Reliability estimation from field return data

In this article statistical inference for the failure time distribution of a product from ``field return data{''}, that records the time between the product being shipped and returned for repair or replacement, is described. The problem that is addressed is that the data are not failure times because they also include the time that it took to ship and install the product and then to return it to the manufacturer for repair or replacement. The inference attempts to infer the distribution of time to failure (that is, from installation to failure) from the data when in addition there are separate data on the times from shipping to installation, and from failure to return. The method is illustrated with data from units installed in a telecommunications network.