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.

翻译：具有非单调风险率函数$\hspace{0.12cm}$的寿命模型在工程和寿命数据分析中有广泛应用。可靠性文献中存在多种浴盆形失效率模型。Kavya和Manoharan（2021）提出了一种称为KM变换的新变换，该变换在可靠性和寿命数据分析中更为有用。幂广义化技术是处理部件串联连接系统的最佳方法，其中部件的分布是任意寿命模型的KM变换。本文提出了一种新的寿命模型——非单调失效率分布的幂广义KM变换（PGKM），该模型在参数取不同值时，风险率函数表现出单调和非单调行为。我们推导了所提分布的矩、矩生成函数、特征函数、分位数、熵等。得到了最小值和最大值的分布。通过极大似然方法对分布参数进行估计。通过模拟研究验证了极大似然估计量（MLE）的有效性。给出了三组真实数据的分析结果。