A new lifetime model, named the Modi linear failure rate distribution, is suggested. This flexible model is capable of accommodating a wide range of hazard rate shapes, including decreasing, increasing, bathtub, upside-down bathtub, and modified bathtub forms, making it particularly suitable for modeling diverse survival and reliability data. Our proposed model contains the Modi exponential distribution and the Modi Rayleigh distribution as sub-models. Numerous mathematical and reliability properties are derived, including the $r^{th}$ moment, moment generating function, $r^{th}$ conditional moment, quantile function, order statistics, mean deviations, Rényi entropy, and reliability function. The method of maximum likelihood is employed to estimate the model parameters. Monte Carlo simulations are presented to examine how these estimators perform. The superior fit of our newly introduced model is proved through two real-world survival data sets.

翻译：本文提出了一种新的寿命模型，称为修正线性失效率分布。该灵活模型能够适应多种失效率形态，包括递减型、递增型、浴盆型、倒浴盆型及修正浴盆型，特别适用于对多样化的生存与可靠性数据进行建模。我们所提出的模型包含修正指数分布和修正瑞利分布作为其子模型。本文推导了该模型的多种数学与可靠性性质，包括$r^{th}$阶矩、矩母函数、$r^{th}$阶条件矩、分位数函数、顺序统计量、平均偏差、Rényi熵以及可靠性函数。采用最大似然法对模型参数进行估计，并通过蒙特卡洛模拟检验估计量的性能。利用两个真实世界生存数据集，证明了新引入模型具有优越的拟合能力。