Applied Stochastic Models in Business and Industry最新文献

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