This article proposed a flexible three-parameter distribution known as the modified Chen distribution (MCD). The MCD is capable of modeling failure rates with both monotonic and non-monotonic behaviors, including the bathtub curve commonly used to represent device performance in reliability engineering. We examined its statistical properties, such as moments, mean time to failure, mean residual life, Rényi entropy, and order statistics. Model parameters, along with survival and hazard functions, were estimated by utilizing maximum likelihood estimators and two types of bootstrap confidence intervals. Bayesian estimates of the model parameters, along with the survival and hazard functions and their corresponding credible intervals, were derived via the Markov chain Monte Carlo method under balanced squared error loss, balanced linear-exponential loss, and balanced general entropy loss. We also provided a simulated dataset analysis for illustration. Furthermore, the MCD's performance was compared with other popular distributions across two well-known failure time datasets. The findings suggested that the MCD offered the best fit for these datasets, highlighting its potential applicability to real-world problems and its suitability as a model for analyzing and predicting device failure times.

The proposed article introduces a novel three-parameter lifetime model called an exponentiated extended extreme-value (EEEV) distribution model. The EEEV distribution is characterized by increasing or bathtub-shaped hazard rates, which can be advantageous in the context of reliability. Various statistical properties of the distribution have been derived. The article discusses four estimation methods, namely, maximum likelihood, least squares, weighted least squares, and Cramér-von Mises, for EEEV distribution parameter estimation. A simulation study was carried out to examine the performance of the new model estimators based on the four estimation methods by using the average bias, mean squared errors, relative absolute biases, and root mean square error. The flexibility and significance of the EEEV distribution are demonstrated by analyzing three real-world datasets from the fields of medicine and engineering. The EEEV distribution exhibits high adaptability and outperforms several well-known statistical models in terms of performance.

In this study, I introduce a new four-parameter lifetime model, termed the flexible exponential power–Weibull (FEPW) distribution, developed by combining the exponential power and Weibull distributions to enhance modeling capability for a wide range of reliability data. The proposed distribution exhibited considerable flexibility in capturing increasing, decreasing, bathtub-shaped, and J-shaped hazard rate behaviors, making it suitable for complex engineering systems. The hazard rate function of the FEPW distribution was derived, and its principal structural properties were rigorously established. Parameter estimation for the FEPW distribution was addressed through maximum likelihood estimation and Bayesian inference. For the Bayesian framework, I implemented Hamiltonian Monte Carlo with the No-U-Turn Sampler (HMC–NUTS) to achieve efficient posterior exploration and stable parameter uncertainty quantification. A detailed simulation study was conducted to evaluate estimator performance under various parameter settings and sample sizes, assessing bias and mean squared error. The practical utility of the proposed model was demonstrated through applications to real-world reliability datasets, where it consistently outperformed several competing lifetime models in terms of goodness-of-fit and information criteria. The results underscored the FEPW distribution as a flexible and useful model for modeling complex failure-time data in reliability engineering and related fields.