Introduction and Survey of Literature

The failure rate of an item in life testing studies is categorized as constant failure rate
(CFR), Increasing failure rate (IFR) and decreasing failure rate (DFR).IFR and DFR
are known as monotone failure rates. A combination of CFR, IFR and DFR over the
range of life time of the random variable is known as Bath-tub failure rate. In
Biological and engineering sciences, Bath-tub failure rate is used to handle the
reliability analysis of the data under consideration. To construct a model for such
type of data, the generalized gamma of Stacy (1962), discrimination among some
parametric models of Prentice (1975), families of probability models of Gaver and
Acard (1979) and a three parameter family proposed by Hjorth (1980) have been
adopted. Rajarshi and Rajarshi (1988) has given a reasonable comprehensive
narration of the models for the Bath-tub shaped failure rates, when the life time
experiment is considered for censoring then the above mentioned models are not
suitable for statistical inferential procedures.