Modeling the Mixture of Lognormal, Gamma and Weibull Distributions for System Reliability Performance

This research develops a statistical framework for modeling system reliability using a mixture of Lognormal, Gamma, and Weibull distributions. The goal is to improve reliability estimation for complex systems exhibiting multiple failure modes. Data for the analysis is obtained from the UCI Machine Learning Repository, specifically the 'Simulated Data for Survival Modeling' dataset. Each distribution is fitted separately, and their mixture is then estimated using maximum likelihood methods. Comparative analyses are performed based on goodness-of-fit indices (AIC, BIC, log-likelihood) and reliability metrics such as mean time to failure (MTTF). Results demonstrate that the mixture model provides superior fit and predictive reliability over single distribution models.