Earticle

본 논문에서는 페르마 퍼지 집합을 이용하여 퍼지 공학 시스템의 신뢰도를 분석하는 방법을 제안한다. 기 존의 직관 퍼지 집합은 소속정도와 비소속정도의 합이 1을 초과하지 않아야 하나, 실제 전문가 판단에서는 이러한 조건을 위배하는 경우가 발생한다. 이를 보완하기 위해 제안된 피타고라스 퍼지집합은 소속정도와 비소속정도의 제곱의 합이 1을 넘지 않도록 하였지만, 여전히 유사한 문제가 발행한다. 본 연구에서는 이러한 한계를 극복하기 위해 소속정도와 비소속정도의 세제곱합이 1을 초과하지 않도록 정의된 페르마 퍼지 집합을 활용한다. 제안한 방 법을 통해 공학 시스템의 신뢰도를 보다 효과적으로 평가할 수 있음을 보인다.

In this paper, we propose a method to analyze the reliability of the fuzzy engineering systems using the Fermatean fuzzy sets. The conventional intuitionistic fuzzy sets have the condition that the sum of the degree of membership and non-membership cannot exceed 1. However, this condition is often violated in expert decisionmaking. To address this problem, the proposed Pythagorean fuzzy sets ensures that the sum of the squares of the membership degree and non-membership not exceeds 1. However, similar problems still arise. To overcome this limitation, this study utilizes the Fermatean fuzzy sets so that the cube sum of the membership degree and non-membership does not exceed 1. We demonstrate that the proposed method can more effectively analysis the reliability of fuzzy engineering systems.

The paper reviews the methodologies of confirmatory data analysis(CDA) and exploratory data analysis(EDA) in statistical quality control(SQC), design of experiment(DOE) and reliability engineering(RE). The study discusses the properties of flexibility, openness, resistance and reexpression for EDA.

The Status quo of the reliability in China is described in this paper, a reliability surge is now spreading in China, covering the fields such as hardware, software, machinery and electronics. The reliability work in China was firstly conducted by the CEPREI Lab as far as early in the 1950s, and the reliability engineering in China has developed from the reliability of electronic products to that of machinery and non-electronic products, from hardware reliability to software reliability, from the attention to the reliability statistical test to emphasis on the reliability engineering test. Concern of Chinese companies about the reliability is the complete import of reliability engineering, the reliability testing, the software reliability and the reliability of lead-free soldering. Demonstration of reliability cases is given.

It is common to measure multiple coverage metrics during software testing. Software reliability growth models and coverage growth functions have been applied to each coverage metric to evaluate software reliability; however, analysis results for the individual coverage metrics may conflict with each other. This paper proposes the virtual coverage metric of a normalized first principal component in order to avoid conflicting cases. The use of the virtual coverage metric causes a negligible loss of information.

Coverage-based NHPP SRGMs have been introduced in order to incorporate the coverage growth behavior into the NHPP SRGMs. The coverage growth function representing the coverage growth behavior during testing is thus an essential factor of the coverage-based NHPP SRGMs. This paper proposes a class of discrete time coverage growth functions and illustrates its application to real data sets.

This paper introduces a systems engineering approach to reliability centered maintenance to address some of the weaknesses. Reliability centered maintenance is a systematic, disciplined process that produces an efficient equipment management strategy to reduce the probability of failure [1]. The study identifies the need for RCM, requirements analysis, design for RCM implementation. Value modeling is used to evaluate the value measures of RCM. The system boundary for the study has been selected as containment spray pump and its motor drive. Failure Mode and Criticality Effects analysis is applied to evaluate the failure modes while the logic tree diagram used to determine the optimum maintenance strategy. It is concluded that condition based maintenance tasks should be enhanced to reduce component degradation and thus improve reliability and availability of the component. It is recommended to apply time directed tasks to age related failures and failure finding tasks to hidden failures.

The objective of this work is to integrate reliability analysis into topology optimization problems. We introduce the reliability constraint in the topology optimization formulation, and the new model is called Reliability-Based Topology Optimization (RBTO). The application of the RBTO model gives a different topology relative to the classical topology optimization that should be deterministic. When comparing the structures resulting from the deterministic topology optimization and from the RBTO model, the RBTO model yields structures that are more reliable than the deterministic ones (for the same weight). Several applications show the importance of this integration.

The following lessons have been learned from the application of reliability methods in the practice of geotechnical engineering: 1. Establishing Goals Is Important; 2. Mitigating Consequences Can Be Effective; 3. Performance Depends on Systems; 4. Physical Factors Are Important in Statistical Models; 5. Too Much and Too Little Conservatism Are Both Problems; 6. Value of Information Depends on Decision Making; and 7. Effective Communication Is Essential. While the potential for application of reliability methods in the future is unlimited, there are major needs related to each of these lessons that will have to be addressed in order to realize this potential.

When Deterministic Design Optimization (DDO) methods are used, deterministic optimum designs are frequently pushed to the design constraint boundary, leaving little or no room for tolerances (or uncertainties) in design, manufacture, and operating processes. In the Reliability-Based Design Optimization (RBDO) model for robust system design, the mean values of uncertain system variables are usually used as design variables, and the cost is optimized subject to prescribed probabilistic constraints as defined by a nonlinear mathematical programming problem. Therefore, a RBDO solution that reduces the structural weight in uncritical regions does not only provide an improved design but also a higher level of confidence in the design. In this work, we seek to improve the quality of RBDO processes using efficient optimization techniques with object of improving the resulting objective function and satisfying the required constraints. Our recent RBDO developments show its efficiency and applicability in this context. So we present some recent structural engineering applications demonstrate the efficiency of these developed RBDO methods.

The main objective of this paper is come up with methodology approach for FPGA-based system in verification and validation lifecycle regarding software reliability using system engineering approach. The steps of both reverse engineering and re-engineering are carried out to implement an FPGA-based of safety critical system in Nuclear Power Plant. The reverse engineering methodology is applied to elicit the requirements of the system as well as gain understanding of the current life cycle and V&V activities of FPGA based-system. The re-engineering method is carried out to get a new methodology approach of software reliability, particularly Software Reliability Growth Model. For measure the software reliability of a given FPGA-based system, the following steps are executed as; requirements definition and measurement, evaluation of candidate reliability model, and the validation of the selected system. As conclusion, a new methodology approach for software reliability measurement using software reliability growth model is developed.

As business looks towards the $21^{\st}$ century, a long-term strategy that focuses on global sourcing will be the vital factor in whether companies win or lose. At the same time, with electronic components, it is important to ensure stable quality and reliability, together with other important parameters. In order to achieve this, creating an effective mechanism of failure analysis and database management for electronic components is essential. The authors introduce the actual mechanism employed by NEC and explain the ideas and insight they have obtained from their experience.

Due to the uncertainties related to the flaw assessment parameters, such as flaw size, fracture toughness, loading spectrum and so on, the probability concept is preferred over deterministic one in flaw assessment. In this study, efforts have been made to develop the reliability based flaw assessment procedure which combines the flaw assessment procedure of BS7910 and first-and second-order reliability methods (FORM/SORM). Both crack length and depth of semi-elliptical surface crack at weld toe were handled as random variable whose probability distribution was defined as Gaussian with certain means and standard deviations. Then the limit state functions from static rupture and fatigue perspective were estimated using FORM and SORM in joint probability space of crack depth and length. The validity of predicted limit state functions were checked by comparing it with those obtained by Monte Carlo simulation. It was confirmed that the developed methodology worked perfectly in predicting the limit state functions without time-consuming Monte Carlo simulation.

In Asia countries the productions of ship building and marine engines have been increasing, specially Japanese marine industries have worked hard after 1960s and Korean ones after 1980s. Recently the other countries, as Taiwan and China, have been working so that these hour Asian countries are occuping the high level of shared ratio of productions for gross tonnages and horse powers, which are 74 and 64[%] of the world ones ($8.6\times10$+6[GT], $8.6\times10$+6[PS]) in 1994. Korean industries had the highest shared ratio of production of tanker vessel and 2 stroke diesel engine as 45[%]($2.2\times10$+6[GT]) and 37[%]($1.0\times10$+6[PS]) which were more than those of Japan as 34 and 16[%] in 1989 respectively. Some marine databases and their network links among Asian countries are proposed due to the posibility of collection and analyses with their own specifications by the marine industries and operators as well as Japanese ship reliability investigation works(SRIW) like SRIC in Japan. During 1966 and 1996 16 times of SRIW in Japan have been carried out by ship reliability investigation group(SRIG) in Japan. There have been collected and evaluated a great number of field data of failures and maintenances($700\times10$+3[occ], $1.6\times10$+6[MH}) during running hours($13.4\times10$+6[Hrs]), from which many kinds of evaluation indices could be gotten as the three indices of occurring rate$\lambda$(52.2[occ/1000Hrs]), average man-hour mh(2.29[MH/occ]) and manning index MI(119[MH/1000Hrs]). An estimation example having the three indices$\lambda$, mh and MI were shown by the SRIC 1990 Data Base in Japan for the two kinds of fuel oil suppling subsystems which are dual fuel oil one(DFOS) and mono fuel oil one(MFOS). Three indices MI, and mh for DFOS and MFOS results in 7.16 and 5.20[MH/1000Hrs], 2.63 and 2.06[occ/1000 Hrs]. Therefore the more simple subsystem MFOS can save approximately 30[%] of maintenance load. Finlly an utilization methods are shown for the SRIC in Japan by means of computer system and worlwide internet links.

Purpose: This study evaluated the validity and reliability of therapeutic communication responses generated by GPT-5 by comparing different prompt-engineering strategies and identifying optimal methods for psychiatric nursing education. Methods: A methodological design compared four strategies?Zero-shot, Few-shot, Chain-of-Thought (CoT), and Role-prompt?applied to ten psychiatric nursing communication questions. Fourteen experts with over ten years of combined clinical and educational experience rated 40 anonymized responses using a 4-point scale. Inter-rater reliability was assessed with Fleiss' κ and Krippendorff's ? from 400 repeated outputs. Semantic consistency was examined using cosine similarity. Analyses were conducted in Python. Results: Role-prompt showed the highest content validity (mean=3.54±0.39, S-CVI/Ave=0.95), followed by CoT and Zero-shot. Inter-rater agreement was slight (κ=0.07; ?=0.15). Semantic consistency was highest for CoT (0.76±0.12) and Role-prompt (0.75±0.11). A Friedman test indicated significant differences among strategies (x2(3)=11.88, p=.008). Conclusion: Role-prompt yielded the most valid therapeutic responses, while CoT produced the most consistent outputs. These findings support the use of Role-prompt and CoT strategies to enhance the validity and reliability of therape.

Since The Korean Reliability Society had been founded in 1999, development history of reliability engineering in Korea is reviewed and research outputs and papers from 2008 to current are analyzed in terms of types of industry, product life cycle, hardware vs software, and theory vs application. The purpose of this research is to review the recent reliability engineering research conducted in Korea including development history as well as published papers to identify the weakness and/or deficiencies in order to suggest the future research directions, which would contribute the development of industries in Korea.

Industrial engineering has played a central role in creating knowledge on quality control and reliability engineering (Q&R) and delivering such knowledge to various industries. This special issue paper is prepared in celebration of the $40^{th}$ anniversary of the Korean Institute of Industrial Engineers (KIIE), and includes discussions on how Q&R areas have evolved over almost 100 years and on the current domestic and international trends of Q&R activities in industry as well as in academia. To identify academic research trends, all Q&R related papers published in the Journal of the Korean Institute of Industrial Engineers (JKIIE) and IE Interfaces are examined and classified according to their research topics. Recent Q&R related papers published in IIE Transactions are also examined and classified in a similar manner, and the papers published in KIIE journals are compared with those in IIE Transactions with respect to the research areas emphasized, yearly trend of each research area, type of systems studied, research approaches and methodologies adopted, etc. In addition, quality control activities in domestic industries are evaluated based on a recent survey conducted by Korea Productivity Center, and for domestic reliability engineering activities, government-led projects and their accomplishments over the past decade are introduced. Based on the above, recommendations are made for the future directions of academic research and Q&R activities in industry.

본 연구는 구독 경제의 급격한 성장 속에서 서비스 제공자가 직면하는 핵심 과제인 고객 유지와 운영 비용 간의 상충관계(Trade-off)를 해결하기 위한 수리적 최적화 프레임워크를 제안한다. 기존 연구들이 주로 가격 책정이나 수요 예측에 집중한 것과 달리, 본 연구는 신뢰성 공학의 예방 정비(Age Replacement) 모델을 구독 서비스 운영에 도입하여 배송 주기와 서비스 중단 시점을 핵심 의사결정 변수로 다룬다. 본 논문에서는 운영 방식에 따라 두 가지 최적화 모델을 제시한다. 첫째, 단일 고정 주기를 유지하며 최적 중단 시점(I*)을 결정하는 기본 모델(Model 1)과, 둘째, 고객의 초기 온보딩 이후 배송 주기를 조정하는 적응형 모델(Model 2)을 분석한다. 특히, 고객 집단의 이질성과 선택 효과(Selection Effect)를 반영하여 조건부 구독 확률인 위험률(Hazard Rate)이 비증가(Non-increasing)한다는 가정하에 이익률을 최대화하는 유일한 최적 정책의 존재 조건을수학적으로 증명하였다. 수치 분석 결과, 초기 전환 확률이 낮을수록 초기 단계를 최소화하고 비용 효율적인 후속 단계를 확장하는 전략이 유효함을 확인하였다. 본 연구는 서비스 제공자가 직관에 의존하던 배송 정책을 데이터 기반의 정량적 기준으로 최적화할수 있는 이론적 토대를 제공하며, 고객 생애 가치(CLV) 극대화를 위한 전략적 도구로서 기여할 것으로 기대된다.

With the rapid expansion of the subscription economy, service providers face the critical challenge of maximizing customer lifetime value while balancing the trade-off between customer churn risk and operational costs. While previous research has focused on dynamic pricing and demand forecasting, this study introduces a novel mathematical framework based on reliability engineering principles?specifically, the age replacement model?to optimize delivery intervals and service termination policies. We propose and analyze two optimization models: (1) Model 1, a baseline model with a single fixed interval and an optimal stopping point (  ), and (2) Model 2, an adaptive model that allows a one-time interval change to transition from an intensive onboarding phase to a maintenance phase. Incorporating the selection effect and population heterogeneity, we mathematically demonstrate the existence of a unique optimal policy under the assumption of a non-increasing hazard rate. Numerical analysis reveals that when initial conversion rates are low, the optimal strategy involves minimizing the first stage and extending a cost-effective second stage to maximize long-term profitability. This research provides service providers with a data-driven methodology to scientifically determine “how often” and “how long” to engage with subscribers, offering a practical tool for maximizing the profit rate in diverse subscription business environments.

Recently, the LRFD and the PSF based on structural reliability assessment have been applied to NPP designs in behalf of the conventional deterministic design methods. In the risk-informed structural integrity, it is especially possible to optimize design procedures considering cost, manufacturing and maintenance because the structural reliability concepts have confirmed the reliability for which a designer aims. Generally, in order to evaluate the PSF, the LRFD which is the design concept for evaluating safety factors respectively on the limit state function including load and resistance. This study certifies the concept and its applications of the PSF using the LRFD based on the structural reliability engineering.

퍼지 공학 시스템의 운용 시 시스템의 오류, 불확실한 데이터, 부정확한 데이터 등으로 오류가 발생하게 된다. 그러므로 이러한 불확실성과 부정확함을 다루는 방법이 필요하게 된다. 이러한 비결정성을 다루는 방법이 퍼지집합 이론이다. 퍼지집합은 0과 1 사이의 실수로 소속정도를 표현한다. 퍼지집합이 하나의 실수로 소속정도를 표현하는 한계를 해결한 방법이 직관 퍼지집합이다. 직관 퍼지집합은 소속정도와 비소속정도를 각각 0과 1 사이의 실수로 각각 표현한다. 소속정도를 단수한 구간이 아닌 수학적인 기본을 가지는 완비격자에 속하는 구간으로 표현한 퍼지집합이 L-퍼지집합이다. L-퍼지집합은 완비격자 L에 속하는 값으로 소속정도를 표현한다. 다중 퍼지집합은 복수 개의 소속정도를 사용하여 다중 퍼지집합의 소속정도를 기술한다. 다중 퍼지집합은 퍼지집합, 직관 퍼지집합 그리고 L-퍼지집합의 확장이 된다. 그러므로 다중 퍼지집합은 이러한 퍼지집합을 사용할 곳에 사용하는 것이 가능한 유연성을 가지게 된다. 이 방법은 공학적 시스템과 다기준 의사결정 시스템에 적용가능하며, 신뢰도 평가를 위해 퍼지집합, 직관 퍼지집합, L-퍼지집합을 사용하는 공학 시스템에서 활용가능한 유연성을 가질 수 있다.

When we operate the fuzzy engineering systems, Several errors may can occur due to system errors, uncertain data, and incomplete data etc.. Therefore, a method to deal with such uncertainty and inaccuracy of data is needed. The fuzzy set theory is proposed to appropriate method to deal with these indeterministics such as uncertain, vague, incomplete data, etc.. The fuzzy sets express the belongingness degree as a real number between 0 and 1. Intuitionistic fuzzy sets are a way to solve the limitation of fuzzy sets expressing the belongingness with a single real number. Intuitionistic fuzzy sets describe the belongingness degree and non-belongingness degree as a real number between 0 and 1, respectively. The L-fuzzy sets are a kind of fuzzy sets whose the belongingness degree is expressed not as a simple interval, but as an interval belonging to a complete lattice with mathematical fundamentals. The L-fuzzy sets express the belongingness degree as a value in the complete lattice L. The multi-fuzzy sets represent the those belongingness degree as multiple belongingnesses. The multi-fuzzy sets are extensions of fuzzy sets, intuitionistic fuzzy sets, and L-fuzzy sets. Therefore, the multi-fuzzy sets may have the flexibility to be used in places using those fuzzy sets. The method can be applied to the engineering systems and the multi-criteria decision-making systems and may have flexibility to use in the engineering systems that use the fuzzy sets, intuitionistic fuzzy sets, and L-fuzzy sets for the reliability assessment.

공학시스템을 설계 및 운용할 경우에 이 시스템의 신뢰도는 중요한 이슈가 된다. 즉, 불확실성과 부정확함을 다루는 것이 필요한다는 것을 의미한게 된다. 이러한 모호함을 포함하고 있는 시스템의 신뢰도를 다루는 방법이 퍼지집합이론이다. 퍼지집합은 0과 1사이의 실수로 소속정도를 표현한다. 직관퍼지집합은 소속정도와 비소속정도를 각각 0과 1사이의 실수로 표현한다. 피타고라스 퍼지집합은 소속정도와 비소속정도의 합이 1을 초과하는 문제를 해결한 퍼지집합이다. 구간값 피타고라스 퍼지집합은 피타고라스 퍼지집합의 상한과 하한을 구간으로 표현한 집합이다. 큐빅집합은 구간값 퍼지집합과 퍼지지합의 쌍으로 표현한다. 큐빅집합은 매개변수를 구간으로 분석을 할 경우 하나의 매개변수를 다룰 수 있는 방법을 제공한다. 또한 큐비 피타고라스 퍼지집합은 구간값 피타고라스 퍼지집합과 피타고라스 퍼지집합의 쌍으로 표현하므로 소속정도와 비소속정도의 합이 1을 초과하는 문제는 발생하지 않는다. 본 연구에서는 큐빅 피타고라스 퍼지집합을 기반으로 하여 퍼지공학시스템의 신뢰도를 평가하는 방법을 제안한다. 큐빅 피타고라스 퍼지집합은 주어지는 조건에 따라 큐빅집합, 피타고라스 퍼지집합 등으로 축약할 수 있다. 그러므로 큐빅 피타고라스 퍼지집합을 사용한 방법은 이들의 방법을 모두 함의 한다고 할 수 있다.

When designing and operating engineering systems, the reliability of these systems become an important issue. This means that it is necessary to deal with uncertainty and uncorrectness. Fuzzy set theory provide a way to deal with the reliability of systems containing such ambiguity. Fuzzy sets express the belongingness degree as a real number between 0 and 1. Intuitionistic fuzzy sets describe the belongingness degree and non-belongingness degree as real number between 0 and 1, respectively. Pythagorean fuzzy sets are a fuzzy set that solves the problem where the sum of the belongingness degree and non-belongingness degree exceeds 1. Interval-valued Pythagorean fuzzy sets are a set that expresses the upper and lower limits of the Pythagorean fuzzy set as intervals. cubic sets are expressed as the pair of an interval-valued fuzzy set and a fuzzy set. Cubic sets provide a way to handle a single parameter when analyzing the parameter as a interval. In addition, the Cubic Pythagorean fuzzy sets are expressed as a pair of an interval-valued Pythagorean fuzzy set and a Pythagorean fuzzy set, so the problem that the sum of the belongingness degree and non-belongingness degree exceeds 1 does not occur. In this study, we propose a method to evaluate the reliability of fuzzy engineering systems based on cubic Pythagorean fuzzy sets. Cubic Pythagorean fuzzy sets can be reduced to cubic sets, Pythagorean fuzzy sets, etc. depending on given conditions. Therefore, it can be said that the method using the cubic Pythagorean fuzzy set implies all of these methods.