• Proceedings of the Korean Reliability Society Conference
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• 2005.06a
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• pp.121-129
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• 2005

In this paper, we consider a periodic preventive maintenance(PM) policy in which each PM reduces the hazard rate of amount proportional to the failure intensity, which increases since the last PM and slows down the wear-out speed to that of new one. And the proportion of reduction in hazard rate decreases with the number of PMs. Our model is similar to $ARI_1$ proposed by Doyen and Gaudoin(2004) in the sense of reduction of hazard rate. Our model has totally different wear-out pattern of hazard rate after PM's, however, and the proportion of reduction depends on the number of PM's. Assuming that the system undergoes only minimal repairs at failures between PM's, the expected cost rate per unit time is obtained. The optimal number N of PM and the optimal period x, which minimize the expected cost rate per unit time are discussed. Explicit solutions for the optimal periodic PM are given for the Weibull distribution case.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.791-798
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• 2014

Wu and Clements-Croome (2005) suggest the preventive maintenance (PM) model with random maintenance quality. They assume that each PM resets the failure rate to zero and the rate of increases of the failure rate gets higher after each additional PM. However a system may not be restored to as good as new immediately after the completion of PM. Thus, this paper modifies the Wu and Clements-Croome's PM model and then the optimal PM policy is suggested. To determine the optimal PM policy, we utilize the expected cost rate per unit time for our model. That is, we obtain the optimal number and the optimal period by minimizing the expected cost rate per unit time. The numerical examples are presented for illustrative purpose.

• Journal of the military operations research society of Korea
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• v.15 no.1
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• pp.54-62
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• 1989

This paper presents a corrective maintenance model to determine either type of maintenance actions upon failure of the system. Types of maintenance actions considered are minimal repair and replacement. Minimal repair cost is assumed to be random, whereas replacement cost is fixed. A policy, B(t), which determines the type of maintenance action based on the estimated minimal repair cost when the system fails at time t is adopted. To obtain an optimal policy, an expected maintenance cost per unit time is derived and is minimized with respect to B(t).

• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.909-923
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• 2008

This paper considers the replacement model and the preventive maintenance model following the expiration of combination warranty for a repairable system. If the system fails after the combination warranty is expired, then it is minimally repaired at each failure. The criterion used to determine the optimal replacement policy and the optimal preventive maintenance policy is the overall value function based on the expected cost rate per unit time and the expected downtime per unit time. The numerical examples are presented for illustrative purpose when the failure time follows a Weibull distribution.

• Journal of the Korean Data and Information Science Society
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• v.21 no.5
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• pp.873-882
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• 2010

This paper considers a Bayesian approach to replacement policy following the expiration of non-renewing combination warranty. The non-renewing combination warranty is the combination of the non-renewing free replacement warranty and the non-renewing pro-rata replacement warranty. We use the criterion based on the expected cost and the expected downtime to determine the optimal replacement period. To do so, we obtain the expected cost rate per unit time and the expected downtime per unit time, respectively. When the failure times are assumed to follow a Weibull distribution with uncertain parameters, we propose the optimal replacement policy based on the Bayesian approach. The overall value function suggested by Jiang and Ji (2002) is utilized to determine the optimal replacement period. Also, the numerical examples are presented for illustrative purpose.

• International Journal of Reliability and Applications
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• v.12 no.1
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• pp.41-48
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• 2011

This paper considers the maintenance model suggested by Jung and Park (2010) to adopt the Bayesian approach and obtain an optimal replacement policy following the expiration of NFRRW. As the criteria to determine the optimal maintenance period, we use the expected cost during the life cycle of the system. When the failure times are assumed to follow a Weibull distribution with unknown parameters, we propose an optimal maintenance policy based on the Bayesian approach. Also, we describe the revision of uncertainty about parameters in the light of data observed. Some numerical examples are presented for illustrative purpose.

• Journal of Korean Society for Quality Management
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• v.48 no.1
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• pp.201-214
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• 2020

Purpose: The purpose of this paper is to determine an optimal number of cycle times for the replacement under the circumstance where the system is replaced at the periodic time and the multiple number of working cycles whichever occurs first and the system is minimally repaired between the replacements if it fails. Methods: The system is replaced at periodic time () or cycle time, whichever occurs first, and is repaired minimally when it fails between successive replacements. To determine the optimal number of cycle times, the expected total cost rate is optimized with respect to the number of cycle times, where the expected total cost rate is defined as the ratio of the expected total cost between replacements to the expected time between replacements. Results: In this paper, we conduct a sensitivity analysis to find the following results. First, when the expected number of failures per unit time increases, the optimal number of cycle times decreases. Second, when the periodic time for replacement becomes longer, the optimal number of cycle times decreases. Third, when the expected value for exponential distribution of the cycle time increases, the optimal number of cycle times increases. Conclusion: A mathematical model is suggested to find the optimal number of cycle times and numerical examples are provided through the sensitivity analysis on the model parameters to see the patterns for changes of the optimal number of cycle times.

• Journal of the Korean Data and Information Science Society
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• v.8 no.1
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• pp.85-89
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• 1997

In this paper, we consider a random replacement model with minimal repair, which is a generalization of the random replacement model introduced Lee and Lee(1994). It is assumed that a system is minimally repaired when it fails and replaced only when the accumulated operating time of the system exceeds a threshold time by a supervisor who arrives at the system for inspection according to Poisson process. Assigning the corresponding cost to the system, we obtain the expected long-run average cost per unit time and find the optimum values of the threshold time and the supervisor's inspection rate which minimize the average cost.

• Proceedings of the Korean Statistical Society Conference
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• 2005.11a
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• pp.73-78
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• 2005

This paper considers a preventive maintenance policy following the expiration of renewing warranty, Most preventive maintenance models assume that each PM costs a fixed predetermined amount regardless of the effectiveness of each PM. However, it seems more reasonable to assume that the PM cost depends on the degree of effectiveness of the PM activity. In this paper we consider a periodic preventive maintenance policy following the expiration of renewing warranty when the PM cost is an increasing function of the PM effect. The optimal number and period for the periodic PM policy with effect dependent cost that minimize the expected cost rate per unit time over an infinite time span are obtained.

• Journal of the military operations research society of Korea
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• v.17 no.1
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• pp.43-60
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• 1991

Consider N queues without arrivals and with m identical servers. All jobs are independent and service requirements of jobs in a queue are i.i.d. random variables. At any time only one server may be assigned to a queue and switching between queues are allowed. A unit cost is imposed per job per unit time. The objective is to minimized the expected total cost. An flow approximation model is considered and an upperbound for the percentage error of best nonswitching policies to an optimal policy is found. It is shown that the best nonswitching policy is not worse than $11\%$ of an optimal policy For the stochastic model, we consider the case in which the service requirements of all jobs are i.i.d. with an exponential distribution. A longest first policy is shown to be optimal and a worst case analysis shows that the nonswitching policy which starts with the longest queues is not worse than $11\%$ of the optimal policy.