of the reliability function for the one-parameter exponential family, is discussed when an outlier observation is present. Bounds of E(R̂_t∣α) and MSE(R̂_t∣α) have been obtained and a new estimator R_t* is proposed, where α reflects the “outlier effect on the scale” parameter. A “semi-Bayesian” approach is discussed when α is treated as a random variable with a Beta-type prior. A similar solution, when δ reflects the “outlier effect of the location” has been obtained.