A New Hybrid Class of Distributions: Model Characteristics and Stress–Strength Reliability Studies

Abstract

This study proposes a generalized family of distributions to enhance flexibility in modeling complex engineering and biomedical data. The framework unifies existing models and improves reliability analysis in both engineering and biomedical applications by capturing diverse system behaviors. We introduce a novel hybrid family of distributions that incorporates a flexible set of hybrid functions, enabling the extension of various existing distributions. Specifically, we present a three-parameter special member called the hybrid-Weibull–exponential (HWE) distribution. We derive several fundamental mathematical properties of this new family, including moments, random data generation processes, mean residual life (MRL) and its relationship with the failure rate function, and its related asymptotic behavior. Furthermore, we compute advanced information measures, such as extropy and cumulative residual entropy, and derive order statistics along with their asymptotic behaviors. Model identifiability is demonstrated numerically using the Kullback–Leibler divergence. Additionally, we perform a stress–strength (SS) reliability analysis of the HWE under two common scale parameters, supported by illustrative numerical evaluations. For parameter estimation, we adopt the maximum likelihood estimation (MLE) method in both density estimation and SS-parameter studies. The simulation results indicated that the MLE demonstrates consistency in both density and SS-parameter estimations, with the mean squared error of the MLEs decreasing as the sample size increases. Moreover, the average length of the confidence interval for the percentile and Student’s t-bootstrap for the SS-parameter becomes smaller with larger sample sizes, and the coverage probability progressively aligns with the nominal confidence level of 95%. To demonstrate the practical effectiveness of the hybrid family, we provide three real-world data applications in which the HWE distribution outperforms many existing Weibull-based models, as measured by AIC, BIC, CAIC, KS, Anderson–Darling, and Cramer–von Mises criteria. Furthermore, the HLW exhibits strong performance in SS-parameter analysis. Consequently, this hybrid family holds immense potential for modeling lifetime data and advancing reliability and survival analysis.