• Proceedings of the Korean Reliability Society Conference
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• 2000.11a
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• pp.387-395
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• 2000

Circular consecutive-k-out-of-n:F system when the failure of component is dependent is studied. We assume that the failure of a component in the system increase the failure rate of the survivor which is working just before the failed component. In this case, a mean time to failure (MTTF), a average failure number of the system, and the expected cost per unit time are obtained. Then the minimum number of consecutive failed components to cause system failure to minimize the expected cost per unit time is determined as searching paths to system failure. And various numerical examples are studied.

• Earthquakes and Structures
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• v.9 no.4
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• pp.851-873
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• 2015

A methodology for estimation of statistical properties (viz. mean and standard deviation) of the expected seismic damage to reinforced concrete framed structures subject to corrosion of reinforcement, over a specified reference time (typically the service life of the structure) is proposed in this paper. The damage to the structure under the earthquake loading is characterised by the damage index, determined using the modified Park and Ang damage model. The reduction in area, yield strength and strain at ultimate of steel reinforcement, and the reduction in compressive strength of cover concrete due to corrosion are taken into account in the estimation of damage. The proposed methodology is illustrated through an example problem. From the results obtained, it is noted that there is an increase of about 70% in the mean value of expected seismic damage to the reinforced concrete frame considered over a reference time of 30 years when effect of corrosion is taken into consideration. This indicates that there is a need to consider the effect of corrosion of reinforcement on the estimation of expected seismic damage.

• International Journal of Quality Innovation
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• v.2 no.2
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• pp.136-144
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• 2001

The Markov Chain approach is used to develop an economic adjustment model of a process whose quality can be affected by a single special cause, resulting in changes of the process mean by incorrect adjustment of the process when it is operating according to its capability. The $\bar{X}$ control chart is thus used to signal the special cause. It is demonstrated that the expressions for the expected cycle time and the expected cycle cost are easier to obtain by the proposed approach than by adopting that in Collani, Saniga and Weigang (1994). Furthermore, this approach would be easily extended to derive the expected cycle cost and the expected cycle time for the case of multiple special causes or multiple control charts. A numerical example illustrates the proposed method and its application.

• Journal of Korean Society for Quality Management
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• v.35 no.4
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• pp.140-146
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• 2007

In this paper, we consider a periodic imperfect preventive maintenance(PM) policy in which the system's failure rate after each PM remains unchanged. The system undergoes only minimal repairs at failures between PMs. Exact mathematical formula of the expected cost rate per unit time is derived. Optimal number of PMs and optimal maintenance period are derived by minimizing the expected cost rate per unit time. A numerical example is provided to illustrate the proposed approach under Weibull lifetime distribution.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.403-420
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• 1994

An economic design of the $\bar{X}-R$ chart using variable sample size (VSS) scheme is proposed in this paper. In this design the sample size at each sampling time changes according to the values of the previous two sample statistics, sample mean and range. The VSS scheme uses large sample if the sample statistics appear near inside the control limits and smaller sample otherwise. The set of process parameters, such as the sampling interval, control limits and the sample sizes, are chosen to minimize the expected cost per hour. The efficiency of the VSS scheme is compared to the fixed sample size one for cases where there is multiple of assignable causes. Percent reductions of the expected cost in the VSS design are calculated for some given sets of cost parameters. It is shown that the VSS scheme improves the confidence of the procedure and performs statistically better in terms of the number of false alarms and the average time to signal, respectively.

• Journal of Applied Reliability
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• v.15 no.1
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• pp.6-11
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• 2015

Maintenance plays an important role in keeping product availability, reliability and quality at an appropriate level. In this paper, two-types of maintenance policies are studied following the expiration of two-dimensional (2D) free replacement warranty. Both the fixed-maintenance-period policy and the variable-maintenance-period policy are based on a specified region of the warranty defined in terms of age and usage where all failures are minimally repaired. An accelerating failure time (AFT) model is used to allow for the effect of usage rate on product degradation. The maintenance model that arises following the expiration of 2D warranty is discussed. The expected cost rates per unit time from the user's point of view are formulated and the optimal maintenance policies are determined to minimize the expected cost rate to the user. Finally numerical examples are given to illustrate the optimal maintenance polices.

• Journal of Applied Reliability
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• v.14 no.2
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• pp.122-128
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• 2014

In this paper, we consider the periodic preventive maintenance model for a repairable system following the expiration of extended warranty under replacement-repair warranty. Under the replacement-repair warranty, the failed system is replaced or minimally repaired by the manufacturer at no cost to the user. Also, under extended warranty, the failed system is minimally repaired by the manufacturer at no cost to the user during the original extended warranty period. As a criterion of the optimality, we utilize the expected cost rate per unit time during the life cycle from the user's perspective. And then we determine the optimal preventive maintenance period and the optimal preventive maintenance number by minimizing the expected cost rate per unit time. Finally, the optimal periodic preventive maintenance policy is given for Weibull distribution case.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.773-788
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• 2000

Statistical process control (SPC) and engineering process control (EPC) are based on different strategies for processes quality improvement. SPC reduces process variability by detecting and eliminating special causes of process variation. while EPC reduces process variability by adjusting compensatory variables to keep the quality variable close to target. Recently there has been needs for a process control proceduce which combines the tow strategies. This paper considers a combined scheme which simultaneously applies SPC and EPC techniques to reduce the variation of a process. The process model under consideration is an integrated moving average(IMA) process with a step shift. The EPC part of the scheme adjusts the process back to target at every fixed monitoring intervals, which is referred to a repeated adjustment scheme. The SPC part of the scheme uses an exponentially weighted moving average(EWMA) of observed deviation from target to detect special causes. A Markov chain model is developed to relate the scheme's expected cost per unit time to the design parameters of he combined control scheme. The expected cost per unit time is composed of off-target cost, adjustment cost, monitoring cost, and false alarm cost.

• International Journal of Reliability and Applications
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• v.9 no.1
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• pp.113-122
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• 2008

In this paper, we consider a periodic preventive maintenance policy in which each preventive maintenance reduces the hazard rate of amount proportional to the failure intensity, which increases since the system started to operate. And the effect of preventive maintenance at each preventive maintenance epoch is different. The expected cost rate per unit time for the proposed model is obtained. We discuss the optimal number N of the periodic preventive maintenance and the optimal period x, which minimize the expected cost rate per unit time and obtain the optimal preventive maintenance schedule for given cost structures of the model. A numerical example is given for the purpose of illustrating our results when the failure time distribution is Weibull distribution.

• Journal of the Korean Operations Research and Management Science Society
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• v.38 no.2
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• pp.25-42
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• 2013

We consider a project time-cost tradeoff problem with two milestones, where one of the jobs has an uncertain processing time. Unless each milestone is completed on time, some penalty cost may be imposed. However, the penalty costs can be avoided by compressing the processing times of some jobs, which requires additional resources or costs. The objective is to minimize the expected total costs subject to the constraint on the expected project completion time. We show that the problem can be solved in polynomial time if the precedence graph of a project is a chain.