Lifetime distributions play a key role in statistical modeling, with extensive applications across biostatistics, reliability engineering, and survival analysis. This paper introduces a novel and flexible bivariate lifetime model, termed the Bi-variate Cubic Transmuted Weibull Distribution (BCTWD), which extends the transmuted Weibull framework proposed by Alsalafi et al. (2025) by incorporating a cubic transmutation mechanism to enhance modeling flexibility and capture complex dependence structures. Existing bivariate Weibull models cannot simultaneously accommodate flexible marginal tail behavior and complex dependence structures, limiting their applicability in scenarios with heterogeneous failure patterns. The theoretical foundations of the proposed BCTWD are rigorously developed, including its joint and marginal probability density and cumulative distribution functions, along with essential statistical and reliability properties. Parameter estimation is performed using both the Maximum Likelihood (ML) and Inference Functions for Margins (IFM) methods, whose performances are systematically evaluated through simulation experiments. The simulation outcomes indicate that the estimators are, For n=200, the maximum absolute bias for shape parameters are 0.048, and the maximum MSE is 0.29, indicating satisfactory finite-sample performance, particularly for the shape parameters under heavy-tailed scenarios. An empirical application to bilateral eye failure time data from a diabetic retinopathy study demonstrates the practical utility of the proposed model. Based on the maximum likelihood estimates and model selection criteria, including AIC, AICc, and BIC, the BCTWD achieves superior goodness-of-fit compared with the Bivariate Transmuted Weibull (BTW) and Bivariate Weibull (BW) distributions. While the BCTWD exhibits slightly greater parameter variability due to its added flexibility, it provides the most accurate representation of the data, confirming its effectiveness in modeling dependent lifetimes. Overall, the BCTWD enriches the family of multivariate lifetime distributions by offering enhanced adaptability and interpretability, making it a valuable tool for applications in reliability analysis, biostatistics, and survival modeling.
Alsalafi et al. (Wed,) studied this question.