Applied Stochastic Models in Business and Industry最新文献

We consider several survival models in heterogeneous settings. Heterogeneity in the failure rates of subpopulations results (as a specific case) in the famous failure rate paradox when the failure rate of a mixture of items with constant failure rates is decreasing. Random failure rate that is due to a point process that increases it at random times on fixed values also results in the “bending down” of the population failure rate. Similar effect is observed while analyzing the extreme shock models with shock processes that possess memory. Finally, another paradox when, due to heterogeneity in a vital parameter of a model, a terminating point process with decreasing rate after “mixing” becomes a non-terminating one with increasing rate is described. Those are the impacts of heterogeneity that are discussed from the unified perspective that employs the “principle”: the weaker subpopulations are dying out first.

Since Lotfi Zadeh introduced fuzzy logic and fuzzy sets, this theory characterizing the uncertainty of classification has a proven record in fields of computation and engineering. These successful applications, however, have been falsely interpreted as competition or replacement of probability theory by those in many statistical and mathematical communities. Such misconceptions are the result of a lack of understanding about types of uncertainties, and anchored attitudes clinging to the past. Nozer Singpurwalla, among other statisticians, came to the realization that probability and fuzzy set theory can and should work in concert (i.e., not in competition) to accommodate two different types of uncertainty present within a problem or system. The authors had the honor to collaborate with Nozer; those works are featured as successful applications of the probability measure of fuzzy sets in reliability where respective uncertainties of the outcome of events and of classification exist. This paper features those works which embody the use of Bayesian analysis and the subjective interpretation of probability.

In this article, we introduce modeling strategies for sequentially learning various types of demand uncertainty in bike-share networks and propose methods for optimal station inventory management. Our approach is motivated by a real bike-share network in Seoul, South Korea, with 40,000 bikes over a network of 2500 stations covering 25 municipal districts. In doing so, we consider novel Bayesian state space models that are suitable for fast and efficient learning of dynamically evolving system parameters for both intra-day and inter-week planning horizons. Our proposed approach provides an overall solution for operation managers where sequential parameter updating, demand prediction, and inventory decision making are addressed simultaneously and is straightforward to implement for the end-user. We illustrate how our approach can be applied to a large metropolitan area like Seoul and discuss practical implementation insights.

Cyber risk has emerged as a significant threat to businesses that have increasingly relied on new and existing information technologies (IT). Across various businesses in different industries and sectors, a distinct pattern of IT network architectures, such as the client-server network architecture, may, in principle, expose those businesses, which share it, to similar cyber risks. That is why in this article, we propose a probabilistic structural framework for loss assessments of cyber risks on the class of client-server network architectures with $��K�$ different client types. To our knowledge, there exist no theoretical models of an aggregate loss distribution for cyber risk in this setting. With this structural framework via the exact mean and variance of losses, we demonstrate how the changing cybersecurity environment of a business's IT network impacts the loss distribution. Furthermore, our framework provides insights into better investment strategies for cybersecurity protection on the client-server network. Motivated by cyberattacks across industries, we apply our framework to four case studies that utilize the client-server network architecture. Our first application is implantable medical devices in healthcare. Our second application is the smart buildings domain. Third, we present an application for ride-sharing services such as Uber and Lyft. The fourth is the application of vehicle-to-vehicle cooperation in traffic management. The results are corresponding exact means and variances of cyber risk loss distributions parameterized by various cybersecurity parameters allowing for liability assessments and decisions in cybersecurity protection investments.

In this article, we show a limit result for the reliability function of a system—that is, the probability that the whole system is still operational after a certain given time—when the number of components of the system grows to infinity. More specifically, we consider a sequence of mixed coherent systems whose components are homogeneous and non-repairable, with failure-times governed by a Lévy-Frailty Marshall–Olkin (LFMO) distribution—a distribution that allows simultaneous component failures. We show that under integrability conditions the reliability function converges to the probability of a first-passage time of a Lévy subordinator process. To the best of our knowledge, this is the first result to tackle the asymptotic behavior of the reliability function as the number of components of the system grows. To illustrate our approach, we give an example of a parametric family of reliability functions where the system failure time converges in distribution to an exponential random variable, and give computational experiments testing convergence.