This thesis is concerned with the methods of estimating lifetime distribution for situations where some additional field data can be gathered after the warranty period. For satisfactory inference about parameters involved, it is desirable to incorporate these after-warranty data in the analysis. It is assumed that the after-warranty data are reported with probability $p_{1}$(＜1), while the warranty data with probability 1.
Field data with and without covariates are considered. For these two cases, general methods of obtaining maximum likelihood estimators and pseudo maximum likelihood estimators are outlined, their asymptotic properties are studied, and specific formulas for exponential or Weibull distribution are obtained. Numerical examples are given and simulation studies are performed to investigate the effects of reporting probabilities. An estimation procedure using the expectation-and-maximization(EM) algorithm is also proposed when the reporting probability is unknown.
