"Bayesian Statistical Inference for a Mixture of Two Independent Generalized Exponential Distributions"

Abstract

The statistical analysis of what are variously referred to as lifetime, survival time or failure time data is an important topic in many areas, including the biomedical, engineering, industry and social sciences. Applications of lifetime distribution methodology range from investigations of the durability of manufactured items to studies of human diseases and their treatment. Some methods of dealing with lifetime data are quite old, but starting about 1970 the field expanded rapidly with respect to methodology, theory and fields of application. Software packages for lifetime data analysis have been widely available since 1980, with the frequent appearance of new features and packages.

In order to obtain information about a particular lifetime distribution F(t) for an item (component I system), it is often necessary to carry out a life test where n identical, numbered items are activated in order to record their lifetimes. If the test is allowed to run until all the n items have failed and the lifetimes are recorded, the data set thus obtained is said to be complete.

Often we have to be satisfied with incomplete data sets. This may be because it is impractical or too expensive to wait until all items have failed, or because individual items are "lost" for one reason or another. For example, individuals in a clinical trial may drop out of the study, or the study may have to be terminated for lack of funds. In an industrial experiment, units may break accidentally. There are, however, many situations in which the removal of units prior to failure is pre-planned. In such situations the data set is said to be censored