Earticle

기계 및 설비는 지속적인 사용으로 인해 물리적, 화학적으로 열화된다. 그 결과, 공정평균은 초기 설정값 을 유지하지 못하고 규격 상한 또는 하한 쪽으로 이동하게 되고, 결국 제품은 규격을 벗어나게 된다. 지속적인 생 산으로 인한 설비의 열화는 공정평균 뿐 만 아니라 공정 분산에도 영향을 미친다. 기존 연구에서는 공정분산의 변 화를 제대로 반영하지 않음으로 인해, 공정평균이동 모형이 생산현장 상황을 제대로 반영하지 못하고 있다. 본 연 구에서는 이를 반영하기 위해, 금속 및 목재 절삭공정에 있어 진동으로 인한 공정분산 분석에 장점이 있는 Gompertz 모형을 적용했다. 또한, 기존 연구들에서 부분적으로 개발되어온 모형의 개별 비용 항목을 통합함으로 써, 장비 비용이 증가하고 운영의 중요성이 강조되는 공장자동화 시대에 현장을 보다 더 반영할 수 있는 공정평균 이동 모형을 제시했다.

Machines and facilities are physically or chemically degenerated by continuous usage. As a result, the process mean cannot maintain the initial setting value and moves toward the upper or lower specification, and ultimately the products deviates from the specification. Deterioration due to continuous production affects not only the process mean but also the process variance. In this case, the effectiveness of the model is greatly reduced because it cannot properly reflect the production site. To compensate for this weakness, we applied the Gompertz model, which has advantages in analyzing process dispersion due to vibration in metal and wood cutting processes. In addition, by integrating the individual cost items of the model that has been partially developed in existing studies, we presented a process average shift model that can better reflect the field in the era of factory automation, where equipment costs increase and the importance of operation is emphasized.

모든 장비는 지속적인 사용에 의해 공정의 생산성과 경제성은 감소한다. 그러므로 일정 시점에서는 공정평 균이동 문제라는 설비에 대한 예방보전이 필요하다. 설비의 보전시기를 결정함에 있어, 우리는 기존 연구에서 부분 적으로 진행되어 온 보전모형들을 확장하고 통합함으로써 다양한 상황이 발생하는 생산 현장을 반영한 보전모형을 제시하고자 한다. 이를 구현하기 위해 제품규격은 상하한의 양쪽을 설정했으며, 적합품에 대해 품질손실함수를 도 입했다. 마모수준에 대한 공정분산은 상수가 아닌 함수로 설정했으며, 특히 제품생산량과 보전비용에 있어서는 마 모수준에 대한 함수를 개발하여 적용했다. 이로써 본 연구는 현장의 다양한 공정에 대부분 적용할 수 있는 보전모 형이 될 것으로 생각한다. 추후 연구에서는 보전모형을 구성하는 부적합비용, 품질손실비용, 보전비용에 더하여 제 품판매로 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.

The problem of determining the maintenance point which minimizes the process-related total cost is called the ‘process mean shift problem’. By expanding and integrating the existing maintenance models that have been partially progressed, we present a expanded and integrated maintenance model which reflects the production site where various situations occur. To implement this, we set both the upper and lower limits of the product specification, and adopted the quality loss function for conforming items. Also, we set the process variance of the wear level as a function rather than a constant. In this study, we developed two general functions to the wear level. One is about the production volume and the other is maintenance cost. As a result, this study is expected to be a maintenance model that can be applied to various processes. In the future, this study can be developed as a profit maximization model by adding profit items from product sales, and expansion to a maintenance model that introduces failure to the model of this study can be considered.

오늘날 반도체나 석유 화학 공정과 같이 프로세스 중심의 산업에서는 관측된 자료들 사이에 자기 상관이 존재한다. 자기상관이 존재하는 공정에 대한 관리 방법으로는 관측치를 이용하여 뱃치 평균이 독립에 가까워지도록 뱃치를 구성하여 관리하거나, 관측치의 EWMA (지수 가중치 이동 평균) 통계량을 EWMA 관리도에 적용하는 방법등이 주로 사용되고 있다. 본 논문에서는 관찰치에 대한 관리 방법으로 일반적으로 사용되는 UBM 의 뱃치 크기를 결정하는 방법을 소개하고, ARL(평균 실행 길이)을 기반으로 최적 뱃치 크기를 정하는 방법과 그러한 뱃치 구성에서 공정의 표준 편차를 추정하는 방법을 제안 한다. 자기상관이 존재하는 공정에 대한 개선된 관리도를 제안하고자 한다.

In today's process-oriented industries, such as semiconductor and petrochemical processes, autocorrelation exists between observed data. As a management method for the process where autocorrelation exists, a method of using the observations is to construct a batch so that the batch mean approaches to independence, or to apply the EWMA (Exponentially Weighted Moving Average) statistic of the observed value to the EWMA control chart. In this paper, we propose a method to determine the batch size of UBM (Unweighted Batch Mean), which is commonly used as a management method for observations, and a method to determine the optimal batch size based on ARL (Average Run Length) We propose a method to estimate the standard deviation of the process. We propose an improved control chart for processes in which autocorrelation exists.

This paper considers the problem of monitoring the mean of a normally distributed process variable when the objective is to effectively detect both a sustained shift and a linear drift. The design and application of a generalized likelihood ratio (GLR) chart for simultaneously monitoring a sustained shift and a linear drift are evaluated. The GLR chart has the advantage that when we design this chart, we do not need to specify the size of the parameter change. The performance of the GLR chart is compared with that of other control charts, such as the standard cumulative sum (CUSUM) charts and the cumulative score (CUSCORE) charts. And we compare the proposed GLR chart with the GLR charts designed for monitoring only a sustained shift and for monitoring only a linear drift. Finally, we also compare the proposed GLR chart with the chart combinations. We show that the proposed GLR chart has better overall performance for a wide range of shift sizes and drift rates relative to other control charts, when a special cause produces a sustained shift and/or a linear drift in the process mean.

공장자동화는 인건비 상승, 에너지 효율, 안전 확보 등의 다양한 이유에 의해 이미 세계적으로 확산하고 있는 추세이며, 자동화 설비는 기본적으로 데이터를 수집하는 센서 및 로봇들로 구성된다. 공장자동화의 가장 큰 장점인 연속 생산을 보장하고, 총 운영비용을 최소화하기 위해서는 무엇보다, 본 연구에서 제시하는 공정평균이동 문제를 포함한 최적화된 설비보전 일정이 필요하다. 자동화 공장에서의 설비보전 모형은 실제 현장에 적용되어야 하므로, 이론적 가정이 포함된 보전모형이나 부분적인 모형은 사용할 수 없다. 그러므로 본 연구에서는 실제 자동화 설비의 총비용을 최소로 하는 마모한계 혹은 보전주기 및 설비의 초기 위치를 찾기 위해, 공정평균이동 모형을 구성하는 세 가지 항목인 부적합 비용, 품질손실비용 및 보전비용을 통합한 모형을 제시한다. 그리고 개별 항목들을 구성하는 공정분산, 생산량 등을 비롯한 여러 매개변수들에 대해 상수가 아니라 해당 항목들의 특성을 반영할 수 있는 일반화 함수를 제시한다. 이로써 센서들에 의해 수집된 데이터를 사용하여 알고리즘을 통해 전체 비용을 최소화하는 매개변수들을 추정할 수 있으며, 최적 보전주기와 초기 설비위치를 도출할 수 있다. 특히, 보전비용에 대해서는 품질보증 정책으로 인해, 일정 기간 이내의 보전에 대해서는 무상 혹은 동일 비용으로 제공하는 경우 및 이 기간 이후의 비용 증가에 대해 다양한 형태로 반영할 수 있도록 보전비용을 함수화 하였다. 이로써 본 연구가 다양한 자동화 설비에 적용 가능하리라 생각한다. 이 설비보전 모형은 지속적인 생산으로 인해 설비가 열화하는 경우에 대한 공정평균이동 모형으로, 정전이나 설비 자체의 불량과 같은 이상원인에 의한 파국고장은 제외한 예방보전 모형에 해당한다.

Factory automation is already spreading globally for various reasons such as rising labor costs, energy efficiency, and ensuring safety. Automated facilities are composed of robots and sensors that collect data. In order to ensure continuous production, which is the biggest advantage of factory automation, and to minimize total operating costs, an optimized facility maintenance schedule including the process mean shift problem presented is needed. Because the facility maintenance models in automated factories must be applied to actual sites, maintenance models that include theoretical assumptions or partial models cannot be used. Therefore, in order to find the wear limit(or maintenance cycle) and initial position of equipment that minimizes the total cost, we propose an integrated process mean shift model which is composed of three items, namely nonconformity cost, quality loss cost, and maintenance cost. We present generalized functions that can reflect the characteristics of individual items rather than constants for various parameters, including process variance and production volume, that make up individual items. This allows us to estimate parameters that minimize total cost through the algorithms using data collected by sensors and derive the optimal maintenance cycle and initial equipment location. Regarding the maintenance cost, due to the quality assurance policy, we considered cases in which maintenance within a certain period is provided free of charge or at the same cost. We converted the maintenance cost into a function so that the cost increase after the warranty period can reflect various types. As a result, we believe that this study can be applied to various automated facilities. This is a process mean shift model for cases where the facility deteriorates due to continuous production and corresponds to a preventive maintenance model that excludes catastrophic failures due to abnormal causes such as power outages or defects in the facility itself.

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.

공장 자동화는 정확하고 일관성 있는 작업을 가능하게 함으로써, 제품 품질을 보장하여 생산 효율성과 비용절감을 크게 향상시킬 수 있다. 이 외에도 작업장 안전을 향상시키고, 파업과 무관하게 사업의 연속성을 보장 등 많은 장점들로 인해 산업계에서 자동화는 지속적으로 확대 도입되고 있다. 자동화 공장에서는 대부분 작업들이 설비에 의해 수행되므로, 설비에 대한 효율적인 운영이 보다 더 중요해 지며, 효율적인 운영에는 매우 큰 비중으로 설비에 대한 보전 정책이 포함된다. 본 연구에서는 이러한 추세에 부응하여 설비와 관련한 두 가지 보전 활동 분야인 부적합품 기준의 공정평균이동 모형과 고장과 연관된 설비의 신뢰성 모형의 특성과 단점을 소개하고, 별도로 진행되어온 두 분야가 실무에 적용되기 위한 통합의 필요성을 언급하고 그 결과를 제시했다. 공정평균이동 모형에서는 공정분산, 품질손실비용 및 재조정비용 항목들에 대해, 설비 및 제품 등과 관련한 대부분의 특성들을 상수가 아닌 함수로 설정한 모형을 도입함으로써, 본 연구가 제시하는 모형이 다양한 공정들에 적용할 수 있도록 했다. 이는 제시된 보전 모형에 포함된 17개의 매개변수들에 대해 생산 현장에서 사용하고 있는 값들을 대입함으로써 가능해 진다. 설비 고장 시 보전정책으로는 수명교환 정책을 도입했다. 본 연구에서는 고장 발생에 대해서는 고장분포함수로 가장 널리 사용되고 있는 와이블분포를 적용했다. 이로써 본 연구에서 제시하는 통합 모형이 생산현장에서 보다 널리 적용될 수 있을 것으로 생각한다.

Factory automation can significantly improve production efficiency and cost savings by ensuring product quality by enabling accurate and consistent operations. In addition to this, automation is continuously being expanded in the industry due to its many advantages, such as improving workplace safety and ensuring business continuity regardless of strikes. In an automated factory, most of the work is performed by equipment, so efficient management of the equipment becomes more important, and efficient management includes a very large portion of equipment maintenance policy. In response to this trend, this study introduces the characteristics and shortcomings of two maintenance activity areas related to equipment: the process mean shift model based on nonconforming products and the reliability model of equipment related to failures. In response to this trend, this study introduced two maintenance activity areas related to equipment: the process mean shift model based on nonconforming products and the reliability model of equipment related to failures, and presented an integrated model for the two areas that have been conducted separately. In this study, the necessity of an integrated model for the two fields that have been conducted separately was mentioned and presented to overcome the shortcomings of the two fields of conservation models and to apply them to practice. In the process mean shift model, most of the characteristics related to equipment and products, such as process variance, quality loss cost, and readjustment cost, are set as functions rather than constants, enabling the model presented in this study to be applied to various processes This is possible by substituting the values in the production field into the 17 parameters in the proposed model. As a maintenance policy in equipment failure, a life replacement policy has been introduced, and the failure rate function related to failure occurrence must satisfy the non-decreasing function condition. In this study, the Weibull distribution, the most widely used failure distribution function, was applied. Therefore, the model presented in this study is expected to be a maintenance model that can be applied more practically in production sites.

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.

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.

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.

The problem of selecting the optimal target values in a canning process is considered for situations where there is a linear shift in the mean of the content of a can which is assumed to be normally distributed with known variance. The target values are initial process mean, length of resetting cycle and controllable upper limit. Profit models are constructed which involve give-away, rework, and resetting costs. Methods of finding the optimal target values are presented and a nemerical example is given.