The quality performance of many vital systems depends on how long the units are performing; hence, research works started focusing on increasing the reliability of systems while taking into consideration that many factors may cause the failures of operating systems. In this study, the combination of a parametric generalized linear failure rate distribution model and an adaptive progressive Type-II censoring scheme for practical purposes is explored. A comprehensive investigation is performed on the risk factors that cause failure and determines which of the factors has a more harmful effect on the units. A lifetime experiment is performed under the condition of an adaptive progressive Type-II censoring scheme to obtain observations as a result of the competing factors of failures. The obtained observations are assumed to follow a three-parameter generalized linear failure rate distribution and are assumed to be competing to cause failure. Two statistical inference methods are employed for estimating this model’s parameters: the frequentist maximum likelihood method and the Bayesian approach. Our model’s validity is demonstrated through extensive simulations and real data applications in the medical and electrical engineering fields.

This paper addresses a fundamental challenge in statistical radar detection systems: optimizing the trade-off between the probability of a false alarm ($P_{FA}$) and the probability of a miss ($P_M$). These two metrics are inversely related and critical for performance evaluation. Traditional detection approaches often enhance one aspect at the expense of the other, limiting their practical applicability. To overcome this limitation, a fuzzy hypothesis testing framework is introduced that improves decision making under uncertainty by incorporating both crisp and fuzzy data representations. The methodology is divided into three phases. In the first phase, we reduce the probability of false alarm $P_{FA}$ while maintaining a constant probability of miss $P_M$ using crisp data characterized by deterministic values and classical statistical thresholds. In the second phase, the inverse scenario is considered: minimizing $P_M$ while keeping $P_{FA}$ fixed. This is achieved through parameter tuning and refined threshold calibration. In the third phase, a strategy is developed to simultaneously enhance both $P_{FA}$ and $P_M$, despite their inverse correlation, by adopting adaptive decision rules. To further strengthen system adaptability, fuzzy data are introduced, which effectively model imprecision and ambiguity. This enhances robustness, particularly in scenarios where rapid and accurate classification is essential. The proposed methods are validated through both real and synthetic simulations of radar measurements, demonstrating their ability to enhance detection reliability across diverse conditions. The findings confirm the applicability of fuzzy hypothesis testing for modern radar systems in both civilian and military contexts, providing a statistically sound and operationally applicable approach for reducing detection errors and optimizing system performance.

Dams are essential infrastructure for managing water resources and providing entry to clean water for human needs. However, the construction and maintenance of dams require careful consideration of their reliability and safety, specifically in the event of extreme weather conditions such as heavy rainfall or flooding. In this study, the stress-strength model provides a useful framework for evaluating the reliability of dams and their ability to cope with external stresses such as water pressure, earthquake activity, and erosion. The Shasta reservoir in the United States is a prime example of a dam that requires regular assessment of its reliability to guarantee the safety of communities and infrastructure. The Gumbel Type II distribution has been suggested as a suitable model for fitting the collected data on the stress and strength of the reservoir behind the Shasta dam. Both classical and Bayesian approaches have been used to estimate the reliability function under the multi-component stress-strength model, and Monte Carlo simulation has been employed for parameter estimation. In addition, some measures of goodness-of-fit are employed to examine the suitability of the suggested model.

Accelerated life tests are usually applied to obtain quick failures of components that may have high reliability. In this research, a comparative statistical study will be conducted between two hydroxylated fullerenes, ${\mathrm{C}}_{60}{\left(\mathrm{OH}\right)}_{29}$ and ${\mathrm{Sc}}_3\mathrm{N}@{\mathrm{C}}_{80}{\left(\mathrm{OH}\right)}_{18}$, to determine which one is more preferable and has the potential to be more applicable in the field of industrial engineering. Some experimental studies showed that ${\mathrm{Sc}}_3\mathrm{N}@{\mathrm{C}}_{80}{\left(\mathrm{OH}\right)}_{18}$ is better than ${\mathrm{C}}_{60}{\left(\mathrm{OH}\right)}_{29}$ in terms of physical and chemical properties. This statistical study confirms the experimental results through some statistical inference methods, such as Bayesian estimation.