The Parametric Failure Time Models

Abstract

Parametric failure time distributions have been widely used in engineering but are new in demography. For example, a failure time model represents an attempt to describe mathematically the length of a first marriage, or duration at a certain parity before progressing to the next. The literature on survival models discussed in the previous chapter shows that there are many causes that affect either individually or collectively the experience of a certain event at a particular time point in the life cycle. It is not always possible to pinpoint all of these causes and mathematically account for all of them. Therefore, the choice of a particular failure time distribution to describe the process remains an art. In real time applications the choice of the hazards function λ(x) is facilitated by considering three general types of failures recognized as having time dependence. The first one, called the initial failure, manifests itself shortly after t = 0 and gradually begins to decrease during the initial period. The second one is called failure by chance, and the third is wearout failure. The famous U curve of human mortality is a clear model for the above description. In general, each specific form of the hazard function leads to a specific survival distribution.