Applied Stochastic Models in Business and Industry最新文献

We consider some key concepts in the application of statistics to real world problem solving which are still relevant in the era of Big Data and Artificial Intelligence (AI). Also, we give an outline of some historical developments in industrial quality improvement where statistical methods are widely applied. In addition, we briefly discuss Big Data, Data Science, and some aspects of machine learning with emphasis on Statistical Thinking and ethical considerations.

The advent of artificial intelligence (AI) technologies has significantly changed many domains, including applied statistics. This review and vision paper explores the evolving role of applied statistics in the AI era, drawing from our experiences in engineering statistics. We begin by outlining the fundamental concepts and historical developments in applied statistics and tracing the rise of AI technologies. Subsequently, we review traditional areas of applied statistics, using examples from engineering statistics to illustrate key points. We then explore emerging areas in applied statistics, driven by recent technological advancements, highlighting examples from our recent projects. The paper discusses the symbiotic relationship between AI and applied statistics, focusing on how statistical principles can be employed to study the properties of AI models and enhance AI systems. We also examine how AI can advance applied statistics in terms of modeling and analysis. In conclusion, we reflect on the future role of statisticians. Our paper aims to shed light on the transformative impact of AI on applied statistics and inspire further exploration in this dynamic field.

Acceptance sampling plans (ASP) help practitioners economically and efficiently verify product quality, serving as a widely applied statistical quality control method. Among ASPs, the simplest form is the single sampling plan (SSP). Recently, acceptance sampling systems incorporating two SSPs as decision rules for lot disposition have gained significant attention due to their superior performance. Depending on the switching mechanism for decision rules, acceptance sampling systems can be categorized into quick switching systems and two-plan sampling systems (TSS), where TSS exhibits greater flexibility and adaptability in its rule-switching mechanism. In this study, we construct a TSS with a sample size adjustment mechanism and integrate it with a third-generation process capability index. Detailed investigation and analysis reveal that the proposed method provides more substantial incentives for suppliers, as its properties penalize suppliers who submit poor-quality lots through increased sample size while rewarding suppliers who submit high-quality lots by requiring smaller sample sizes. Finally, we demonstrate the application of the proposed method through a practical case study.

This article presents a novel extension of the GARCH model incorporating weighted liquidity, modeled by fractional Brownian motion. The existence of a stationary solution is proven, and the higher-order moments are calculated to illustrate the statistical properties of the model. Analysis of the auto-correlation function of the squared process confirms the long-term memory characteristic of the model. Numerical simulations are employed to validate the theoretical findings, demonstrating the significance of the model in the financial market.

We propose a computational approach to constructing exact designs on finite design spaces that are optimal for multiresponse regression experiments under a combination of the standard linear and specific ‘sparsity’ constraints. The linear constraints address, for example, limits on multiple resource consumption and the problem of optimal design augmentation, while the sparsity constraints control the set of distinct trial conditions utilized by the design. The key idea is to construct an artificial optimal design problem that can be solved using any existing mathematical programming technique for univariate-response optimal designs under pure linear constraints. The solution to this artificial problem can then be directly converted into an optimal design for the primary multivariate-response setting with combined linear and sparsity constraints. We demonstrate the utility and flexibility of the approach through a dose-response case study with multivariate responses that sequentially adds constraints on safety, efficacy, and cost, where cost also depends on the number of distinct doses used.

Accelerated destructive degradation tests (ADDTs) play a crucial role in providing timely reliability information for long-life products. Previous research has primarily focused on identifying optimal ADDT plans for accurately predicting specific quantiles of the failure-time distribution under use conditions, utilizing a given degradation model. However, a common challenge during the experimental design phase is the lack of confidence in selecting a model that accurately represents the underlying data. In this paper, we introduce a novel approach that specifically addresses optimal ADDT planning for model discrimination. We propose KL-optimal design criteria to enhance the model discrimination capability of ADDTs. Moreover, we present compound DKL- and CKL-optimal design criteria to ensure that ADDT plans can simultaneously achieve effective model discrimination alongside accurate parameter estimation or precise quantile prediction. We establish equivalence theorems to validate the optimality of the proposed designs. Meanwhile, we employ the particle swarm optimization algorithm to efficiently compute optimal ADDT plans. Through a practical application and sensitivity analysis, we demonstrate the effectiveness and robustness of our optimal designs. Our proposed method offers engineers with a valuable solution for developing optimal ADDT plans that meet multiple objectives.

The redundancy allocation problem (RAP) is considered as one of the important problems in reliability theory. In this paper, we consider a series system with several subsystems wherein each subsystem is a weighted $��k�$-out-of-$��n�$ system formed by different types of multi-state components. The degradation of the performance level (i.e., the probability of changing from a given state $��i�$ to the next state $��(�i�-�1�)�$) of a component of the system is modeled by the Markov process. Then, we study the multi-objective RAP problem for this system, that is, we determine the optimum number of components of each type in each subsystem so that the maximum system reliability is achieved at minimum cost. Note that the given RAP problem is of NP-hard type, and consequently, we use the controlled elitism non-dominated ranked genetic algorithm (CE-NRGA) to solve this problem. At the end, we illustrate the proposed methodology through a numerical example. Moreover, we discuss a case study to validate the proposed model.

This article develops a valuation model for mortgages with partial prepayment risk under the equal principal payment method. To model partial prepayment, we assume prepayment events occur at the jump times of a point process. The proportion of the prepayment amount to the outstanding principal balance is characterized by a stochastic process. By defining specific forms for the point process and stochastic process, we derive explicit valuation formulas for the mortgage loan. Finally, after resolving the computational challenge of multiple integrals via matrix exponentiation techniques, numerical results are presented to investigate the impact of some parameters on the valuation.