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Marksmanship data is a staple of military and law enforcement evaluations. This ubiquitous nature creates a critical need to use all relevant information and to convey outcomes in a meaningful way for the end users. The purpose of this study is to demonstrate how simple simulation techniques can improve interpretations of marksmanship data.

This study uses three simulations to demonstrate the advantages of small arms combat modeling, including (1) the benefits of incorporating a Markov Chain into Monte Carlo shooting simulations; (2) how small arms combat modeling is superior to point-based evaluations; and (3) why continuous-time chains better capture performance than discrete-time chains.

The proposed method reduces ambiguity in low-accuracy scenarios while also incorporating a more holistic view of performance as outcomes simultaneously incorporate speed and accuracy rather than holding one constant.

This process determines the probability of winning an engagement against a given opponent while circumventing arbitrary discussions of speed and accuracy trade-offs. Someone wins 70% of combat engagements against a given opponent rather than scoring 15 more points. Moreover, risk exposure is quantified by determining the likely casualties suffered to achieve victory. This combination makes the practical consequences of human performance differences tangible to the end users. Taken together, this approach advances the operations research analyses of squad-level combat engagements.

For more than a century, marksmanship evaluations have used point-based systems to classify shooters. However, these scoring methods were developed for competitive integrity rather than lethality as points do not adequately capture combat capabilities. The proposed method thus represents a major shift in the marksmanship scoring paradigm.

This chapter presents a model of distribution dynamics in the presence of measurement error in the underlying data. Studies of international growth convergence generally ignore the fact that per capita income data from the Penn World Table (PWT) are not only continuous variables but also measured with error. Together with short-time scale fluctuations, measurement error makes inferences potentially unreliable. When first-order, time-homogeneous Markov models are fitted to continuous data with measurement error, a bias towards excess mobility is introduced into the estimated transition probability matrix. This chapter evaluates different methods of accounting for this error. An EM algorithm is used for parameter estimation, and the methods are illustrated using data from the PWT Mark 6.1. Measurement error in income data is found to have quantitatively important effects on distribution dynamics. For instance, purging the data of measurement error reduces estimated transition intensities by between one- and four-fifths and more than halves the observed mobility of countries.

I review the burgeoning literature on applications of Markov regime switching models in empirical finance. In particular, distinct attention is devoted to the ability of Markov Switching models to fit the data, filter unknown regimes and states on the basis of the data, to allow a powerful tool to test hypotheses formulated in light of financial theories, and to their forecasting performance with reference to both point and density predictions. The review covers papers concerning a multiplicity of sub-fields in financial economics, ranging from empirical analyses of stock returns, the term structure of default-free interest rates, the dynamics of exchange rates, as well as the joint process of stock and bond returns.

Credit ratings serve as an important input in several applications in risk management of the financial firms. The level of credit rating changes from time to time because of random credit risk and, thus, can be modeled by an appropriate stochastic process. Markov chain models have been widely used in the literature to generate credit migration matrices; however, emergent empirical evidences suggest that the Markov property is not appropriate for credit rating dynamics. The purpose of this article is to address the non-Markov behavior of the rating dynamics.

This paper proposes a model based on Markov regenerative process (MRGP) with subordinated semi-Markov process (SMP) to obtain the estimates of rating migration probability matrices and default probabilities. Numerical example is given to illustrate the applicability of the proposed model with the help of historical Standard & Poor’s (S&P) credit rating data.

The proposed model implies that rating of a firm in the future not only depends on its present rating, but also on its previous ratings. If a firm gets a rating lower than its previous ratings, there are higher chances of further downgrades, and the issue is called the rating momentum. The model also addresses the ageing problem of credit rating evolution.

The contribution of this paper is a more general approach to study the rating dynamics and overcome the issues of inappropriateness of Markov process applied in rating dynamics.

I survey applications of Markov switching models to the asset pricing and portfolio choice literatures. In particular, I discuss the potential that Markov switching models have to fit financial time series and at the same time provide powerful tools to test hypotheses formulated in the light of financial theories, and to generate positive economic value, as measured by risk-adjusted performances, in dynamic asset allocation applications. The chapter also reviews the role of Markov switching dynamics in modern asset pricing models in which the no-arbitrage principle is used to characterize the properties of the fundamental pricing measure in the presence of regimes.

Using a case study for electrical power equipment, the purpose of this paper is to investigate the importance of dependence between series-connected system components in maintenance decisions.

A continuous-time Markov decision model is formulated to find a minimum cost maintenance policy for a circuit breaker as an independent component while considering a downstream transformer as a dependent component. Maintenance of the dependent component is included implicitly in terms of the costs associated with certain state-action pairs. For policy and cost comparisons, a separate model is also formulated that considers only the circuit breaker as the independent component. After uniformizing the continuous-time models to discrete time, standard methods are used to solve for the average-cost-optimal policies of each model.

The optimal maintenance policy and its cost differ significantly depending on whether or not the dependent component is considered.

Data used are from manufacturer databases; additional model validation could be conducted if applied to an electric utility asset fleet within their generation, transmission, and/or distribution system. This model and methodology are already being applied in other contexts such as industrial machinery and equipment, jet engines, amusement park rides, etc.

The outcome of this model can be utilized by asset and operations managers to make maintenance decisions based on prediction rather than more traditional time- or condition-based maintenance methodologies. This model is being developed for use as a module in a larger maintenance information system, specifically linking condition monitor data from the field to a predictive maintenance model. Similar methods are being applied to other applications outside the electrical equipment case detailed herein.

This model provides a structured approach for managers to decide how to best allocate their resources across a network of inter-connected equipment. Work in this area has not fully considered the importance of dependency on systems maintenance, particularly in applications with highly variable repair and replacement costs.

This paper aims to present a model of a multi‐phase multi‐product manufacturing system considering a CONstant work‐in‐process (CONWIP) control mechanism and using continuous‐time Markov chain modelling approach.

The model includes defining a state space then constructing the rate matrix, which contains the transition rates, followed by formulating the transition matrix. The time‐dependent probabilities that a product is in a particular state at a certain time are characterized. Performance measures related to the statistics on the waiting time and average number of work‐in‐process in the production system have been determined. Consequently, a numerical example is presented to illustrate the computations of different model aspects.

The analyses explain a foundation needed for analyzing the steady state behavior of manufacturing systems. Results have shown how production data can be easily modified for what‐if analyses by the use of Excel add‐in tool.

The multi‐level model outlines a framework that provides a practical tool for production engineers seeking to enhance the performance of their production system by selecting the best order release mechanism.

A novel aspect of the work reported in this paper is the application of Chapman‐Kolmogrov mathematics and CONWIP ordering theory, which is developed for evaluating and managing CONWIP controlled production systems.

The purpose of this study is to determine the proportion of the population that will be susceptible to the COVID-19 pandemic, as well as the proportions of infections, recoveries and fatalities from the COVID-19 pandemic.

The design was a longitudinal survey of COVID-19 infections, recoveries and fatalities in Nigeria using the data on the daily updates of the Nigeria Centre for Disease Control for the period 1 May to 23 August 2020. Markov chain analysis was performed on the data.

The results showed that in the long run, 8.4% of the population will be susceptible to COVID-19 infections, 26.4% of them will be infected, 61.2% of the infected will recover and 4% will become fatal. Thus, if this pattern of infections and recoveries continue, the majority of the infected people in Nigeria will recover whilst a very small proportion of the infected people will die.

A dearth of the extant literature on the problem, especially from the management science perspective.

Results of the study will facilitate policymakers’ response to the curtailment of the pandemic in Nigeria.

Curtailing the pandemic through the results of this study will assist in easing the social consequences of the pandemic.

The proposed adjustment to the susceptibilities, infections and recoveries model through the introduction of a fourth state (fatality) to get the susceptibilities, infections, recoveries and fatalities model, signalling a point of departure from previous studies.

Over the past two decades, online booking has become a predominant distribution channel of tourism products. As online sales have become more important, understanding booking conversion behavior remains a critical topic in the tourism industry. The purpose of this study is to model airline search and booking activities of anonymous visitors.

This study proposes a stochastic approach to explicitly model dynamics of airline customers’ search, revisit and booking activities. A Markov chain model simultaneously captures transition probabilities and the timing of search, revisit and booking decisions. The suggested model is demonstrated on clickstream data from an airline booking website.

Empirical results show that low prices (captured as discount rates) lead to not only booking propensities but also overall stickiness to a website, increasing search and revisit probabilities. From the decision timing of search and revisit activities, the author observes customers’ learning effect on browsing time and heterogeneous intentions of website visits.

This study presents both theoretical and managerial implications of online search and booking behavior for airline and tourism marketing. The dynamic Markov chain model provides a systematic framework to predict online search, revisit and booking conversion and the time of the online activities.

In the present fast-paced and globalized age of war, special operations forces have a comparative advantage over conventional forces because of their small, highly-skilled units. Largely because of these characteristics, special operations forces spend a disproportionate amount of time deployed. The amount of time spent deployed affects service member’s quality of life and their level of preparedness for the full spectrum of military operations. In this paper, the authors ask the following question: How many force packages are required to sustain a deployed force package, while maintaining predetermined combat-readiness and quality-of-life standards?

The authors begin by developing standardized deployment-to-dwell metrics to assess the effects of deployments on service members’ quality of life and combat readiness. Next, they model deployment cycles using continuous time Markov chains and derive closed-form equations that relate the amount of time spent deployed versus at home station, rotation length, transition time and the total force size.

The expressions yield the total force size required to sustain a deployed capability.

Finally, the authors apply the method to the US Air Force Special Operations Command. This research has important implications for the force-structure logistics of any military force.