A new version of the three-parameter Weibull model, called the new extended Weibull (NEW), has been introduced in the literature to provide an increased or inverted bathtub failure rate. In a survival context, adaptive progressive Type-Ⅱ censoring encourages the statistical inference's efficiency and minimizes the overall testing period during a lifetime experiment. By gathering a NEW sample from the proposed strategy, both likelihood and Bayesian inferential evaluations for the NEW model parameters of life were derived. For each unknown subject, asymptotic confidence intervals by normality and the log-transformed-normality approximations were constructed. Given independent uniform and gamma density priors against squared-error and general-entropy loss functions, Bayesian point and credible estimations were created utilizing several Monte-Carlo Markov-Chain techniques. To appreciate the usefulness of the acquired estimators, a comprehensive simulation analysis was performed by offering different experimental scenarios. To examine the superiority of the proposed model and to exhibit the viability of the proposed approaches in real practice, a pair of data examples, one based on the strength (in gigapascal) of carbon fibers and the other based on the failure times of conductors, were analyzed and the results were observed.

When a researcher wants to perform a life-test comparison study of items made by two separate lines inside the same institution, joint censoring strategies are particularly important. In this paper, we present a new joint Type-Ⅰ hybrid censoring that enables an experimenter to stop the investigation as soon as a pre-specified number of failures or time is first achieved. In the context of newly censored data, the estimates of the unknown mean lifetimes of two different Rayleigh populations are acquired using maximum likelihood and Bayesian inferential techniques. The normality characteristic of classical estimators is used to offer asymptotic confidence interval bounds for each unknown parameter. Against gamma conjugate priors, the Bayes estimators and related credible intervals are gathered about symmetric and asymmetric loss functions. Since classical and Bayes estimators are acquired in closed form, simulation tests can be easily made to evaluate the effectiveness of the proposed methodologies. The efficiency of the suggested approaches is examined in terms of four metrics, namely: Root mean squared error, average relative absolute bias, average confidence length, and coverage probability. To demonstrate the applicability of the offered approaches to real events, two real applications employing data sets from the engineering area are analyzed. As a result, when the experimenter's primary goal is to complete the test as soon as the total number of failures or the threshold period is recorded, the numerical results reveal that the recommended strategy is adaptable and very helpful in completing the study.

This study introduces a reliability-based framework that quantifies perovskite solar cell (PSC) degradation by estimating the T80 lifetime (time to 80% of initial power conversion efficiency) from experimental aging data using exponential regression. The resulting failure times, collected under an adaptive progressive Type-Ⅱ censoring scheme, were analyzed using the Proportional Hazard Chen (PHC) distribution. This model accommodates increasing hazard rates characteristic of PSC aging mechanisms. Model parameters were estimated using maximum likelihood estimation (MLE) and Bayesian inference, enabling comprehensive reliability metrics including survival probability, hazard rate, and mean time to failure (MTTF). The procedure was validated using degradation data from PSCs with titanium dioxide and nickel oxide transport layers, supplemented by Solar Cell Capacitance Simulator (SCAPS). The empirical results show that the survival probability decreases from approximately 0.98 at 0.5 hours to below 0.02 at 17 hours, while the hazard rate increases from approximately 0.04 to above 0.75, confirming an accelerating degradation pattern. The Monte Carlo simulation study further demonstrates that both MLE and Bayesian approaches can estimate the PHC model effectively, with improved accuracy when the effective number of observed failures and the termination time increase. Bayesian inference provides more conservative long-term reliability and MTTF predictions under heavy censoring, making it useful for risk-aware lifetime assessment. Overall, the proposed framework provides a practical statistical tool for predicting, comparing, and benchmarking PSC lifetimes in photovoltaic reliability studies.

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.