Applied Stochastic Models in Business and Industry最新文献

Minimally repaired items are considered. In practice, minimal repair can be unsuccessful, and in this case, it should be repeated. The Polya-Aeppli process, which is a generalization of the Poisson process is used in the article for the corresponding modeling. Some properties, useful for optimal maintenance, are derived. An important generalization to the case when the probability of the unsuccessful attempt is time-dependent is described. An application of the derived results to obtaining the optimal time of replacement for a system with multiattempt minimal repairs is discussed. The study is illustrated by detailed numerical examples.

An effective way to increase system reliability is to use redundancies (spares) into the systems either in component level or in system level. In this prospect, it is a significant issue that which set of available spares providing better system reliability in some stochastic sense. In this paper, we derive sufficient conditions under which a coherent system with a set of active redundancy at the component level or the system level provide better system reliability than that of the system with another set of redundancy, with respect some stochastic orders. We have derived the results for the component lifetimes following accelerated life (AL) model. The results obtained help us to design more reliable systems by allocating appropriate redundant components from the set of available options for the same. Various examples satisfying the sufficient conditions of the theoretical results are provided. Some results are illustrated with real-world data.

This article presents a novel dynamic model for internal fraud losses in the retail banking sector, incorporating internal factors such as ethical quality of workers and bank risk controls. The model's parameters are calibrated for each bank in the Operational Riskdata eXchange (ORX) consortium, based only on publicly available exposure indicators. The model generates simulated internal operational losses, exhibiting standard stochastic properties and tail behavior that closely align with actual operational losses. At an aggregate level, the model endeavors to replicate the average frequency and severity of losses observed within the internal fraud—retail banking category. Moreover, we identify macro-environmental factors that exert influence over the severity and frequency of model-simulated losses, consistent with findings in the existing literature.

Congratulations on this great and comprehensive achievement. Undoubtedly, Bayesian inference plays an increasingly important role in reliability data analysis, dictated on the one hand by the usually small sample sizes per experimental condition, which bring standard frequentist procedures to their limits, and on the other hand by the fact that uncertainty quantification and communication are more straightforward in a Bayesian setup. Reliability data are mostly censored, with many realistic censoring schemes leading to complicated likelihood functions and posterior distributions that can be only approximated numerically with Markov Chain Monte Carlo (MCMC) methods. With the advances in Bayesian computation techniques and algorithms, this is however not a limitation anymore. The authors managed in this enlightening work to embed the reliability perspective view, grounded on the practitioners' needs, in a Bayesian theoretic setup, providing and commenting fundamental literature from both fields. This paper will be a valuable reference for practitioning Bayesian inference in reliability applications and, most importantly, for understanding the effect of the priors' choice. The provided insight on the role of a sensitivity analysis for the prior distribution is very important as well, especially when extrapolating results. Furthermore, the technical details and hints on the implementation in R will be highly appreciated.

It is not surprising, but good to see, that the essential role of the independence Jeffreys (IJ) priors is verified also in this context, for example, in cases of Type-I censoring with few observed failures. A crucial statement of the paper I would like to highlight is that in case of limited observed data, the usually “safe” choice of a noninformative prior can deliver misleading conclusions, since it may consider unlikely or impossible parts of the parameter space with high probability. Therefore, in reliability applications weakly informative priors that reflect the underlying framework or known effect of experimental conditions have to be prioritized. Moreover, along these lines, in case of experiments combining more than one experimental condition, if the level of the experimental condition has a monotone effect on the quantity of interest, say the expected lifetime, the choice of the priors under the different conditions should reflect this ordering. This is a direction of future research on Bayesian procedures for reliability applications with high expected impact.

In a Bayesian inferential framework, the derivation and use of credible intervals (CIs) is more natural and flexible than frequentist confidence intervals. In this work the focus lies on equal tailed CIs. For highly skewed posteriors, it would be of interest to consider in the future highest posterior density (HPD) CIs as well.

Motivated by the reference of the authors to Reference 1 and the priors in the framework of a

Firstly, I want to congratulate the authors in Reference 1 for their practical contextualization in describing the Bayesian method in real-world problems with reliability data. Undoubtedly, one of the main strengths of this article is its highly practical approach, starting from real situations and examples, and showing why Bayesian inference is many times a nice alternative for making estimations. The authors nicely describe how, in reliability applications, there are generally few failure records and, therefore, little information available. For example, this is often the case in the study of the reliability of engineering systems in the army, such as some types of weapons. Since the specific prior is a key aspect of the Bayesian framework, they are primarily concerned with guiding readers on how to make this choice properly.

Once the parameter of interest $��\theta �=�(�\mu �,�\sigma �)�$ has been identified, and without losing sight of real-world applications, the authors develop their exposition based on three essential premises. Firstly, they remind us that the distribution of $��\theta �$ may not always be the main focus of our interest in practical situations. Instead, our key objective might involve estimating cumulative failure probabilities at a specific time or a failure-time distribution $��p�$-quantile, given by the expression $��{�t�}_{�p�}�=�\exp �[�\mu �+�{�\Phi �}^{�-�1�}�(�$