[en] We calculate the spectral gap of the Markov matrix of the totally asymmetric simple exclusion process (TASEP) on a ring of L sites with N particles. Our derivation is simple and self-contained and extends a previous calculation that was valid only for half-filling. We use a special property of the Bethe equations for TASEP to reformulate them as a one-body problem. Our method is closely related to the one used to derive exact large deviation functions of the TASEP

[en] The hazard rate function is always applied to make maintenance policy, and the usual hazard rate function is computed by the data of failure times of systems working in constant environment, thus for systems working in dynamic environment it cannot be directly applied. In this paper, hazard rate function of system in the dynamic environment is computed, and the effects of current environment status and the environmental history on hazard rate function are explicitly presented. For system with the known degradation process, hazard rate function is studied by the Markov additive process. The environment evolution process is modeled as a stochastic process with two states, one state represents normal environment, the other represents severe environment, and system degrades more quickly under severe environment than under normal environment. The relationship between hazard rate functions of system in time-invariant and dynamic environment is researched, from which three important facts are revealed, firstly hazard rate function jumps as the environment jumps, secondly the form of hazard rate function is determined Wby current environment state, and thirdly the effective age of system is determined by the environmental history. For system with the unknown degradation process, based on the above facts, this paper derives the hazard rate function in dynamic environment, and proposes a method to compute the effective age under given environmental history. Finally the optimal maintenance policy for system in dynamic environment is studied. - Highlights: ●Compute hazard rate function (HRF) in dynamic environment with the Markov additive process. ●The history of environment is took into consideration when compute HRF. ●Compute HRF in dynamic environment with estimated classical HRF. ●Effective age of system is computed when environment is changed

[en] The distortion of the first entry map of interval maps is given by the real bounds theorem. As an application, some equivalent conditions about Markov properties of unimodal maps are generalized to multimodal maps

[en] In this work we study the diffusion of non-interacting overdamped particles, moving on unbiased disordered correlated potentials, subjected to Gaussian white noise. We obtain an exact expression for the diffusion coefficient which allows us to prove that the unbiased diffusion of overdamped particles on a random polymer does not depend on the correlations of the disordered potentials. This universal behavior of the unbiased diffusivity is a direct consequence of the validity of the Einstein relation and the decay of correlations of the random polymer. We test the independence on correlations of the diffusion coefficient for correlated polymers produced by two different stochastic processes, a one-step Markov chain and the expansion-modification system. Within the accuracy of our simulations, we found that the numerically obtained diffusion coefficient for these systems agree with the analytically calculated ones, confirming our predictions. (paper)

No abstract available

[en] We elucidate the structure of the hierarchy of the connected operators that commute with the Markov matrix of the totally asymmetric exclusion process. We derive the combinatorial formula for the connected operators that was conjectured in our previous work

[en] In this paper, we design AVTMR (All Voting Triple Modular Redundancy) and dual-duplex system which have a fault-tolerant characteristic, and two systems are compared in the evaluation of RAMS (Reliability, Availability, Maintainability and Safety) and MTTF (Mean Time To Failure). AVTMR system is designed in a triplicated voter technique and dual-duplex system in a comparator, and two systems are based on MC68000. To evaluate system characteristic, Markov modeling method is designed for reliability, availability, safety and MTTF (Mean Time To Failure), and RELEX6.0 tool is used for the calculation of failure rate of electrical components that is based on MILSPEC-217F. In this paper, we can see two systems are more high dependability than a single system, and AVTMR or dual-duplex system can be selected for a specific application system. Especially, because AVTMR and dual-duplex system have high RAMS better than a single system, they can be applied to life critical system such as an airplane and a high-speed railway system

[en] Semi-Markov models for systems undergoing periodic test and maintenance are developed. In particular, systems undergoing specific changes of state at predetermined instances of time and transiting to states with generally distributed sojourn times are considered. Problems addressed by the models are those concerned with optimum assessment of test intervals, and allowable outage times. Equivalent Markovian models allowing for the decomposition of a system of dimensionality N+M into two smaller problems of dimensionality N and M, respectively are developed. The general model is also specialized to systems with instantaneously testable components, unmonitored components undergoing tests (repair, maintenance) of fixed duration, and systems containing components characterized by limited allowable outage time (under test, or repair). Approximate equivalent Markov models are derived in these cases. Simple numerical examples are also presented

[en] This paper considers a condition-based maintenance policy for a two-unit deteriorating system. Each unit is subject to gradual deterioration and is monitored by sequential non-periodic inspections. It can be maintained by good as new preventive or corrective replacements. Every inspection or replacement entails a set-up cost and a component-specific unit cost but if actions on the two components are combined, the set-up cost is charged only once. A parametric maintenance decision framework is proposed to coordinate inspection/replacement of the two components and minimize the long-run maintenance cost of the system. A stochastic model is developed on the basis of the semi-regenerative properties of the maintained system state and the associated cost model is used to assess and optimize the performance of the maintenance model. Numerical experiments emphasize the interest of a control of the operation groupings

[en] A firm’s potential reward in future time from a customer can be determined by customer lifetime value (CLV). There are some mathematic methods to calculate it. One method is using Markov chain stochastic model. Here, a customer is assumed through some states. Transition inter the states follow Markovian properties. If we are given some states for a customer and the relationships inter states, then we can make some Markov models to describe the properties of the customer. As Markov models, CLV is defined as a vector contains CLV for a customer in the first state. In this paper we make a classification of Markov Models to calculate CLV. Start from two states of customer model, we make develop in many states models. The development a model is based on weaknesses in previous model. Some last models can be expected to describe how real characters of customers in a firm. (paper)