The purpose of this dissertation is to study four statistical inference problems for the lifetime distribution based on censored Wiener degradation data. We first propose an effective method for collecting intermediate, non-failure threshold-crossing data from a highly reliable product and prove the asymptotic properties of our proposed estimators of the parameters for the inverse Gaussian lifetime distribution. A numerical study shows our method performs well as compared to two other traditional methods. As an alternative to the Kolmo-gorov-Smirnov test, we propose a model selection method and a goodness-of-fit test proce-dure to choose a better-fitted distribution to a censored lifetime dataset. We show our method has the same performance with traditional goodness-of-fit test by efficiency of Bahadur (1960). We obtain some sufficient conditions for the existence of an almost unbiased estima-tor (under the definition of Haldane) when an unbiased estimator does not exist under a gen-eral setting. We then demonstrate that some existing results in the Binomial case are special cases. Finally we show that, for the complete data case, unbiased estimators and almost unbi-ased estimators of the percentiles of the inverse Gaussian distribution do not exist, and, con-sequently, propose asymptotically unbiased estimators for complete and Type 2 censored sample cases.

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