Estimating distribution functions from partially observed samples

Suppose that some components are initially operated in a certain condition and then switched to operating in a different condition. Working hours of the components in condition 1 and condition 2 are respectively observed. Of interest is the lifetime distribution F of the component in the second condition only, i.e., the distribution without the prior exposure to the first condition. In this paper, we propose a method to transform the lifetime obtained in condition 1 to an equivalent lifetime in condition 2 and then use the transformed data to estimate F. Both parametric and nonparametric approaches each with complete and censored data are discussed. Numerical studies are presented to investigate the performance of the method.