• 제목/요약/키워드: mean-variance cost function

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고장을 고려한 공정평균 이동에 대한 조정시기 결정 (Determination of Resetting Time to the Process Mean Shift with Failure)

  • 이도경
    • 산업경영시스템학회지
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    • 제42권4호
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    • pp.145-152
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    • 2019
  • All machines deteriorate in performance over time. The phenomenon that causes such performance degradation is called deterioration. Due to the deterioration, the process mean of the machine shifts, process variance increases due to the expansion of separate interval, and the failure rate of the machine increases. The maintenance model is a matter of determining the timing of preventive maintenance that minimizes the total cost per wear between the relation to the increasing production cost and the decreasing maintenance cost. The essential requirement of this model is that the preventive maintenance cost is less than the failure maintenance cost. In the process mean shift model, determining the resetting timing due to increasing production costs is the same as the maintenance model. In determining the timing of machine adjustments, there are two differences between the models. First, the process mean shift model excludes failure from the model. This model is limited to the period during the operation of the machine. Second, in the maintenance model, the production cost is set as a general function of the operating time. But in the process mean shift model, the production cost is set as a probability functions associated with the product. In the production system, the maintenance cost of the equipment and the production cost due to the non-confirming items and the quality loss cost are always occurring simultaneously. So it is reasonable that the failure and process mean shift should be dealt with at the same time in determining the maintenance time. This study proposes a model that integrates both of them. In order to reflect the actual production system more accurately, this integrated model includes the items of process variance function and the loss function according to wear level.

손실함수를 적용한 공정평균 이동에 대한 조정시기 결정 (Determination of the Resetting Time to the Process Mean Shift by the Loss Function)

  • 이도경
    • 산업경영시스템학회지
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    • 제40권1호
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    • pp.165-172
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    • 2017
  • Machines are physically or chemically degenerated by continuous usage. One of the results of this degeneration is the process mean shift. Under the process mean shift, production cost, failure cost and quality loss function cost are increasing continuously. Therefore a periodic preventive resetting the process is necessary. We suppose that the wear level is observable. In this case, process mean shift problem has similar characteristics to the maintenance policy model. In the previous studies, process mean shift problem has been studied in several fields such as 'Tool wear limit', 'Canning Process' and 'Quality Loss Function' separately or partially integrated form. This paper proposes an integrated cost model which involves production cost by the material, failure cost by the nonconforming items, quality loss function cost by the deviation between the quality characteristics from the target value and resetting the process cost. We expand this process mean shift problem a little more by dealing the process variance as a function, not a constant value. We suggested a multiplier function model to the process variance according to the analysis result with practical data. We adopted two-side specification to our model. The initial process mean is generally set somewhat above the lower specification. The objective function is total integrated costs per unit wear and independent variables are wear limit and initial setting process mean. The optimum is derived from numerical analysis because the integral form of the objective function is not possible. A numerical example is presented.

생산량과 공정분산이 변하는 공정평균이동 문제의 마모한계 결정 (Determination of the Wear Limit to the Process Mean Shift Problem with Varying Product and Process Variance)

  • 이도경
    • 산업경영시스템학회지
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    • 제43권3호
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    • pp.95-100
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    • 2020
  • Machines and facilities are physically or chemically degenerated by continuous usage. One of the results of this degeneration is the process mean shift. The representative type of the degeneration is wear of tool or machine. According to the increasing wear level, non-conforming products cost and quality loss cost are increasing simultaneously. Therefore a periodic preventive resetting the process is necessary. The total cost consists of three items: adjustment cost (or replacement cost), non-conforming cost due to product out of upper or lower limit specification, and quality loss cost due to difference from the process target value and the product characteristic value among the conforming products. In this case, the problem of determining the adjustment period or wear limit that minimizes the total cost is called the 'process mean shift' problem. It is assumed that both specifications are set and the wear level can be observed directly. In this study, we propose a new model integrating the quality loss cost, process variance, and production volume, which has been conducted in different fields in previous studies. In particular, for the change in production volume according to the increasing in wear level, we propose a generalized production quantity function g(w). This function can be applied to most processes and we fitted the g(w) to the model. The objective equation of this model is the total cost per unit wear, and the determining variables are the wear limit and initial process setting position that minimize the objective equation.

Cpm+ 기준에서의 공정평균이동에 대한 재조정 기간 결정 (Determination of the Resetting Time to the Process Mean Shift based on the Cpm+)

  • 이도경
    • 산업경영시스템학회지
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    • 제41권1호
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    • pp.110-117
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    • 2018
  • Machines and facilities are physically or chemically degenerated by continuous usage. One of the results of this degeneration is the process mean shift. By the result of degeneration, non-conforming products and malfunction of machine occur. Therefore a periodic preventive resetting the process is necessary. This type of preventive action is called 'preventive maintenance policy.' Preventive maintenance presupposes that the preventive (resetting the process) cost is smaller than the cost of failure caused by the malfunction of machine. The process mean shift problem is a field of preventive maintenance. This field deals the interrelationship between the quality cost and the process resetting cost before machine breaks down. Quality cost is the sum of the non-conforming item cost and quality loss cost. Quality loss cost is due to the deviation between the quality characteristics from the target value. Under the process mean shift, the quality cost is increasing continuously whereas the process resetting cost is constant value. The objective function is total costs per unit wear, the decision variables are the wear limit (resetting period) and the initial process mean. Comparing the previous studies, we set the process variance as an increasing concave function and set the quality loss function as Cpm+ simultaneously. In the Cpm+, loss function has different cost coefficients according to the direction of the quality characteristics from target value. A numerical example is presented.

생산량이 감소하는 공정평균이동 문제에서 Cpm+ 기준의 손실함수를 적용한 보전모형 (A Maintenance Model Applying Loss Function Based on the Cpm+ in the Process Mean Shift Problem in Which the Production Volume Decreases)

  • 이도경
    • 산업경영시스템학회지
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    • 제44권1호
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    • pp.45-50
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    • 2021
  • Machines and facilities are physically or chemically degenerated by continuous usage. The representative type of the degeneration is the wearing of tools, which results in the process mean shift. According to the increasing wear level, non-conforming products cost and quality loss cost are increasing simultaneously. Therefore, a preventive maintenance is necessary at some point. The problem of determining the maintenance period (or wear limit) which minimizes the total cost is called the 'process mean shift problem'. The total cost includes three items: maintenance cost (or adjustment cost), non-conforming cost due to the non-conforming products, and quality loss cost due to the difference between the process target value and the product characteristic value among the conforming products. In this study, we set the production volume as a decreasing function rather than a constant. Also we treat the process variance as a function to the increasing wear rather than a constant. To the quality loss function, we adopted the Cpm+, which is the left and right asymmetric process capability index based on the process target value. These can more reflect the production site. In this study, we presented a more extensive maintenance model compared to previous studies, by integrating the items mentioned above. The objective equation of this model is the total cost per unit wear. The determining variables are the wear limit and the initial process setting position that minimize the objective equation.

절삭공정에서 가공공구의 초기위치와 마모한계 결정 (Determination of Wear Limit and the Initial Setting Position of Tool for a Machining Process)

  • 이도경
    • 산업경영시스템학회지
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    • 제17권31호
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    • pp.91-98
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    • 1994
  • Most of machines are physically or chemically degenerated by continuous usage. There- fore, a preventive maintenance is necessary. Producing defects are caused by process shift in mean and variance which are due to three types of degeneration. We develope the function of process variance from the experimental data and determine the optimal tool wear limit and the initial setting position of tool by considering the percent defective cost and the preventive maintenance cost.

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보전비용 증가와 생산량 감소를 고려한 공정평균이동 모형 (A Process Mean Shift Model Considering The Increasing Maintenance Cost and The Decreasing Production Volume)

  • 이도경
    • 융합정보논문지
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    • 제11권3호
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    • pp.125-131
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    • 2021
  • 모든 장비는 지속적인 사용에 의해 공정의 생산성과 경제성은 감소한다. 그러므로 일정 시점에서는 공정평균이동 문제라는 설비에 대한 예방보전이 필요하다. 설비의 보전시기를 결정함에 있어, 우리는 기존 연구에서 부분적으로 진행되어 온 보전모형들을 확장하고 통합함으로써 다양한 상황이 발생하는 생산 현장을 반영한 보전모형을 제시하고자 한다. 이를 구현하기 위해 제품규격은 상하한의 양쪽을 설정했으며, 적합품에 대해 품질손실함수를 도입했다. 마모수준에 대한 공정분산은 상수가 아닌 함수로 설정했으며, 특히 제품생산량과 보전비용에 있어서는 마모수준에 대한 함수를 개발하여 적용했다. 이로써 본 연구는 현장의 다양한 공정에 대부분 적용할 수 있는 보전모형이 될 것으로 생각한다. 추후 연구에서는 보전모형을 구성하는 부적합비용, 품질손실비용, 보전비용에 더하여 제품판매로 인한 수익 항목을 추가한 전체 수익 최대화 문제로 전개할 수 있을 것이며, 크게는 본 연구의 모형에 고장률을 도입한 보전모형으로의 확장도 생각해 볼 수 있을 것이다.

은닉층 다차원공간의 Vertex를 이용한 MLP의 은닉 노드 축소방법 (Reducing the Number of Hidden Nodes in MLP using the Vertex of Hidden Layer's Hypercube)

  • 곽영태;이영직;권오석
    • 한국통신학회논문지
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    • 제24권9B호
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    • pp.1775-1784
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    • 1999
  • 본 논문은 학습하는 동안 은닉 노드의 출력에 대한 분산과 평균을 평가하는 새로운 cost function을 이용하여 불필요한 은닉 노드를 축소하는 방법을 제안한다. 제안한 cost function은 필요한 은닉 노드를 활성화시키고 불필요한 은닉 노드를 상수화 시켜 제거한다. 필기체 숫자인식을 통한 실험에서 제안한 방법은 높은 인식률과 단축된 학습 시간을 나타내며 은닉 노드의 수를 37.2%까지 축소할 수 있었다.

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Mean-Variance Analysis for Optimal Operation and Supply Chain Coordination in a Green Supply Chain

  • Yamaguchi, Shin;Goto, Hirofumi;Kusukawa, Etsuko
    • Industrial Engineering and Management Systems
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    • 제16권1호
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    • pp.22-43
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    • 2017
  • It is urgently-needed to construct a green supply chain (GSC) from collection of used products through recycling of them to sales of products using the recycled parts. Besides, it is necessary to consider the uncertainty in product demand as a risk in a GSC. This study proposes the optimal operations for a GSC with a retailer and a manufacturer. A retailer pays an incentive for collection of used products from customers and sells a single type of products in a market. A manufacturer produces the products ordered by the retailer, using recyclable parts with acceptable quality and compensates the collection cost of used products as to the recycled parts. This paper discusses the following risk attitudes: risk-neutral attitude, risk-averse attitude, and risk-prone attitude. Using mean-variance analysis, the optimal decisions for product order quantity, collection incentive, and lower limit of quality level, in the decentralized GSC (DGSC) and the integrated GSC (IGSC) are made. DGSC optimizes the utility function of each member. IGSC does that of the whole system. The analysis numerically investigates how (i) risk attitude and (ii) quality of recyclable parts affect the optimal operations. Supply chain coordination between GSC members to shift IGSC from DGSC is discussed.

위험도기반 최적송전확장계획 (Risk-based Optimal Transmission Expansion Planning)

  • 손민균;김동민;김진오
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 2006년도 추계학술대회 논문집 전력기술부문
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    • pp.393-395
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    • 2006
  • In competitive market, it is important to establish a plan of transmission expansion considering uncertainty of future generation and load behavior. For this reason, revised transmission expansion model is proposed in this paper. In the proposed model, information of predictable future condition are included in a cost function of transmission expansion investment. Also, to reduce risk of the investment, mean-variance Markowitz approach is added to the objective function of cost. By optimization programming, the most robust and the minimum cost plan can be obtained.

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