This paper introduces the Beta Linear Failure Rate Geometric (BLFRG) distribution, a flexible model that encompasses various well-known distributions as special cases, including the exponentiated linear failure rate geometric, linear failure rate geometric, linear failure rate, exponential geometric, Rayleigh geometric, Rayleigh, and exponential distributions. The BLFRG distribution generalizes the linear failure rate distribution and provides a broader framework for modeling lifetime data. The paper thoroughly investigates the model's properties, including its moments, conditional moments, deviations, Lorenz and Bonferroni curves, and entropy, offering a comprehensive understanding of its behavior. The paper also discusses the estimation methods for the model parameters. To demonstrate its practical utility, the BLFRG distribution is applied to real data examples, showcasing its effectiveness in capturing various patterns in lifetime data. The BLFRG distribution provides a versatile tool for reliability analysis and can be utilized in various applications involving lifetime data with different failure patterns.
This study focuses on the mean first exit time for a compound Poisson process characterized by positive jumps and an upper horizontal boundary. The compound Poisson process is an important model for events occurring at random intervals, where the size of each jump follows a specific distribution. The study derives an explicit formula for calculating the mean first exit time, which refers to the expected time it takes for the process to hit the upper boundary for the first time. This measure is crucial for applications where the time until a specific threshold is reached is of interest. Furthermore, an application of the derived formula is provided in the context of traffic accidents, where the first exit time can model the time until a traffic system reaches a critical congestion level or failure point. This approach offers valuable insights for understanding the dynamics of complex stochastic systems, with potential applications in risk management, transportation, and other fields that involve compound Poisson processes. The results demonstrate the utility of the derived formula in practical scenarios, highlighting the significance of first exit times in modelling real-world processes.
This paper introduces bivariate Weibull distributions derived from copula functions to model survival data, incorporating cure fraction, censored observations, and covariates. The study explores two copula functions: the FGM (Farlie-Gumbel-Morgenstern) copula and the Gumbel copula. These copulas are used to describe the dependence structure between two survival times while accounting for the cure fraction, a scenario where a certain proportion of subjects are assumed to be immune or never experience the event of interest. The analysis also addresses the presence of censored data, which occurs when the event of interest is not observed for some subjects within the study period. To estimate the model parameters, we adopt a Bayesian inference approach using standard Markov Chain Monte Carlo (MCMC) methods. The proposed methodology is applied to a medical dataset, illustrating its practical applicability in real-world scenarios. The results highlight the advantages of using copula-based bivariate Weibull models for survival data analysis, especially when dealing with complex data structures, including censoring and cure fractions. This approach provides a robust framework for modelling dependencies between survival times and offers a comprehensive method for parameter estimation under Bayesian inference. The findings suggest that the incorporation of copula functions into the bivariate Weibull model enhances its flexibility and ability to capture the inherent dependence between survival times in various medical and reliability studies.
Accelerated life testing (ALT) is crucial for evaluating high-reliability units, requiring effective goodness-of-fit (GOF) techniques to test the underlying lifetime distribution across multiple stress levels. However, challenges arise due to the need to combine failure times from different stress levels to assess the adequacy of a lifetime distribution. This paper introduces a modified version of Neyman’s smooth test, called the adapted extended Neyman’s smooth test (AENST), to address these challenges within the accelerated failure time (AFT) model framework. The AENST is designed to test both Weibull and exponential distributions under constant stress with complete sampling. To evaluate its performance, the AENST is compared with the conditional probability integral transformation test (CPITT) using a simulation study. The results indicate that the AENST outperforms the CPITT in terms of power, making it a recommended tool for testing AFT models. A real dataset is also provided to demonstrate the application of the AENST.
This paper introduces a novel integrated validity index for evaluating and comparing the balance-variation order pairs of different Decision-Making Trial and Evaluation Laboratory (DEMATEL) methods. Specifically, when one DEMATEL model exhibits higher balance and lower variation, while another displays the opposite, the proposed index—combining Liu’s balanced coefficient and Liu’s variation coefficient—offers a comprehensive assessment of their validity. Using this new metric, three DEMATEL approaches with the same direct relational matrix are analyzed: traditional DEMATEL, shrinkage DEMATEL, and balance DEMATEL. A comparative validity experiment demonstrates that balance DEMATEL outperforms the other methods, followed by shrinkage DEMATEL, which exhibits superior performance over the traditional DEMATEL. These findings highlight the effectiveness of the proposed validity index in distinguishing and assessing DEMATEL variations, providing valuable insights for decision-making model optimization.