In this article, reliability estimation for a system of multi-component stress-strength model is considered. Working under progressively censored samples is of great advantage over complete and usual censoring samples, therefore Type-II right progressive censored sample is selected. The lifetime of the components and the stress and strength components are following the power Lomax distribution. Consequently, the problem of point and interval estimation has been studied from different points of view. The maximum likelihood estimate and the maximum product spacing of reliability are evaluated. Also approximate confidence intervals are constructed using the Fisher information matrix. For the traditional methods, bootstrap confidence intervals are calculated. Bayesian estimation is obtained under the squared error and linear-exponential loss functions, where the numerical techniques such as Newton-Raphson and the Markov Chain Monte Carlo algorithm are implemented. For dependability, the largest posterior density credible intervals are generated. Simulations are used to compare the results of the proposed estimation methods, where it shows that the Bayesian estimation method of the reliability function is significantly better than the other methods. Finally, a real data of the water capacity of the Shasta reservoir is examined for illustration.

Dependent competing risks usually arise in modern reliability and survival studies, but remain under‑explored because of the mathematical and computational complexity they introduce. This paper developed a flexible inferential framework for systems based on mutually dependent failure causes when the lifetimes are governed by the proportional hazard Weibull (PHW) distribution. Data were collected through the generalized progressive hybrid censoring scheme (GPHCS), which reduced test duration while preserving information with a prefixed number of failures. From a computational perspective, the maximum likelihood estimators (MLEs) were derived via numerical optimization, such as the Newton-Raphson algorithm. To incorporate prior knowledge and quantify parameter uncertainty, Bayesian estimates were produced using conjugate gamma priors and a Metropolis within Gibbs sampler. Estimator performance was assessed through an extensive Monte Carlo simulation study. Results show that MLE and Bayesian procedures were unbiased, and Bayesian credible intervals were noticeably shorter than their asymptotic counterparts. The procedure was applied to a land-based surveillance radar data set in which the target loss risks are dependent. The fitted PHW model accurately captures the dynamics of radar return signals, and posterior analyses revealed how each covariate modulates detection reliability.

Continuous developments in unit interval distributions have shown effectiveness in modeling proportional data. However, challenges persist in diverse dispersion characteristics in real-world scenarios. This study introduces the unit logistic-exponential (ULE) distribution, a flexible probability model built upon the logistic-exponential distribution and designed for data confined to the unit interval. The statistical properties of the ULE distribution were studied, and parameter estimation through maximum likelihood estimation, Bayesian methods, maximum product spacings, and least squares estimates were conducted. A thorough simulation analysis using numerical techniques such as the quasi-Newton method and Markov chain Monte Carlo highlights the performance of the estimation methods, emphasizing their accuracy and reliability. The study reveals that the ULE distribution, paired with tools like randomized quantile and Cox-Snell residuals, provides robust assessments of goodness of fit, making it well-suited for real-world applications. Key findings demonstrate that the unit logistic-exponential distribution captures diverse data patterns effectively and improves reliability assessment in practical contexts. When applied to two real-world datasets—one from the medical field and the other from the economic sector—the ULE distribution consistently outperforms existing unit interval models, showcasing lower error rates and enhanced flexibility in tail behavior. These results underline the distribution's potential impact in areas requiring precise proportions modeling, ultimately supporting better decision-making and predictive analyses.

Accurate estimation and modeling of infant mortality rates are essential for public health planning and medical research, as they are influenced by a wide range of biological, environmental, and socio-economic factors. To capture the underlying failure patterns, we proposed the inverse power–modified Chris–Jerry (IPMCJ) distribution, a generalized lifetime model particularly suited for decreasing failure rates. Progressive censoring (PC) was incorporated to address the common challenge of incomplete data collection in mortality studies. The statistical properties of the IPMCJ model were studied in detail, and parameter estimation was conducted through maximum likelihood and Bayesian approaches. Bayesian inference was further explored under symmetric squared error and asymmetric linear exponential (LINEX) loss functions, supported by confidence and credible intervals constructed via bootstrap, asymptotic, and Markov chain Monte Carlo (MCMC) methods. The practical relevance of the IPMCJ model was demonstrated using two real infant mortality datasets, where it consistently outperformed ten competing distributions. Convergence was evaluated using maximum likelihood checks and standard Bayesian diagnostics. Model performance of the IPMCJ distribution was validated using (a) the nonparametric Kaplan-Meier estimator and (b) comparisons with the complete-sample analysis. Extensive simulation studies confirmed the robustness and accuracy of the proposed estimators. The results emphasized the value of combining PC with the IPMCJ distribution, offering an effective framework for analyzing infant mortality data and informing health policy decisions.