Dr Mohanty - I believe "bathtub shaped" failure means a distribution with high early failure, then a relatively long period of low failure risk, then increased frequency of failure again at the high end.
This is similar to general population life expectancy in the absence of famine or war, relatively high mortality rates in the first few years of life through adolescence, then a fairly long floor during young - middle adulthood where mortality risk is low, then increased mortality in the elderly.
Weibul distribution can be used to fit bathtub shaped failure for parametric survival analysis. I think Klein and Moschberger discuss this (though hardly "latest" research) in their survival analysis text.
its a standard survival analysis text, most of the focus is on standard non/semi parametric approaches (ie Kaplan-Meier / Cox models), but early on there is a good discussion around parametric models and model fitting as I recall.
Survival Analysis: Techniques for Censored and Truncated Data (Statistics for Biology and Health) Hardcover – March 10, 2005
by John P. Klein (Author), Melvin L. Moeschberger (Author)