Applied Stochastic Models in Business and Industry最新文献

Repairable systems, crucial in reliability studies, are characterized by recurrent failure times modeled as counting processes with intensity functions. This paper explores models for these failure times incorporating imperfect repairs, addressing unobserved heterogeneity via shared frailty models. In this context, our approach involves scenarios with general imperfect repairs, which offer a more realistic perspective compared to the minimal or perfect repair assumptions commonly employed in the reliability literature. We propose hierarchical Bayesian methods to estimate parameters, leveraging the Power-Law Process for initial intensities and gamma distributions for frailty terms. Bayesian methods are highly flexible and can accommodate complex shared frailty models that include random effects and dependencies between units. Applying Bayesian inference with gamma and beta distribution priors, coupled with Monte Carlo simulations, provides a robust methodology for estimating unknown parameters and deriving posterior distributions. This flexibility is crucial for capturing the underlying structure of the data in repairable systems with imperfect repairs. Our hierarchical Bayesian framework accommodates multiple systems, providing insights into failure processes and supporting enhanced maintenance strategies. We demonstrate our approach using a real failure times dataset and evaluate its performance through simulation studies, showcasing its applicability and relevance in practical settings.

In this article analysis of a simple step-stress accelerated life test is considered under progressive type-II censoring. A cumulative exposure model is considered when the latent lifetimes of test units follow the Gompertz distribution with different shape parameters and a common scale parameter. We explore the study by estimating all unknown parameters using classical and Bayesian techniques. The model parameters are estimated using maximum likelihood and Bayesian methods. Subsequently, interval estimates are derived based on the observed Fisher information matrix. Bayesian estimates are obtained using squared error and linear exponential loss functions. Subsequently highest posterior density intervals are also constructed. We examine the efficiency of all estimators through simulation studies. Finally, we provide a real-life example in support of the considered model.

During the manufacturing processes for the integrated circuit (IC) products, defective units may not be screened out by the quality inspections. The defective units often lead to infant mortality failure in the early stages of operation, while non-defective units will eventually fail due to wear-out failure. The general limited failure population (GLFP) model can be used to describe such a phenomenon in which defective units induce failure affected by both failure mechanisms, but failure of non-defective units is only due to wear-out. Besides, when a failure occurs, it is not known whether it is defective and yet which failure mode causes the failure. This article proposes an EM algorithm along with the missing information principle for the GLFP models under multiply censored Weibull distributions to simplify the maximum likelihood (ML) inference. It resolves the computational instability and provides more accurate reliability inference. With the embedded latent variables, failure mode detection and defect identification are also made for masked data, consequently. Furthermore, the proposed method can be extended to the GLFP models of interval data. The simulation study shows that the proposed method provides more accurate results. Two illustrative examples highlight the feasibility and advantages of the proposed approach.

The complexity and dynamic nature of cyber risks pose considerable challenges to risk management. From an actuarial perspective, we propose an advanced aggregate loss process using a variant of the Hawkes process as its frequency model. The refined Hawkes process first considers the impact of loss magnitude on the frequency of risk occurrences by integrating the loss covariate into the conditional intensity function. Second, we employ a more flexible kernel function in place of the classical exponential case. By incorporating the concept of age-dependent population structure, we calculate the probabilistic properties (mean, variance) for the proposed aggregate loss process. Furthermore, numerical simulations for cyber insurance pricing are conducted based on two pricing principles. Finally, we verify the feasibility of the proposed model based on a publicly available cyber breach data set. Considering the complex and dynamic nature of cyber risks, the efficiency of the proposed model is still limited by some factors, such as the authenticity and accuracy of the data. These are worthy of further consideration in future studies.

Consider a non-standard renewal risk model in which claims arrive in pairs $��\left\{�\right(�{�X�}_{�1�i�}�,�{�X�}_{�2�i�}�)�;�i�\in �\mathbb{N}�\}�$ and the stochastic discounting process is given by $��\{�{�e�}^{�-�\xi �\left(�t�\right)�}�;�t�\ge �0�\}�$, where $��\xi �(�·�)�$ is a Lévy process. We are interested in the joint tail probability of $��{�L�}_{�1�}�\left(�t�\right)�$ and $��{�L�}_{}$