Estimation of distribution functions using data from different environments

Suppose that when a unit operates in a certain environment, its lifetime has distribution G, and when the unit operates in another environment, its lifetime has a different distribution, say F. Moreover, suppose the unit is operated for a certain period of time in the first environment and is then transferred to the second environment. Thus we observe a censored lifetime in the first environment and a failure time of a "used" unit in the second environment. We propose an EM algorithm approach for obtaining a self-consistent estimator of F using observations from both environments. The case where failure times are subject to right censoring is considered as well. We also establish the maximum likelihood estimator of F when the unit is repairable. Application and simulation studies are presented to illustrate the methods derived.