Applied Stochastic Models in Business and Industry最新文献

The aim of this paper is to investigate the problem of one and two active redundant components allocation in a k-out-of-n system with dependent components. Here, some necessary and sufficient conditions are presented under which the redundancies are optimally allocated to the system components based on the usual stochastic order criterion. In addition, it is shown that, unlike the independence mode, a redundant component is not necessarily allocated to the weakest component. Further, in the case of the two redundant components, the weak (strong) redundant component is not necessarily allocated to the stronger (weaker) component of the system. Some algorithms are also presented for calculating the reliability of the considered system under the assumption of dependency between the main and redundant components. Using different copula functions for describing the dependencies between components, various examples are given to illustrate the optimal allocation of redundant components.

Cryptocurrencies exhibit high volatility, emphasizing the importance of accurately measuring tail risk in their markets. This research incorporates a threshold-switching mechanism into Taylor's ES-CAViaR models that unveil features such as asymmetry and jump phenomena. These enhancements effectively capture the diverse tail risks of cryptocurrencies while enabling the simultaneous forecasting of both Value-at-Risk (VaR) and Expected Shortfall (ES). The proposed models incorporate two types of functions to address the VaR and ES nexus with the option to use the rolling standard deviation of returns as a short-term volatility proxy as a regressor. We estimate the parameters and forecast tail risk within a Bayesian framework. Taking the two largest cryptocurrencies by market capitalization, Bitcoin and Ethereum, we assess the one-step-ahead forecasting performance over a four-year out-of-sample period using a rolling window approach. The comparative results from backtests and five scoring functions among eight competing models support the conclusion that models with a threshold mechanism capture the tail risk of cryptocurrencies more accurately than other risk models.

The fourth industrial revolution has driven the emergence of Digital Twins (DTs) and Industrial Internet of Things (IIoT) in manufacturing. However, the use of different definition has led to varied interpretations and inconsistent understanding of DTs. Thus, by exploring the gap between theoretical frameworks and practical implementations of IIoT-based DTs in manufacturing, this paper aims to shed light on the DT phenomenon by considering the historical evolution and fundamental concepts of IIoT-based DTs. Therefore, a systematic literature review was conducted to assess the ambiguity concerning DTs, particularly in distinguishing architectures and types. Therefore, this paper identifies IIoT-based DTs in manufacturing by reviewing application-oriented literature. As a result of a subsequent classification, this paper proposes a hierarchical classification based on communication dynamics (i.e., Uni-directional and Bi-directional) and information processing (i.e., use or non-use of machine learning). Conclusively, this study proposes a comprehensive classification approach for IIoT-based DTs and thus contributes to a more consistent understanding of the DT phenomenon. Moreover, this paper discusses key findings, as well as implications for research and practice. Finally potential avenues for future research are derived and the limitations of this study are discussed.

A flexible model for analysing load-sharing data is developed by approximating the cumulative hazard functions of component lifetimes by piecewise linear functions. The proposed model is data-driven and does not depend on restrictive parametric assumptions on underlying component lifetimes. Maximum likelihood estimation and construction of confidence intervals for model parameters are discussed. Estimates of reliability characteristics such as reliability at a mission time, quantile function, mean time to failure and mean residual time for load-sharing systems are developed in this setting. As the proposed model is capable of providing a good fit for load-sharing data, it also results in a better estimation of these important reliability characteristics. The performance of the proposed model is observed to be quite satisfactory through a detailed Monte Carlo simulation study. The analyses of two load-sharing datasets, one pertaining to the lives of two-motor load-sharing systems and another related to basketball games, are provided as illustrative examples. In summary, this article presents a comprehensive discussion on a flexible model that can be used for load-sharing systems efficiently.

This article compares the information content of a sample for two competing Bayesian approaches. One approach follows Dennis Lindley's Bayesian standpoint, where one begins by formulating a prior for a parameter related to the problem in question and incorporates a likelihood to transition to a posterior. This contrasts with the usual Bayesian approach, where one starts with a likelihood model, formulates a prior distribution for its parameters, and derives the corresponding posterior. In both cases, the sample information content is measured using the difference between the prior and posterior entropies. We investigate this contrast in the context of learning about the moments of a variable. The maximum entropy principle is used to construct the likelihood model consistent with the given moment parameters. This likelihood model is then combined with the prior information on the parameters to derive the posterior. The model parameters are the Lagrange multipliers for the moment constraints. A prior for the moments induces a prior for the model parameters; however, the data provides differing amounts of information about them. The results obtained for several problems show that the information content using the two formulations can differ significantly. Additional information measures are derived to assess the effects of operating environments on the lifetimes of system components.

The limitations of physics-based models and the constraints posed by data-driven models have motivated the development of fusion models for degradation modeling. These fusion models are designed to overcome the shortcomings inherent to either type of these models when used in isolation. In reliability analysis, particularly for highly reliable systems or units, the available datasets often exhibit small sample sizes. In such instances, the amount of data may not suffice for training powerful data-driven models, which typically require large datasets. Additionally, physics-based models may fail to capture all relevant information present in the data. This article focuses on addressing small sample-size datasets related to highly reliable systems, exploring various statistical and machine learning models tailored for such datasets, from statistical and AI models to fusion models. Furthermore, to address the challenges of using these models in isolation, a combination approach is presented involving employing simple data-driven models accompanied by essential data preprocessing and a physics-based model. This combination enables the models to capture the majority of pertinent information within the data. Also, a time-windowed multilayer perceptron is adapted to the dataset, showing that a meticulously prepared artificial neural network model might surpass the performance of some robust data-driven and even fusion models.