• Journal of the Korean Data and Information Science Society
• /
• 제16권4호
• /
• pp.725-733
• /
• 2005

A system subject to random shocks is considered. The shocks arrive according to a Poisson process and the amount of each shock is exponentially distributed. In this paper, a periodic inspection policy for the system is compared with a random inspection policy. After assigning several maintenance costs to the system, we calculate and compare the long-run average costs per unit time under two policies.

• International Journal of Reliability and Applications
• /
• 제1권1호
• /
• pp.49-64
• /
• 2000

We consider a system whose inherent life follows an Erlang distribution, which is subject to two heterogeneous random shocks. Minor shocks arrive according to a renewal process and each causes the system to fail independently with a certain probability. A major shock whose interarrival times follow an Erlang distribution causes the system to fail with probability one. The Laplace transform of the distribution of the time to system failure is derived in a functional form of the Laplace transform of the interarrival time distribution of minor shocks. An algorithm is given for the computation of the moments of the time to system failure.

• Journal of the Korean Statistical Society
• /
• 제24권1호
• /
• pp.141-147
• /
• 1995

A diffusion model for a system subject to random shocks is introduced. It is assumed that the state of system is modeled by a Brownian motion with negative drift and an absorbing barrier at the origin. It is also assumed that the shocks coming to the system according to a Poisson process decrease the state of the system by a random amount. It is further assumed that a repairman arrives according to another Poisson process and repairs or replaces the system i the system, when he arrives, is in state zero. A forward differential equation is obtained for the distribution function of X(t), the state of the systme at time t, some boundary conditions are discussed, and several interesting characteristics are derived, such as the first passage time to state zero, F(0,t), the probability of the system being in state zero at time t, and F(0), the limit of F(0,t) as t tends to infinity.

• 대한안전경영과학회지
• /
• 제23권4호
• /
• pp.105-112
• /
• 2021

This paper presents a periodic replacement policy for a system subject to shocks when the system is operating for a finite random horizon. The system is subject to shocks during operation, and each shock causes downgrading of the system performance and makes it more expensive to run by the additional running cost. Shocks arrive according to a nonhomogeneous or a renewal process, and we develop periodic replacement policies under a finite random operating horizon. The optimum periodic replacement interval which minimizes the total operating cost during the horizon is found. Numerical examples are presented to demonstrate the results.

• East Asian Economic Review
• /
• 제19권1호
• /
• pp.3-38
• /
• 2015

Fama's (1984) volatility relations show that the risk premium in foreign exchange markets is more volatile than, and is negatively correlated with the expected rate of depreciation. This paper studies these relations from the perspective of goods markets frictions. Using a sticky-price general equilibrium model, we show that near-random walk behaviors of both exchange rates and consumption, in response to monetary shocks, can be derived endogenously. Based on this approach, the paper provides quantitative results on Fama's volatility relations.

• Smart Structures and Systems
• /
• 제14권4호
• /
• pp.559-567
• /
• 2014

The model of unit dynamic reliability of repairable k/n (G) system with unit strength degradation under repeated random shocks has been developed according to the stress-strength interference theory. The unit failure number is obtained based on the unit failure probability which can be computed from the unit dynamic reliability. Then, the transfer probability function of the repairable k/n (G) system is given by its Markov property. Once the transfer probability function has been obtained, the probability density matrix and the steady-state probabilities of the system can be retrieved. Finally, the dynamic reliability of the repairable k/n (G) system is obtained by solving the differential equations. It is illustrated that the proposed method is practicable, feasible and gives reasonable prediction which conforms to the engineering practice.

• 한국국방경영분석학회지
• /
• 제10권1호
• /
• pp.23-39
• /
• 1984

Consider a failure model for a stochastic system. A shock is any perturbation to the system which causes a random amount of damage to the system. Any of the shocks can cause the system to fail at shock times. The amount of damage at each shock is a function of the sum of the magnitudes of damage caused from all previous shocks. The times between shocks form a sequence of independent and identically distributed random variables. The system must be replaced upon failure at some cost but it also can be replaced before failure at a lower cost. The long term expected cost per unit time criterion is used. Structural relationships of the optimal replacement policy under the appropriate regularity conditions will be developed. And these relationships will provide theoretical background for the algorithm development.

• Journal of the Korean Statistical Society
• /
• 제24권2호
• /
• pp.471-479
• /
• 1995

A random shock model for a linearly deteriorating system is introduced. The system deteriorating linearly with time is subject to random shocks which arrive according to a Poisson process and decrease the state of the system by a random amount. The system is repaired by a repairmen arriving according to another Poisson process if the state when he arrives is below a threshold. Explicit expressions are deduced for the characteristic function of the distribution function of X(t), the state of the system at time t, and for the distribution function of X(t) if X(t) is over the threshold. The stationary case is briefly discussed.

• Earthquakes and Structures
• /
• 제27권4호
• /
• pp.303-315
• /
• 2024

This study proposes a comprehensive methodology for estimating accumulative damage of bridge structures under multiple seismic excitations, in the framework of site-specific probabilistic hazard analysis. Specifically, a typical earthquake-prone region in China is chosen to perform probabilistic seismic hazard analysis (PSHA) to find the mean annual rate (MAR) of ground motion intensity at a specific level, based on which, a mass of ground motion observations is selected to construct random earthquake sequences with various number of shocks. Then, nonlinear time history analysis is implemented on the finite element (FE) model of a RC girder bridge at the site of interest, to investigate structural responses under different earthquake sequences, and to develop predictive model for cumulative damage computation, in which, a scalar seismic intensity measure (IM) is adopted and its performance in damage prediction is discussed by an experimental column. Furthermore, a mathematic model is established to calculate occurrence probability of earthquakes with various number of shocks, based on PSHA and homogenous Poisson random process, and a modified cumulative damage indicator is proposed, accounting for probabilistic occurrence of various earthquake scenarios. At end, the applicability of the proposed methodology to main shock and aftershock scenarios is validated, and characteristics of damage accumulation under different multiple earthquake scenarios are discussed.

• 품질경영학회지
• /
• 제24권3호
• /
• pp.31-36
• /
• 1996

A Markovian stochastic model for a system subject to random shocks is considered. Each shock arriving according to a Poisson process decreases the state of the system by a random amount. A repairman arrives at the system periodically for inspection and repairs the system only if the state is below a threshold. Costs are assigned to each inspection of the repairman, to each repair, and to the system being in bad states below the threshold. The expected long run average cost is obtained and compared with that of the random inspection introduced by Lee and Lee(1994).