This thesis focuses on the analysis of repairable systems with a bathtub-shaped failure intensity function, specifically using a modified Log-normal Weibull distribution. It proposes an optimal preventive maintenance policy under the assumption of minimal repair. The study addresses the challenge of modeling failure rates that exhibit three distinct phases: early failure (infant mortality), useful life, and wear-out. Traditional models like the power law and log-linear processes are insufficient for this purpose, as they cannot capture the bathtub shape with a flat useful life phase. The research adapts the Log-normal Weibull modified distribution to create a non-homogeneous Poisson process (NHPP) capable of modeling such failure rates. It also develops an optimal preventive maintenance strategy based on this NHPP model. The study includes simulation experiments, parameter estimation, and performance evaluation using real-world data. The results demonstrate the effectiveness of the proposed NHPP model in accurately fitting bathtub-shaped failure data and provide a basis for optimal maintenance policies. The work contributes to the field of reliability engineering by offering a flexible and accurate method for modeling and maintaining repairable systems with complex failure patterns.This thesis focuses on the analysis of repairable systems with a bathtub-shaped failure intensity function, specifically using a modified Log-normal Weibull distribution. It proposes an optimal preventive maintenance policy under the assumption of minimal repair. The study addresses the challenge of modeling failure rates that exhibit three distinct phases: early failure (infant mortality), useful life, and wear-out. Traditional models like the power law and log-linear processes are insufficient for this purpose, as they cannot capture the bathtub shape with a flat useful life phase. The research adapts the Log-normal Weibull modified distribution to create a non-homogeneous Poisson process (NHPP) capable of modeling such failure rates. It also develops an optimal preventive maintenance strategy based on this NHPP model. The study includes simulation experiments, parameter estimation, and performance evaluation using real-world data. The results demonstrate the effectiveness of the proposed NHPP model in accurately fitting bathtub-shaped failure data and provide a basis for optimal maintenance policies. The work contributes to the field of reliability engineering by offering a flexible and accurate method for modeling and maintaining repairable systems with complex failure patterns.