• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.989-999
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• 2001

In this paper we show that certain notions of negative dependence are preserved under a bivariate homogenous poisson shock model in which two devices shocks form two independent poisson processes.

• Journal of the Korean Data and Information Science Society
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• v.15 no.4
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• pp.773-782
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• 2004

In this paper, a random shock model for a system is considered. Each shock arriving according to a Poisson process decreases the state of the system by a random amount. A repairman arriving according to another Poisson process of rate $\lambda$ repairs the system only if the state of the system is below a threshold $\alpha$. After assigning various costs to the system, we calculate the long-run average cost and show that there exist a unique value of arrival rate $\lambda$ and a unique value of threshold $\alpha$ which minimize the long-run average cost per unit time.

• 한국데이터정보과학회:학술대회논문집
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• 2004.10a
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• pp.33-42
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• 2004

In this paper, a random shock model for a system is considered. Each shock arriving according to a Poisson process decreases the state of the system by a random amount. A repairman arriving according to another Poisson process of rate $\lambda$ repairs the system only if the state of the system is below a threshold $\alpha$. After assigning various costs to the system, we calculate the long-run average cost and show that there exist a unique value of arrival rate $\lambda$ and a unique value of threshold $\alpha$ which minimize the long-run average cost per unit time.

• International Journal of Reliability and Applications
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• v.4 no.2
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• pp.71-77
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• 2003

We propose, in this paper, the discrete version of NBU$_{Mg}$and show that the NBU$_{Mg}$ class is preserved under both the non-homo geneous poisson shock model and the general shock model.

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.471-479
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• 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.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.725-733
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• 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
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• v.15 no.1
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• pp.11-22
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• 2014

New classes of life distributions called new better (worse) than used at age $t_0$ in Laplace transform order, NBUL- $t_0$(NWUL - $t_0$) are introduced. For the classes NBUL - $t_0$(NWUL - $t_0$), preservation under convolution, mixture, mixing and the homogeneous Poisson shock model are studied. In the sequel, we obtain a test for $H_0$ : F is exponential versus $H_1$ : F is NBUL - $t_0$ and not exponential. The critical values and the powers of this test are calculated to assess the performance of the test. It is shown that the proposed test has high efficiencies for some commonly used distributions in reliability. Sets of real data are used as examples to elucidate the use of the proposed test for practical problems.

• International Journal of Reliability and Applications
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• v.17 no.2
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• pp.107-119
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• 2016

A new concept of aging classes namely new better (worse) than used at age $t_0$ in moment generating function order, $NBU_{mgf}-t_0$ ($NWU_{mgf}-t_0$) is introduced. For the classes $NBU_{mgf}-t_0$ ($NWU_{mgf}-t_0$), preservation under convolution, mixture, mixing and the homogeneous Poisson shock model are studied. In the sequel, nonparametric test is proposed, the asymptotic normality of the class is established and the asymptotic null variance is estimated. The percentiles and powers of this test are tabulated. The asymptotic efficiencies for some alternatives distributions are derived. Finally sets of real data are used as examples to elucidate the use of the proposed test in practical application.

• Journal of Korean Society for Quality Management
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• v.24 no.3
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• pp.31-36
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• 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).

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.29 no.2
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• pp.109-120
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• 2017

A discounted cost model for preventive maintenance of armor units of rubble-mound breakwaters is mathematically derived by combining the deterioration model based on a discrete-time stochastic process of shock occurrence with the cost model of renewal process together. The discounted cost model of condition-based maintenance proposed in this paper can take into account the nonlinearity of cumulative damage process as well as the discounting effect of cost. By comparing the present results with the previous other results, the verification is carried out satisfactorily. In addition, it is known from the sensitivity analysis on variables related to the model that the more often preventive maintenance should be implemented, the more crucial the level of importance of system is. However, the tendency is shown in reverse as the interest rate is increased. Meanwhile, the present model has been applied to the armor units of rubble-mound breakwaters. The parameters of damage intensity function have been estimated through the time-dependent prediction of the expected cumulative damage level obtained from the sample path method. In particular, it is confirmed that the shock occurrences can be considered to be a discrete-time stochastic process by investigating the effects of uncertainty of the shock occurrences on the expected cumulative damage level with homogeneous Poisson process and doubly stochastic Poisson process that are the continuous-time stochastic processes. It can be also seen that the stochastic process of cumulative damage would depend directly on the design conditions, thus the preventive maintenance would be varied due to those. Finally, the optimal periods and scale for the preventive maintenance of armor units of rubble-mound breakwaters can be quantitatively determined with the failure limits, the levels of importance of structure, and the interest rates.