Ordered and censored lifetime data in reliability: An illustrative review

The present review provides a survey on basic models of ordered data and censoring mechanisms with a focus on lifetime data, failure data, and reliability applications. Throughout, illustrations of the data generation process as well as of the censoring mechanisms are used to visualize these procedures. By example we present basic results assuming a life testing model with independent and identically distributed measurements and focus on selected inferential results for exponentially distributed lifetimes. In particular, we aim to illustrate similarities between the models as well as to highlight some interesting exact statistical results. It is not intended to survey all possible model assumptions, probabilistic results, and used inferential methods used in this framework. For this purpose as well as for further reading, we provide an extensive bibliography.