Applied Stochastic Models in Business and Industry最新文献

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.

The allocation of redundant components to a system is a common method for enhancing the system's lifetime. This study explores the optimal allocation of redundancies in series and parallel systems with two components by assuming components and redundancies are dependent. That is, we perform the stochastic comparisons of the series (parallel) systems in the case of two redundancies at the component level. Specifically, we examine the stochastic comparisons across three scenarios: (i) components (and redundancies) have dependent lifetimes but are independent of each other, and components (redundancies) have identical marginal distributions in the two generated systems; (ii) components (and redundancies) have dependent lifetimes and are independent of each other, but the marginal distributions of components (redundancies) are different in the two generated system; and (iii) components and redundancies are interdependent and the marginals of the components (redundancies) in the two generated systems are same. In this study, we model the dependency using the concept of copula and perform the desired stochastic comparisons using generalized distorted distribution functions. Furthermore, we demonstrate our findings through various examples and counterexamples. Finally, we provide a simulation-based study and a real data analysis to illustrate our findings.

In this article, an overview of Nozer Singpurwalla's work in reliability and risk analysis is provided. Rather than presenting a chronological review of his work, the emphasis is given to those areas of his research which better reflect Nozer's scientific personality.

In the context of Industry 4.0, a production line must be flexible and adaptable to stochastic or real-world environments. As a result, the assembly line balancing (ALB) problem involves managing uncertainty or stochasticity. Several methods have been proposed, including stochastic mathematical programming models and simulations. However, programming models can only incorporate a few sources of uncertainty that result in impractical or unfeasible solutions to implement due to overlooked complexities, while simulation is only used to test solutions from deterministic approaches or adjust parameters without maintaining their optimum value. The proposed methodology uses a deterministic mathematical model to minimize the cycle time, followed by the simulation to measure the impact of selected sources of uncertainty on the cycle time. Finally, the optimum value of the stochastic parameters is computed using simulation-based optimization to maintain the average cycle time close to the deterministic one. A real-life assembly line balancing problem for a motorcycle manufacturing company is solved to test the proposed methodology. The sources of uncertainty are the tasks' stochastic processing times, inter-arrival time, the number of workers in each station, and the speed of the material handling system. Results show that the average cycle time is above 2.7% from the deterministic value computed by the programming model when the inter-arrival time is set to 270 $��\pm �$ 60 s; the processing times are allowed to increase or decrease by 3 s; the material handling system's speed is 1.5 m/s; and the number of workers in cells is between 4 and 6, with a speed of 2 m/s. The reader can download the source code and the simulation model to apply the methodology to other instances.

We consider gamma processes of homogeneous type, which live in a random environment or media represented by a pure jump Markov process. The aim of this paper is to approximate such gamma processes by a diffusion. Since gamma processes are increasing, the diffusion approximation requires an average approximation first. This averaged process will serve as an equilibrium to the initial gamma process. We present two main results: averaging and normal deviation. An application for degradation systems in reliability modeling is discussed.

Consider multi-state series and multi-state parallel systems consisting of $��N�$ independent components each. It is assumed that (i) each component and both the systems take values in the set $��\{�0�,�1�,�2�\}�$, (ii) each system and each component start out in state 2, the perfect state, and they make the transition to state 1, depending upon system configuration, and, eventually, each system enters state 0, the failed state. This multi-state nature of components and systems leads to $��N�$ scenarios under which each of the systems makes the transition from state 2 to state 1, and eventually to state 0. The joint probability function for times spent in state 2 and state 1 is obtained based on these $��N�$ scenarios for each of the systems. It is interesting to note that by merely changing set $��\{�0�,�1�\}�$ of a standard binary series (parallel) system to a set $��\{�0�,�1�,�2�\}�$ of a multi-state series (multi-state parallel) system, renders expression of the joint probability function of system spending times in state 2 and state 1 of a multi-state series (multi-state parallel) system is quite complex as compared to the univariate survival probability of the binary series (parallel) system being in the functioning state. As a proof of concept, graphical comparison between these analytical joint probability functions and joint e