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AbstractA single regression model is unlikely to hold throughout a large and complex spatial domain. A finite mixture of regression models can address this issue by clustering the data and assigning a regression model to explain each homogenous group. However, a typical finite mixture of regressions does not account for spatial dependencies. Furthermore, the number of components selected can be too high in the presence of skewed data and/or heavy tails. Here, we propose a mixture of regression models on a Markov random field with skewed distributions. The proposed model identifies the locations wherein the relationship between the predictors and the response is similar and estimates the model within each group as well as the number of groups. Overfitting is addressed by using skewed distributions, such as the skew-t or normal inverse Gaussian, in the error term of each regression model. Model estimation is carried out using an EM algorithm, and the performance of the estimators and model selection are illustrated through an extensive simulation study and two case studies. [ABSTRACT FROM AUTHOR]

The asymmetric simple exclusion process (ASEP) is a paradigmatic driven-diffusive system that describes the asymmetric diffusion of particles with hardcore interactions in a lattice. Although the ASEP is known as an exactly solvable model where physical quantities can be evaluated without approximations, most exact results are limited to one-dimensional systems. Recently, the exact steady states in the multi-dimensional ASEP have been proposed (Ishiguro and Sato 2024 Phys. Rev. Res. 6 033030). The research focused on the situations where the number of particles is conserved. In this paper, we consider the two-dimensional ASEP with attachment and detachment of particles (ASEP-LK), where particle number conservation is violated. By applying the results from (Ishiguro and Sato 2024 Phys. Rev. Res. 6 033030), we construct the exact steady states of the ASEP-LK and reveal their properties through the exact computation of physical quantities. [ABSTRACT FROM AUTHOR]

Mainstream bridge management systems use Markov chains of bridge condition ratings (CRs) to simulate temporal bridge health degradations and apply Markov decision processes to find optimal repair schemes. However, CR-based Markov models fail to consider the effect of structural age. Ongoing research aims to develop alternative models that incorporate the time factor, including multidimensional Markov models. In this study, bridge health degradation is described using a three-dimensional (3D) Markov model, and a corresponding condition-based bridge maintenance management framework is proposed. The proportional hazard model with a Weibull baseline hazard function translates the state of the 3D Markov model into a single hazard indicator for decision making. To demonstrate the proposed framework, concrete bridge decks were taken as the element of interest. The proposed management framework can provide time-variant decision thresholds, which outperform the CR-based Markov models in terms of information richness and total life-cycle costs. This paper also briefly discusses how to apply the proposed method to element-level inspection data. [ABSTRACT FROM AUTHOR]

A qualitative analysis of the communication process of subway teams was performed from the perspective of cognitive psychology in this study. The findings revealed that the communication process exhibited characteristics consistent with a Markov process, and then a model was approved to calculate the probability of miscommunication based on Markov processes. As communication within subway teams is a two-way process, a model for the dynamic probability of miscommunication based on the Markov two-way communication mode was derived. The model was subsequently validated through a case study involving a screen door fault event. The research results indicate that the actual cognitive communication process yields a significantly lower probability of miscommunication compared to the values obtained from the technique for human error rate prediction (THERP) manual. This demonstrates the effectiveness of dynamic two-way communication as a means of reducing miscommunication and confirms the feasibility and effectiveness of the proposed calculation model. [ABSTRACT FROM AUTHOR]

Avian influenza virus type A causes an infectious disease that circulates among wild bird populations and regularly spills over into domesticated animals, such as poultry and swine. As the virus replicates in these intermediate hosts, mutations occur, increasing the likelihood of emergence of a new variant with greater transmission to humans and a potential threat to public health. Prior models for spread of avian influenza have included some combinations of the following components: multi-host populations, spillover into humans, environmental transmission, seasonality, and migration. We develop an ordinary differential equation (ODE) model for spread of a low pathogenic avian influenza virus that combines all of these factors, and we translate this into a stochastic continuous-time Markov chain model. Linearization of the ODE near the disease-free solution leads to the basic reproduction number R 0 , a threshold for disease extinction in both the ODE and Markov chain. The linearized Markov chain leads to a branching process approximation which provides an estimate for probability of disease extinction, i.e., probability no major disease outbreak in the multi-host system. The probability of disease extinction depends on the time and the population into which infection is introduced and reflects the seasonality inherent in the system. Some of the most sensitive parameters to model outcomes include wild bird recovery and environmental transmission. We find that migratory wild birds can drive infection numbers in other populations even when transmission parameters for those populations are low, and that environmental transmission can be a significant driver of infections. [ABSTRACT FROM AUTHOR]

Objective: Autonomously functioning thyroid nodules (AFTN) can be treated with antithyroid drugs, radioactive iodine (RAI), thyroid lobectomy or radiofrequency ablation (RFA). Although surgery is most definitive, some patients require lifelong hormone supplementation. RFA avoids this sequela, but its efficacy depends on nodule size. This study aims to compare the relative cost‐effectiveness of RAI, RFA and lobectomy for treatment of AFTNs. Study Design: A Markov analysis model was created to simulate clinical outcomes, costs and utilities for three AFTN treatments: (1) thyroid lobectomy, (2) RAI, and (3) RFA. Patients: This mathematical model was created using published literature and modeling. Measurements: Transition probabilities, utilities and costs were extracted from published literature, Medicare, and RedBook. The willingness to pay threshold was set to $100,000 per quality‐adjusted life year. The model simulated 2‐year outcomes, reflecting RFA literature. Sensitivity analyses were conducted to account for uncertainty in model variables. Results: In the base model, RAI dominated both lobectomy and RFA, with lower estimated cost ($2000 vs. $9452 and $10,087) and higher cumulative utility (1.89 vs. 1.82 and 1.78 quality‐adjusted life years). One‐way sensitivity analyses demonstrated that relative cost‐effectiveness between surgery and RFA was driven by the probability of euthyroidism after RFA and hypothyroidism after lobectomy. RFA becomes more cost‐effective than surgery if the rate of euthyroidism after ablation is higher than 69% (baseline 54%). Conclusion: Based on published data, RAI is most cost‐effective in treating most AFTN. Surgery is more cost‐effective than RFA in most scenarios, but RFA may be more resource‐efficient for smaller nodules with a high likelihood of complete treatment. [ABSTRACT FROM AUTHOR]

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We define a class of not necessarily linear C 0 -semigroups (P t) t ≥ 0 on C b (E) (more generally, on C κ (E) : = 1 κ C b (E) , for some bounded function κ , which is the pointwise limit of a decreasing sequence of continuous functions) equipped with the mixed topology τ 1 M for a large class of topological (not necessarily Polish) state spaces E. If these semigroups are linear, classical theory of operator semigroups on locally convex spaces as well as the theory of bicontinuous semigroups apply to them. In particular, they are infinitesimally generated by their generator (L , D (L)) and thus reconstructable through an Euler formula from their strong derivative at zero in (C b (E) , τ 1 M). In the linear case, we prove that such (P t) t ≥ 0 can be characterized as integral operators given by measure kernels satisfying certain tightness properties. As a consequence, transition semigroups of Markov processes are C 0 -semigroups on (C b (E) , τ 1 M) , if they leave C b (E) invariant and they are jointly weakly continuous in space and time. Hence, they can be reconstructed from their strong derivative at zero and thus have a fully infinitesimal description. This solves an open problem for Markov processes. We show that our results apply to a large number of Markov processes, e.g., those given as the laws of solutions to SDEs and SPDEs, including the stochastic 2D Navier-Stokes equations and the stochastic fast and slow diffusion porous media equations. Furthermore, we introduce the notion of a Markov core operator (L 0 , D (L 0)) for the above generators (L , D (L)) and prove that uniqueness of the Fokker-Planck-Kolmogorov equations corresponding to (L 0 , D (L 0)) for all Dirac initial conditions implies that (L 0 , D (L 0)) is a Markov core operator for (L , D (L)). As a consequence, we identify the Kolmogorov operators of a large number of SDEs on finite and infinite dimensional state spaces as Markov core operators for the infinitesimal generators of the C 0 -semigroups on (C κ (E) , τ κ M) given by their transition semigroups. Furthermore, if each P t is merely convex, we prove that (P t) t ≥ 0 gives rise to viscosity solutions to the Cauchy problem given by its associated (nonlinear) infinitesimal generator. We also show that value functions of optimal control problems, both, in finite and infinite dimensions are particular instances of convex C 0 -semigroups on (C κ (E) , τ κ M). [ABSTRACT FROM AUTHOR]

ABSTRACT This study considers the stationary higher‐order Markov process for circular data by employing the mixture transition distribution modeling. The underlying circular transition distribution is based on Wehrly and Johnson's bivariate joint circular models. The structures of the circular autocorrelation function, together with the circular partial autocorrelation function, are investigated. They are found to be similar to those of the autocorrelation and partial autocorrelation functions of the real‐valued autoregressive process when the underlying binding density has zero sine moments. The validity of the model is assessed by applying it to some Monte Carlo simulations and real directional data. [ABSTRACT FROM AUTHOR]

We consider Palm distributions arising in a Markov process with time homogeneous transitions which is jointly stationary with multiple point processes. Motivated by a BAR approach studied in the recent paper (Braverman et al. in the BAR approach for multi-class queueing networks with SBP service policies, 2023), we are interested in two problems; when this Markov process inherits the same Markov structure under the Palm distributions, and how the state changes at counting instants of the point processes can be handled to derive stationary equations when there are simultaneous counts and each of them influences the state changes. We affirmatively answer the first problem, and propose a framework for resolving the second problem, which is applicable to a general stationary process, which is not needed to be Markov. We also discuss how those results can be applied in deriving BAR's for the diffusion approximation of queueing models in heavy traffic. In particular, as their new application, the heavy traffic limit of the stationary distribution is derived for a single-server queue with a finite waiting room. [ABSTRACT FROM AUTHOR]

Facing the challenges posed by increasingly complex, dynamic, and unforeseen requirements, the design process is grappling with the critical issue of ensuring sustained product satisfaction amid changing demands. This paper introduces an approach for evaluating design adaptability, considering potential future requirements. Entropy serves as a crucial indicator to quantify design effort and the Markov process is employed to simulate potential requirement changes. The information contents of design requirements and design solutions are defined based on information entropy theory, and the design adaptability of a design candidate is evaluated by calculating the extra design effort for satisfying the design requirements, which is the difference in information content between the design candidate and design requirements. Moreover, a simulation method for requirement evolution is proposed, which integrates information entropy theory and the Markov process to accommodate potential future requirements. The general design adaptability of design solutions is then calculated based on conditional entropy, taking into account the evolving design requirements. Finally, the effectiveness of the proposed approach is validated through a case study involving the design and evaluation of a hybrid additive manufacturing device. [ABSTRACT FROM AUTHOR]

Invariance times are stopping times $ \tau $ such that local martingales with respect to some reduced filtration and an equivalently changed probability measure, stopped before $ \tau $, are local martingales with respect to the original model filtration and probability measure. They arise naturally for modeling the default time of a dealer bank, in the mathematical finance context of counterparty credit risk. Assuming an invariance time endowed with an intensity and a positive Azéma supermartingale, this work establishes a dictionary relating the semimartingale calculi in the original and reduced stochastic bases, regarding conditional expectations, martingales, stochastic integrals, random measure stochastic integrals, martingale representation properties, semimartingale characteristics, Markov properties, transition semigroups and infinitesimal generators, and solutions of backward stochastic differential equations. [ABSTRACT FROM AUTHOR]

This research aims to evaluate the reliability indices of a public address system (PAS) through the Markovian approach. Many organizations and businesses use this system to address or broadcast a message or pass on important information to the huge gatherings assembled at big premises. This system is the nerve of these organizations and businesses. The major components of a PAS are a microphone, mixer, amplifier, and speaker. These components should work in harmony with one another to execute the intended task. Any failure in these components leads to big issues for the public, and they may miss very important information. Therefore, the reliability assessment of this system is of utmost importance. The authors used the Markovian decision process to model the PAS by analyzing the various failure rates and repairs of the components. The explicit expressions for reliability, availability, and MTTF have been obtained for clear understanding about the PAS behavior with time as well as different failures. The sensitivity analysis of reliability is performed as well to determine the critical components of the system. The obtained results show that the reliability of the PAS at 2000 operated hours is 0.8. Also, the finding reflects that the PAS reliability is much sensitive with the failure rate of microphone, mixer, and amplifier. [ABSTRACT FROM AUTHOR]

Predicting stochastic spreading processes across large-scale multi-layered networks remains a significant computational challenge due to the intricate interplay between network structure and spread dynamics. This study introduces FastGEMF, a novel, scalable simulation framework for exact, high-speed modeling of Markov chain processes on complex multi-layer networks. Inspired by the Gillespie algorithm and optimized for efficiency, FastGEMF achieves logarithmic time complexity per event, enabling simulations on networks with millions of nodes and edges without sacrificing accuracy. It introduces an event-driven algorithm with cautious update strategies, supporting diverse multi-compartment spreading processes. FastGEMF is implemented in Python programming language as an open-source package, providing accessibility to researchers and practitioners across domains such as epidemiology, cybersecurity, and information propagation, establishing an exact baseline for model validation and comparative analysis.

We considered three types of stochastic models of a single population growth: with diffusion-type noise; with parameters replaced by stochastic processes; and with random jumps describing a sudden decrease in population size. We presented methods for studying stochastic processes modeling population growth, in particular, the long-time behavior of sample paths and their distributions. We were especially interested in the asymptotic stability of the density of the distributions of these processes. We gave biological interpretations, examples, and numerical simulations of theoretical methods and results.

We considered two periodic review perishable inventory systems. The first system is controlled by a periodic review (T , S) policy, where orders are triggered at each review period T and when the stock is less than S. The second one is controlled by a periodic review (s , S) policy, where orders are triggered only if the stock level is below s. For both models, the lifetime of each product was assumed to follow a general distribution, whereas the lead time was constant. The demands followed a Poisson process, and all unsatisfied demand was lost. Using an approximate solution of the steady-state probabilities of the inventory level, we obtained a closed form of cost expression. Next, we conducted a simulation study to identify our solution accuracy. Finally, we performed a sensitivity analysis to evaluate the effect of the lifetime variation and cost parameters on the best policy and its cost. The obtained results were close to those of the optimal policy with an average accuracy of 3.7% for the periodic review (T , S) policy and 3.8% for the periodic review (s , S) policy. For the worst cases, where the accuracy is higher than 7%, we provided an analytical approach to improve the system accuracy. [ABSTRACT FROM AUTHOR]

This research aims to evaluate the reliability indices of a public address system (PAS) through the Markovian approach. Many organizations and businesses use this system to address or broadcast a message or pass on important information to the huge gatherings assembled at big premises. This system is the nerve of these organizations and businesses. The major components of a PAS are a microphone, mixer, amplifier, and speaker. These components should work in harmony with one another to execute the intended task. Any failure in these components leads to big issues for the public, and they may miss very important information. Therefore, the reliability assessment of this system is of utmost importance. The authors used the Markovian decision process to model the PAS by analyzing the various failure rates and repairs of the components. The explicit expressions for reliability, availability, and MTTF have been obtained for clear understanding about the PAS behavior with time as well as different failures. The sensitivity analysis of reliability is performed as well to determine the critical components of the system. The obtained results show that the reliability of the PAS at 2000 operated hours is 0.8. Also, the finding reflects that the PAS reliability is much sensitive with the failure rate of microphone, mixer, and amplifier.

We study the evolution of the friendship index in complex social networks over time. The elements of the networks are the users, and the connections correspond to the interactions between them. The friendship index of a node is defined as the ratio of the average degree of its neighbors to the degree of the node itself. Obviously, in the process of network growth, the value of the friendship index for any node in the network may change due to the fact that new edges can be attached to this node or its neighbors. In this paper, we study the dynamics of the friendship index of a single node over time for growth networks generated on the basis of the preferential attachment mechanism. We find both the asymptotics of their expected values and the variances over time. In addition, we analyze the behavior of the friendship index for five real networks.

Due to the improvement of seismic design standards, viscoelastic dampers have been rapidly developed and widely applied in bridge structures. Currently, there is limited research on dynamic reliability analysis of large bridge structures equipped with fractional-order dampers. In this paper, a hybrid method combining the time-domain explicit method and Markov process is proposed for the dynamic reliability analysis of multi-span continuous girder bridges with fractional-order dampers under non-stationary random excitation. This method introduces a fractional damping system and non-stationary random excitation to simulate both the bridge structure and external forces. The response coefficient matrix of the fractional damping structure is solved using the time-domain explicit method, and the response variance is directly calculated using the moment algorithm. The dynamic reliability analysis is then performed by applying the Markov process based on the structural response variance. Compared to traditional methods for structural dynamic reliability analysis, this approach offers higher computational efficiency and greater accuracy. By analyzing the response variance and dynamic reliability of a four-span continuous girder bridge equipped with viscoelastic dampers, the proposed method is validated using the Monte Carlo method. [ABSTRACT FROM AUTHOR]

This article studies the output feedback control (OFC) issue for fuzzy Markov jump systems with actuator faults and deception attacks. To describe the nonlinear characteristics, the Takagi–Sugeno (T–S) fuzzy rule scheme is utilized. A general network environment with deception attacks is considered, and Bernoulli distributed variable is adopted to describe the randomly occurring attacks. To alleviate the actuator faults and attacks in the networked data transmission, a new reliable OFC protocol is forwarded to ensure the prescribed system performance. Meanwhile, a hidden Markov model is resorted to treat the nonsynchronous phenomena between system mode and controller mode. By a stochastic Lyapunov function, some criteria are proposed such that the closed-loop dynamic is stochastically stable. Finally, the effectiveness and application of the obtained results are confirmed by a physical mass-spring-damper model. [ABSTRACT FROM AUTHOR]

In this article, we investigate the following stochastic tempered fractional general diffusion equation driven by tempered fractional Brownian motion (TFBM) ∂ t β , η u (t , x) = L u (t , x) + u (t , x) B ˙ H , λ (t) , (t , x) ∈ R + × R d , where ∂ t β , η denotes the Caputo tempered fractional derivative with order β ∈ (0 , 1) and tempered parameter η > 0, is the infinitesimal generator of some general time-homogeneous symmetric strong Markov process { X t } t ≥ 0 with the corresponding transition semigroup { P t , t ≥ 0 } defined by Ptf(x): = x[f(Xt)], and { B H , λ (t) } t ≥ 0 is a TFBM with Hurst index H ∈ (1 2 , 1) and tempering parameter λ > 0 which is independent of { X t } t ≥ 0 . First of all, a novel estimate of multiple stochastic integrals with respect to the inverse tempered β-stable subordinator Dβ, η(t) is presented, which greatly contributes to the stochastic analysis. Then after establishing the Fubini Theorem for the stochastic integrals with respect to TFBM BH, λ(t) and the inverse tempered β-stable subordinator Dβ, η(t), we show that the Feynman-Kac representation u (t , x) = E D [ P D β , η (t) f (x) e ∫ 0 t ∫ 0 t δ (s − r) d D β , η (s) d B H , λ (r) ] is the weak solution of the stochastic tempered fractional general diffusion equation driven by TFBM with the initial value f by means of the techniques of Malliavin calculus and convergence analysis. From the Feynman-Kac formula, several kinds of continuity of the solutions with respect to time and tempered parameter η of tempered fractional derivative are proved by using the scaling property of the inverse tempered β-stable subordinator Dβ, η(t) and the novel estimate of stochastic integrals with respect to BH, λ(t) and Dβ, η(t). In particular for the stochastic fractional general diffusion equation driven by fractional Brownian motion (FBM) but in the time fractional derivative case, we can also obtain the sharp upper and lower bounds for the Hölder regularity and the moments of the solution. [ABSTRACT FROM AUTHOR]

This paper studies the stochastic single-machine scheduling problem with workload-dependent maintenance activities, in which the processing times of all jobs are independently subject to a common discrete distribution, and the aim is to find the optimal policy so as to minimize the expected total discounted holding cost. Based on the definition of Markov process, for each of the two cases with the discount rate being zero or a positive number, we present two dynamic programming algorithms to produce the optimal static policy and the optimal dynamic policy, respectively. [ABSTRACT FROM AUTHOR]

• A novel degradation process with abrupt jumps caused by operation state transition is proposed. • Analytical reliability solutions of the model are derived in the form of one-dimensional Laplace-Stieltjes transform. • The limit reliability solutions are investigated, as alternative strategy under long-term service. • Analytical solutions regarding statistical characteristics of degradation amount during regeneration epoch are proposed. • The case of spool valve is implemented to verify the effectiveness and the feasibility of the solutions. This paper proposes a novel type of degradation process incorporating continuous degradation and abrupt degradation jump under dynamic operation states. By analyzing the failure mechanism of practical application, the abrupt degradation jump is comprehensively considered, and it is triggered by some certain state switching processes. Then, the reliability solutions of the degradation process (reliability function and moments of lifetime) are derived in the form of Laplace-Stieltjes transform. To a further step, inspired by the advanced equipment with long service span, the reliability solutions in limit region are explored, where an effective calculation method regarding statistical characteristics of degradation amount during regeneration epoch is pioneeringly proposed. To verify the proposed solutions in the form of Laplace-Stieltjes transform and their limit case, the representative example, spool valve, is implemented, and the results show the effectiveness and the feasibility of the solutions. [ABSTRACT FROM AUTHOR]

This paper presents a dynamic event-triggered output feedback controller for networked control systems under Markovian deception attacks. A dynamic event-triggered scheme is applied to curtail redundant sensor-to-observer data transfers. Given the prevalence of deception attacks in network signal transmission, these are modeled by a Markov process, and construct an augmented system. Utilizing Lyapunov stability theory, conditions are established for the system's asymptotic stability. Controller gains and event-triggering parameters are derived through the solution of linear matrix inequalities. Simulation results substantiate the controller's effectiveness in countering the impacts of network attacks on the NCSs. [ABSTRACT FROM AUTHOR]

With the development of economic globalization and increasing international trade, the maritime transportation system (MTS) is becoming more and more complex. A failure of any supply line in the MTS can seriously affect the operation of the system. Resilience describes the ability of a system to withstand or recover from a disaster and is therefore an important method of disaster management in MTS. This paper analyzes the impact of disasters on MTS, using the data of Suez Canal "Century of Congestion" as an example. In practice, the severity of a disaster is dynamic. This paper categorizes disasters into different levels, which are then modelled by the Markov chain. The concept of a repair line set is proposed and is determined with the aim to minimize the total loss and maximize the resilience increment of the line to the system. The resilience measure of MTS is defined to determine the repair line sequence in the repair line set. Finally, a maritime transportation system network from the Far East to the Mediterranean Sea is used to validate the applicability of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, random environment and random time delay are introduced into general nonlinear autoregressive models to improve the applicability of these models. The introduction of random environment makes nonlinear autoregressive models more flexible and more widely used. Random time delay is a new way for models to be applied in new fields. In order to analyze the properties of the proposed new model, we construct a new stochastic process and prove that it is an irreducible and aperiodic time-homogeneous Markov chain. The nonrecurrence of the proposed new type of models is considered, and some sufficient conditions for nonrecurrence are investigated. [ABSTRACT FROM AUTHOR]

We study the evolution of the friendship index in complex social networks over time. The elements of the networks are the users, and the connections correspond to the interactions between them. The friendship index of a node is defined as the ratio of the average degree of its neighbors to the degree of the node itself. Obviously, in the process of network growth, the value of the friendship index for any node in the network may change due to the fact that new edges can be attached to this node or its neighbors. In this paper, we study the dynamics of the friendship index of a single node over time for growth networks generated on the basis of the preferential attachment mechanism. We find both the asymptotics of their expected values and the variances over time. In addition, we analyze the behavior of the friendship index for five real networks. [ABSTRACT FROM AUTHOR]

This article presents an exploration of mathematical modeling and performance enhancement of a casting system in the steel industry. The study employs the implementation of Markov processes and genetic algorithm to achieve these objectives. The system comprises of four subsystems namely transfer laddle, continuous casting machine, shot blasting machine and grinding machine. These are arranged in a way that failing of a single subsystem halts the working of overall system. Using probabilistic approach, differential equations have been developed from transition diagram based on Markov process. Failure and repair rates follow exponential distribution. To ascertain steady state availability, differential equations are solved using normalizing conditions. Further, genetic algorithm is applied to find optimal values of failure/repair rates to estimate the optimal plant availability. [ABSTRACT FROM AUTHOR]

This paper investigates the asymptotic analysis of the hitting time of Markov-type jump processes (i.e., semi-Markov, Markov, in continuous or discrete time) with a small probability of entering a non-empty terminal subset. This means that absorption is a rare event. The mean hitting time function of all four type processes obeyed the same equation. We obtain unified results of asymptotic approximation in a series scheme or, equivalently, a functional type of mean hitting time. [ABSTRACT FROM AUTHOR]

The main purpose of this study is to examine the behavior of certain industrial systems under the conditions of product warranty policy. Given this policy, we are interested in considering all the parameters of the system in order to study them and show their impact on the proposed system. In order to increase the efficiency of the system and activate the product warranty policy, the system will undergo a preliminary examination for any system failure occurrence to determine the reasons that led to the failure. After completing the initial inspection, the mechanic will decide whether it is a user-caused failure or a manufacturing defect to determine whether or not the repair of the broken appliance is covered by the manufacturer's contractual warranty policy. All times in the system are assumed as a negative exponential distribution. The expressions for some measures of system effectiveness such as reliability, mean time to system failure (MTSF), and availability are derived using the supplementary variable technique and Laplace transform. Sensitivity analysis and a relative sensitivity are then carried out in order to recognize how each system parameter affects performance measures. Finally, some numerical examples are designed and performed to show how the change of each system parameter affects system performance. [ABSTRACT FROM AUTHOR]

In this paper, we present a general formula to calculate transition probabilities for six different types of systems based on their redundancy strategy and the status of the components. The systems are under periodic inspection policy and their components are repairable. The investigated systems include system I – active redundancy without any component to be replaced or repaired; system II – active with the component(s) to be replaced and repaired; system III – active with the component(s) to be repaired; system IV – standby without any component(s) to be replaced or repaired; system V – standby with the component(s) to be replaced and repaired; and system VI – standby with the component(s) to be repaired. In addition, all components in a system are considered non-identical. To calculate the transition probabilities for systems IV, V, and VI, we first consider a system with n non-identical components and cold standby configuration (NIC-CSC) and calculate the system state probabilities using Markov theory. Then, we present the general formula transition probabilities for systems IV, V, and VI using the results of the NIC-CSC system inspection interval. We demonstrate how to calculate the transition probabilities and matrixes for the six above-mentioned systems using the provided formulas. Moreover, we use the provided formulas to optimize the inspection interval of these systems using a modified full enumeration technique. [ABSTRACT FROM AUTHOR]

We investigate the stabilization problem of positive Markov jump linear systems by optimizing their transition probability rates. By using the convex property of posynomials and the standard mathematical programming that deals with the difference in convex functions, we show that transition probability rate synthesis problems can be solved via difference‐of‐convex (DC) programming. A numerical example is used to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

Laboratory experiments are one of the important means used to investigate travel choice behavior under strategic uncertainty. Many experiment-based studies have shown that the Nash equilibrium can predict aggregated route choices, while the fluctuations, whose mechanisms are still unclear, continue to exist until the end. To understand the fluctuations, this paper proposes a route-dependent attraction-based stochastic process model, which shares exactly the same behavioral foundation introduced in Part I of the study (Qi et al., 2023), i.e., route-dependent inertia and route-dependent preference. The model predictions are carefully compared with the experimental observations obtained from the congestible parallel-route laboratory experiments containing 312 subjects and eight decision-making scenarios (Qi et al., 2023). The results show that the proposed stochastic process model can precisely reproduce the random oscillations both in terms of flow switching and route flow evolution. Subsequently, an approximated model is developed to enhance the efficiency in evaluating the equilibrium distribution, providing a practical tool to evaluate the impacts of transportation policies in both long- and short-term runs. To the best of our knowledge, this paper is the first attempt to model and explain experimental phenomena by introducing stochastic process theories, as well as a successful example of applying experimental economics methodology to improve our understanding of human travel choice behavior.

We present contrast information, a novel application of some specific cases of relative entropy, designed to be useful for the cognitive modelling of the sequential perception of continuous signals. We explain the relevance of entropy in the cognitive modelling of sequential phenomena such as music and language. Then, as a first step to demonstrating the utility of constrast information for this purpose, we empirically show that its discrete case correlates well with existing successful cognitive models in the literature. We explain some interesting properties of constrast information. Finally, we propose future work toward a cognitive architecture that uses it. [ABSTRACT FROM AUTHOR]