Interval censored lifetime data arise when individuals in a study are inspected intermittently so that a lifetime is observed to lie between two successive times. In settings where only these two times are available, methods exist for nonparametric or parametric estimation of lifetime distributions. However, there has been virtually no discussion of how inspection processes may be estimated or identified. Such estimates are needed if one is to generate interval-censored data by simulation. In this study, the interval censoring and its importance are briefly defined. The existing methods of determination of distribution function and survivor function under interval censoring are reviewed. The concept of adjacency probability is discussed and calculated. This study identifies which aspects of an independent inspection process are estimable from interval censored data, and shows how to obtain nonparametric estimates. The results allow interval-censored data from any specified distribution to be generated. An omnibus goodness-of-fit test is introduced.