Failure Rate Transform of the Weibull Variate and its Properties

The failure rate of a life time distribution has so for been studied in the time domsin. The present paper extends the failure rate transform in the frequency domain. For this purpose, the parent life time distribution has been taken as the Weibull distribution and different properties of the distribution of the failure rate transform have been presented including some characterisations of the Weibull distribution. Some comparative studies have also been made between the parent distribution and the failure rate transform distribution in respect of convex, star shaped and super additive orderings and expectation.