A New Topp–Leone Juchez Distribution with Applications to Accelerated Life-Test and Aircraft Window-Glass Strength Data

This study introduces the Topp–Leone Juchez (TLJ) distribution, a flexible two-parameter lifetime model constructed from the one-parameter Juchez distribution through the Topp–Leone transformation. The proposed model provides additional shape and hazard-rate flexibility while remaining parsimonious. Several distributional and reliability properties are derived, including the survival and hazard functions, quantile function, moments, entropy measures, and stress–strength reliability. Classical and Bayesian estimation procedures are investigated, and their finite-sample performance is examined through Monte Carlo simulations. Two real-data applications involving accelerated life-test and aircraft window-glass strength data are also considered. The results show that the TLJ model provides competitive fits relative to several established lifetime distributions. For the aircraft window-glass data, the TLJ and Gamma models provide very similar empirical support, with an AIC difference of only 0.0858. Importantly, the TLJ model is not a nested extension of the Juchez distribution, since setting α=1 does not recover the original Juchez model. Overall, the results demonstrate the usefulness of the TLJ construction as a flexible alternative for lifetime-data analysis.