  Lifetime models with a non-monotone hazard rate $\hspace{0.12cm}$ function
have a wide range of applications in engineering and lifetime data analysis.
There are different bathtub shaped failure rate models that are available in
reliability literature. Kavya and Manoharan (2021) introduced a new
transformation called KM-transformation which was found to be more useful in
reliability and lifetime data analysis. Power generalization technique would be
the best approach to deal with a system whose components are connected in
series, in which the distribution of the component is KM-transformation of any
lifetime model. In this article, we introduce a new lifetime model, Power
Generalized KM-Transformation (PGKM) for Non-Monotone Failure Rate
Distribution, which shows monotone and non-monotone behavior for the hazard
rate function for different choices of values of parameters. We derive the
moments, moment generating function, characteristic function, quantiles,
entropy etc of the proposed distribution. Distributions of minimum and maximum
are obtained. Estimation of parameters of the distribution is performed via
maximum likelihood method. A simulation study is performed to validate the
maximum likelihood estimator (MLE). Analysis of three sets of real data are
given.
