Effect of Non-Metallic Inclusion from the Continuous Casting Process on the Multi-Stage Forging Process and the Tensile Strength of the Bolt: A Case Study

The paper presents the influence of non-metallic inclusions on the multi-stage forging process and the mechanical properties of the dodecagon socket bolt used in the automotive industry. The detected metallurgical defect was so large that it directly influenced the mechanical properties of the bolt and resulted in failure to meet the requirements of the mechanical property class. In order to assess the defect, an X-ray examination and metallographic examination of the defective bolt were performed, showing exogenous non-metallic inclusion. The size of the defect on the cross section was 0.531 mm in width and 1.523 mm in length; the defect was continuous along the entire axis of the bolt. In analysis, a finite element method (FEM) simulation of the multi-stage forging process was designed, taking into account a non-metallic inclusion parallel to the sample axis, reflecting the studied case. The process of defect propagation due to material upset in the head area was analyzed. The final forging stage in shaping the dodecagonal socket and filling the flange area was particularly studied. The effect of the defect was observed to significantly reduce the effective cross-section as a result of the expansion of the defect perpendicular to the axis of the bolt. The mechanical properties of products with and without the defect were analyzed. In the first step, the hardness test confirmed that the required value for the mechanical class 8.8 of both bolt types was obtained. In the second step, the bolts were subjected to a static tensile test. The bolts without the defect gave a positive result, while all 10 bolts with the defect gave a negative result, achieving a tensile strength below the requirements. Tensile strength tests were confirmed by metallographic tests and FEM simulation with perpendicular inclusion spread in the area of the head. The bolts were damaged directly under the bolt head, which is inconsistent with the requirements of ISO 898-1. It has been shown that non-metallic inclusions with orientation in accordance with the axis of the bolt can directly cause loss of functionality and these defects should be detected even before assembling in the machine element.

Enhancement of Mechanical and Dissolution Properties of a Cast Magnesium Alloy via Equal Angular Channel Processing

Two decades of the Shale Revolution has transforming transformed the global energy market, in part by the adaption of multi-stage dissolvable frac plugs. Magnesium has been favored for the bulk of plugs, requiring development of materials to suit specific field requirements. Herein, the mechanical and dissolution results from equal channel angular pressing (ECAP) of two cast dissolvable magnesium alloy are described. ECAP was selected as a route to increase the mechanical properties of two formulations of dissolvable magnesium, as solutionizing failed. In this study, 1” square cross section samples cast Mg alloys formulations containing rare earth were processed at temperatures ranging from 200 to 350 °C, at a rate of 0.005”/s, with a backpressure from 0 to 70 MPa, in a brass, or brass + graphite sheet. Generally, the yield and ultimate tensile strength (UTS) doubled for all. For formulation DM-2, the yield increased from 100 MPa to 250 MPa; UTS from 175 MPa to 325 MPa, but the strain fell from 2 to 1%. Formulation DM-3 yield increased from 75 MPa to 200 MPa, UTS from 150 MPa to 275 MPa, with strain increasing from 1 to 3%. Meanwhile, ECAP has also been found to reduce the dissolution rate significantly. A microstructural analysis showed grain refinement of the alloy and the movement of secondary phases away from the grain boundary. It is believed that reconfiguration of the grain boundary phases increased the mechanical properties and decreased the dissolution rate. ECAP processing of dissolvable high rare earth content magnesium is possible despite the brittleness of the material. ECAP is a possible processing route to increase mechanical properties for dissolvable aluminum alloys that do not extrude.

Economic Efficiency of Cassava Production in Nimba County, Liberia: An Output-Oriented Approach

In Liberia, many of the agricultural households cultivate cassava for either sustenance purposes, or to generate farm income. Many of the concentrated cassava farmers reside in Nimba, a north-eastern County that borders two other economies: the Republics of Cote D’Ivoire and Guinea. With a high demand for cassava output and products in emerging Asian markets coupled with an objective of the Liberia agriculture policies to increase the competitiveness of valued agriculture crops; there is a need to examine the level of resource-use efficiency for many agriculture crops. However, there is a scarcity of information on the efficiency of many agriculture crops, including cassava. Hence the study applying an output-oriented method seeks to assess the economic efficiency of cassava farmers in Nimba County, Liberia. A multi-stage sampling technique was employed to generate a sample for the study. From 216 cassava farmers, data related to on-farm attributes, socio-economic and institutional factors were collected. The stochastic frontier models, using the Translog functional forms, of production and revenue, were used to determine the level of revenue efficiency and its determinants. The result showed that most of the cassava farmers are male (60%). Many of the farmers are either married, engaged or living together with a spouse (83%), with a mean household size of nine persons. Farmland is prevalently obtained by inheritance (95%), average farm size is 1.34 hectares, and most cassava farmers did not access agriculture credits (76%) and extension services (91%). The mean cassava output per hectare is 1,506.02 kg, which estimates average revenue of L$23,551.16 (Liberian dollars). Empirical results showed that the revenue efficiency of cassava farmers varies from 0.1% to 73.5%; with the mean revenue efficiency of 12.9%. This indicates that on average, there is a vast potential of 87.1% to increase the economic efficiency of cassava farmers in Nimba by improving technical and allocative efficiencies. For the significant determinants of revenue efficiency, age and group membership had negative effects on revenue efficiency of cassava production; while farming experience, access to extension, formal education, and average wage rate have positive effects. The study recommends the setting-up and incentivizing of farmer field schools for cassava farmers to primarily share their farming experiences with others and to learn robust cultivation techniques of sustainable agriculture. Also, farm managers and farmers should consider a fix wage rate in labor contracts for all stages of cassava farming.

Evaluating the Understanding of the University Students (Basic Sciences and Engineering) about the Numerical Representation of the Average Rate of Change

The present study aimed to evaluate the understanding of the students in Tehran universities (Iran) about the numerical representation of the average rate of change based on the Structure of Observed Learning Outcomes (SOLO). In the present descriptive-survey research, the statistical population included undergraduate students (basic sciences and engineering) in the universities of Tehran. The samples were 604 students selected by random multi-stage clustering. The measurement tool was a task whose face and content validity was confirmed by math and mathematics education professors. Using Cronbach's Alpha criterion, the reliability coefficient of the task was obtained 0.95, which verified its reliability. The collected data were analyzed by descriptive statistics and inferential statistics (chi-squared and independent t-tests) under SPSS-24 software. According to the SOLO model in the prestructural, unistructural, and multistructural levels, basic science students had a higher percentage of understanding than that of engineering students, although the outcome was inverse at the relational level. However, there was no significant difference in the average understanding of both groups. The results indicated that students failed to have a proper understanding of the numerical representation of the average rate of change, in addition to missconceptions when using physics formulas in solving the problem. In addition, multiple solutions were derived along with their dominant methods during the qualitative analysis. The current research proposed to focus on the context problems with approximate calculations and numerical representation, using software and connection common relations between math and physics in the teaching process of teachers and professors.

Formation of Protective Aluminum-Oxide Layer on the Surface of Fe-Cr-Al Sintered-Metal-Fibers via Multi-Stage Thermal Oxidation

The objective of this paper is to investigate the formation and adhesion of a protective aluminum-oxide (Al2O3, alumina) layer on the surface of Iron-Chromium-Aluminum Alloy (Fe-Cr-Al) sintered-metal-fibers. The oxide-scale layer was developed via multi-stage thermal oxidation at 930 oC for 1 hour, followed by 1 hour at 960 oC, and finally at 990 oC for 2 hours. Scanning Electron Microscope (SEM) images show that the multi-stage thermal oxidation resulted in the formation of predominantly Al2O3 platelets-like and whiskers. SEM images also reveal non-uniform oxide-scale growth on the surface of the fibers. Furthermore, peeling/spalling of the alumina protective layer occurred after minimum handling, which indicates weak adhesion forces between the protective layer and the base metal alloy.  Energy Dispersive Spectroscopy (EDS) analysis of the heat-treated Fe-Cr-Al sintered-metal-fibers confirmed the high aluminum content on the surface of the protective layer, and the low aluminum content on the exposed base metal alloy surface. In conclusion, the failure of the oxide-scale protective layer exposes the base metal alloy to further oxidation, and the fragile non-uniform oxide-scale is not suitable as a support for catalysts.

Availability, Accessibility and Utilization of Information and Communication Technology in Teaching and Learning Islamic Studies in Colleges of Education, North-Eastern, Nigeria

The use of Information and Communication Technology (ICT) in tertiary institutions by lecturers and students has become a necessity for the enhancement of quality teaching and learning. This study examined availability, accessibility and utilization of ICT in Teaching-Learning Islamic Studies in Colleges of Education, North-East, Nigeria. The study adopted multi-stage sampling technique, in which, five out of the eleven Colleges of Education (both Federal and State owned) were purposively selected for the study. Primary data was drawn from the respondents by the use of questionnaire, interviews and observations. The results of the study, generally, indicate that the availability and accessibility to ICT facilities in Colleges of Education in North-East, Nigeria, especially in teaching/learning delivery of Islamic studies were relatively inadequate and rare to lecturers and students. The study further reveals that the respondents’ level of utilization of ICT is low and only few computer packages and internet services were involved in the ICT utilization, which is yet to reach the real expected situation of the globalization and advancement in the application of ICT if compared to other parts of the world, as far as the teaching and learning of Islamic studies is concerned. Observations and conclusion were drawn from the findings and finally, recommendations on how to improve on ICT availability, accessibility and utilization in teaching/ learning were suggested.

Multi-Stage Multi-Period Production Planning in Wire and Cable Industry

This paper presents a methodology for serial production planning problem in wire and cable manufacturing process that addresses the problem of input-output imbalance in different consecutive stations, hoping to minimize the halt of machines in each stage. To this end, a linear Goal Programming (GP) model is developed, in which four main categories of constraints as per the number of runs per machine, machines’ sequences, acceptable inventories of machines at the end of each period, and the necessity of fulfillment of the customers’ orders are considered. The model is formulated based upon on the real data obtained from IKO TAK Company, an important supplier of wire and cable for oil and gas and automotive industries in Iran. By solving the model in GAMS software the optimal number of runs, end-of-period inventories, and the possible minimum idle time for each machine are calculated. The application of the numerical results in the target company has shown the efficiency of the proposed model and the solution in decreasing the lead time of the end product delivery to the customers by 20%. Accordingly, the developed model could be easily applied in wire and cable companies for the aim of optimal production planning to reduce the halt of machines in manufacturing stages.

Study on the Integration Schemes and Performance Comparisons of Different Integrated Solar Combined Cycle-Direct Steam Generation Systems

The integrated solar combined cycle (ISCC) system has a series of advantages such as increasing the system power generation, reducing the cost of solar power generation, less pollutant and CO2 emission. In this paper, the parabolic trough collectors with direct steam generation (DSG) technology are considered to replace the heat load of heating surfaces in heat regenerator steam generation (HRSG) of a conventional natural gas combined cycle (NGCC) system containing a PG9351FA gas turbine and a triple pressure HRSG with reheat. The detailed model of the NGCC system is built in ASPEN PLUS software and the parabolic trough collectors with DSG technology is modeled in EBSILON software. ISCC-DSG systems with the replacement of single, two, three and four heating surfaces are studied in this paper. Results show that: (1) the ISCC-DSG systems with the replacement heat load of HPB, HPB+LPE, HPE2+HPB+HPS, HPE1+HPE2+ HPB+HPS are the best integration schemes when single, two, three and four stages of heating surfaces are partly replaced by the parabolic trough solar energy collectors with DSG technology. (2) Both the changes of feed water flow and the heat load of the heating surfaces in ISCC-DSG systems with the replacement of multi-stage heating surfaces are smaller than those in ISCC-DSG systems with the replacement of single heating surface. (3) ISCC-DSG systems with the replacement of HPB+LPE heating surfaces can increase the solar power output significantly. (4) The ISCC-DSG systems with the replacement of HPB heating surfaces has the highest solar-thermal-to-electricity efficiency (47.45%) and the solar radiation energy-to-electricity efficiency (30.37%), as well as the highest exergy efficiency of solar field (33.61%).

Impact of Ownership Structure on Provision of Staff and Infrastructure for Implementing Computer Aided Design Curriculum in Universities in South-East Nigeria

Instruction towards acquiring skills in the use of Computer Aided Design technologies has become a vital part of architectural education curriculum in the digital era. Its implementation, however, requires deployment of extra resources to build new infrastructure, acquisition and maintenance of new equipment, retraining of staff and recruitment of new ones who are knowledgeable in this area. This study sought to examine the impact that ownership structure of Nigerian universities had on provision of staff and infrastructure for implementing computer aided design curriculum with a view to developing a framework for the evaluation for appropriate implementation by the institutions. Survey research design was employed. The focus was on departments of architecture in universities in south-east Nigeria accredited by the National Universities Commission. Data were obtained in the areas of infrastructure and personnel for CAD implementation. A multi-stage stratified random sampling method was adopted. The first stage of stratification involved the accredited departments. Random sampling by balloting was then carried out. At the second stage, sampling size formulae was applied to obtain respondents’ number. For data analysis, analysis of variance tool for testing differences of means was used. With ρ < 0.5, the study found that there was significant difference between private-funded, state-funded and federal-funded departments of architecture in the provision of personnel and infrastructure. The implications of these findings were that for successful implementation leading to attainment of CAD proficiency to occur in every institution regardless of ownership structure, minimum evaluation guidelines needed to be set. A regular comparison of implementation in institutions was recommended as a means of rating performance. This will inform better interaction with those who consistently show weakness to challenge them towards improvement.

The Corporate Vision Effect on Rajabhat University Brand Building in Thailand

This study aims to (1) investigate the corporate vision factor influencing Rajabhat University brand building in Thailand and (2) explore influences of brand building upon Rajabhat University stakeholders’ loyalty, and the research method will use mixed methods to conduct qualitative research with the quantitative research. The qualitative will approach by Indebt-interview the executive of Rathanagosin Rajabhat University group for 6 key informants and the quantitative data was collected by questionnaires distributed to stakeholder including instructors, staff, students and parents of the Rathanagosin Rajabhat University group for 400 sampling were selected by multi-stage sampling method. Data was analyzed by Structural Equation Modeling: SEM and also provide the focus group interview for confirming the model. Findings corporate vision had a direct and positive influence on Rajabhat University brand building were showed direct and positive influence on stakeholder’s loyalty and stakeholder’s loyalty was indirectly influenced by corporate vision through Rajabhat University brand building.

A Genetic Algorithm Based Permutation and Non-Permutation Scheduling Heuristics for Finite Capacity Material Requirement Planning Problem

This paper presents a genetic algorithm based permutation and non-permutation scheduling heuristics (GAPNP) to solve a multi-stage finite capacity material requirement planning (FCMRP) problem in automotive assembly flow shop with unrelated parallel machines. In the algorithm, the sequences of orders are iteratively improved by the GA characteristics, whereas the required operations are scheduled based on the presented permutation and non-permutation heuristics. Finally, a linear programming is applied to minimize the total cost. The presented GAPNP algorithm is evaluated by using real datasets from automotive companies. The required parameters for GAPNP are intently tuned to obtain a common parameter setting for all case studies. The results show that GAPNP significantly outperforms the benchmark algorithm about 30% on average.

Non-Population Search Algorithms for Capacitated Material Requirement Planning in Multi-Stage Assembly Flow Shop with Alternative Machines

This paper aims to present non-population search algorithms called tabu search (TS), simulated annealing (SA) and variable neighborhood search (VNS) to minimize the total cost of capacitated MRP problem in multi-stage assembly flow shop with two alternative machines. There are three main steps for the algorithm. Firstly, an initial sequence of orders is constructed by a simple due date-based dispatching rule. Secondly, the sequence of orders is repeatedly improved to reduce the total cost by applying TS, SA and VNS separately. Finally, the total cost is further reduced by optimizing the start time of each operation using the linear programming (LP) model. Parameters of the algorithm are tuned by using real data from automotive companies. The result shows that VNS significantly outperforms TS, SA and the existing algorithm.

Productivity Effect of Urea Deep Placement Technology: An Empirical Analysis from Irrigation Rice Farmers in the Northern Region of Ghana

This study examined the effect of Urea Deep Placement (UDP) technology on the output of irrigated rice farmers in the northern region of Ghana. Multi-stage sampling technique was used to select 142 rice farmers from the Golinga and Bontanga irrigation schemes, around Tamale. A treatment effect model was estimated at two stages; firstly, to determine the factors that influenced farmers’ decision to adopt the UDP technology and secondly, to determine the effect of the adoption of the UDP technology on the output of rice farmers. The significant variables that influenced rice farmers’ adoption of the UPD technology were sex of the farmer, land ownership, off-farm activity, extension service, farmer group participation and training. The results also revealed that farm size and the adoption of UDP technology significantly influenced the output of rice farmers in the northern region of Ghana. In addition to the potential of the technology to improve yields, it also presents an employment opportunity for women and youth, who are engaged in the deep placement of Urea Super Granules (USG), as well as in the transplantation of rice. It is recommended that the government of Ghana work closely with the IFDC to embed the UDP technology in the national agricultural programmes and policies. The study also recommends an effective collaboration between the government, through the Ministry of Food and Agriculture (MoFA) and the International Fertilizer Development Center (IFDC) to train agricultural extension agents on UDP technology in the rice producing areas of the country.

Predictive Factors of Exercise Behaviors of Junior High School Students in Chonburi Province

Exercise has been regarded as a necessary and important aspect to enhance physical performance and psychology health. Body weight statistics of students in junior high school students in Chonburi Province beyond a standard risk of obesity. Promoting exercise among Junior high school students in Chonburi Province, essential knowledge concerning factors influencing exercise is needed. Therefore, this study aims to (1) determine the levels of perceived exercise behavior, exercise behavior in the past, perceived barriers to exercise, perceived benefits of exercise, perceived self-efficacy to exercise, feelings associated with exercise behavior, influence of the family to exercise, influence of friends to exercise, and the perceived influence of the environment on exercise. (2) examine the predicting ability of each of the above factors while including personal factors (sex, educational level) for exercise behavior. Pender’s Health Promotion Model was used as a guide for the study. Sample included 652 students in junior high schools, Chonburi Provience. The samples were selected by Multi-Stage Random Sampling. Data Collection has been done by using self-administered questionnaires. Data were analyzed using descriptive statistics, Pearson’s product moment correlation coefficient, Eta, and stepwise multiple regression analysis. The research results showed that: 1. Perceived benefits of exercise, influence of teacher, influence of environmental, feelings associated with exercise behavior were at a high level. Influence of the family to exercise, exercise behavior, exercise behavior in the past, perceived self-efficacy to exercise and influence of friends were at a moderate level. Perceived barriers to exercise were at a low level. 2. Exercise behavior was positively significant related to perceived benefits of exercise, influence of the family to exercise, exercise behavior in the past, perceived self-efficacy to exercise, influence of friends, influence of teacher, influence of environmental and feelings associated with exercise behavior (p < .01, respectively) and was negatively significant related to educational level and perceived barriers to exercise (p < .01, respectively). Exercise behavior was significant related to sex (Eta = 0.243, p=.000). 3. Exercise behavior in the past, influence of the family to exercise significantly contributed 60.10 percent of the variance to the prediction of exercise behavior in male students (p < .01). Exercise behavior in the past, perceived self-efficacy to exercise, perceived barriers to exercise, and educational level significantly contributed 52.60 percent of the variance to the prediction of exercise behavior in female students (p < .01).

Primary School Teachers’ Conceptual and Procedural Knowledge of Rational Number and Its Effects on Pupils’ Achievement in Rational Numbers

The study investigated primary school teachers’ conceptual and procedural knowledge of rational numbers and its effects on pupil’s achievement in rational numbers. Specifically, primary school teachers’ level of conceptual knowledge about rational numbers, primary school teachers’ level of procedural knowledge about rational numbers, and the effects of teachers conceptual and procedural knowledge on their pupils understanding of rational numbers in primary schools is investigated. The study was carried out in Bauchi metropolis in the Bauchi state of Nigeria. The design of the study was a multi-stage design. The first stage was a descriptive design. The second stage involves a pre-test, post-test only quasi-experimental design. Two instruments were used for the data collection in the study. These were Conceptual and Procedural knowledge test (CPKT) and Rational number achievement test (RAT), the population of the study comprises of three (3) mathematics teachers’ holders of Nigerian Certificate in Education (NCE) teaching primary six and 210 pupils in their intact classes were used for the study. The data collected were analyzed using mean, standard deviation, analysis of variance, analysis of covariance and t- test. The findings indicated that the pupils taught rational number by a teacher that has high conceptual and procedural knowledge understand and perform better than the pupil taught by a teacher who has low conceptual and procedural knowledge of rational number. It is, therefore, recommended that teachers in primary schools should be encouraged to enrich their conceptual knowledge of rational numbers. Also, the superiority performance of teachers in procedural knowledge in rational number should not become an obstruction of understanding. Teachers Conceptual and procedural knowledge of rational numbers should be balanced so that primary school pupils will have a view of better teaching and learning of rational number in our contemporary schools.

Factors Influencing Household Expenditure Patterns on Cereal Grains in Nasarawa State, Nigeria

This study aims at describing the expenditure pattern of households on millet, maize and sorghum across income groups in Nasarawa State. A multi-stage sampling technique was used to select a sample size of 316 respondents for the study. The Almost Ideal Demand System (AIDS) model was adopted in this study. Results from the study shows that the average household size was five persons with dependency ratio of 52 %, which plays an important role on the household’s expenditure pattern by increasing the household budget share. On the average 82 % were male headed households with an average age of 49 years and 13 years of formal education. Results on expenditure share show that maize has the highest expenditure share of 38 % across the three income groups and that most of the price effects are significantly different from zero at 5 % significant level. This shows that the low price of maize increased its demand as compared to other cereals. Household size and age of household members are major factors affecting the demand for cereals in the study. This agrees with the fact that increased household population (size) will bring about increase consumption. The results on factors influencing preferences for cereal grains reveals that cooking quality and appearance (65.7 %) were the most important factors affecting the demand for maize in the study area. This study recommends that cereal crop production should be prioritized in government policies and farming activities that help to boost food security and alleviate poverty should be subsidized.

Comparing Abused and Normal Male Students in Tehran Guidance Schools: Emphasizing the Co-Dependency of Their Mothers

The aim of this study is to compare abused and normal male students in Tehran guidance schools with emphasis on the co-dependency of their mothers. The method of this study is based on survey method and comparison (Ex-Post Facto). The method of sampling is also multi-stage cluster. Accordingly, we did sampling from secondary schools of education and training in Tehran, including 12 schools with levels of first, second and third. Each of the schools represents the three – high, medium and low- economic and social conditions. In the following, three classes from every school and 20 students from each class were randomly selected. By (CTQ) abused and normal students were separated that 670 children were recognized as normal and 50 children as abused. Then, 50 children were randomly selected from normal group and compared with abused group. Using Spanned-Fischer Co-dependency Scale, we compared mothers of abused and normal students. The results showed that mothers of the abused children have higher co- dependency average comparing to the mothers of the normal children.

Awareness and Attitudes of Primary Grade Teachers (1-4thGrade) towards Inclusive Education

The present research aimed at studying the awareness and attitudes of teachers towards inclusive education. The sample consisted of 60 teachers, teaching in the primary section (1st – 4th) of regular schools affiliated to the SSC board in Mumbai. Sample was selected by Multi-stage cluster sampling technique. A semi-structured self-constructed interview schedule and a self-constructed attitude scale was used to study the awareness of teachers about disability and Inclusive education, and their attitudes towards inclusive education respectively. Themes were extracted from the interview data and quantitative data was analyzed using SPSS package. Results revealed that teachers had some amount of awareness but an inadequate amount of information on disabilities and inclusive education. Disability to most (37) teachers meant “an inability to do something”. The difference between disability and handicap was stated by most as former being cognitive while handicap being physical in nature. With regard to Inclusive education, a large number (46) stated that they were unaware of the term and did not know what it meant. Majority (52) of them perceived maximum challenges for themselves in an inclusive set up, and emphasized on the role of teacher training courses in the area of providing knowledge (49) and training in teaching methodology (53). Although, 83.3% of teachers held a moderately positive attitude towards inclusive education, a large percentage (61.6%) of participants felt that being in inclusive set up would be very challenging for both children with special needs and without special needs. Though, most (49) of the teachers stated that children with special needs should be educated in regular classroom but they further clarified that only those should be in a regular classroom who have physical impairments of mild or moderate degree.

A New Reliability Allocation Method Based On Fuzzy Numbers

Reliability allocation is quite important during early design and development stages for a system to apportion its specified reliability goal to subsystems. This paper improves the reliability fuzzy allocation method, and gives concrete processes on determining the factor and sub-factor sets, weight sets, judgment set, and multi-stage fuzzy evaluation. To determine the weight of factor and sub-factor sets, the modified trapezoidal numbers are proposed to reduce errors caused by subjective factors. To decrease the fuzziness in fuzzy division, an approximation method based on linear programming is employed. To compute the explicit values of fuzzy numbers, centroid method of defuzzification is considered. An example is provided to illustrate the application of the proposed reliability allocation method based on fuzzy arithmetic.

The Application of Queuing Theory in Multi-Stage Production Lines

The purpose of this work is examining the multiproduct multi-stage in a battery production line. To improve the performances of an assembly production line by determine the efficiency of each workstation. Data collected from every workstation. The data are throughput rate, number of operator, and number of parts that arrive and leaves during part processing. Data for the number of parts that arrives and leaves are collected at least at the amount of ten samples to make the data is possible to be analyzed by Chi-Squared Goodness Test and queuing theory. Measures of this model served as the comparison with the standard data available in the company. Validation of the task time value resulted by comparing it with the task time value based on the company database. Some performance factors for the multi-product multi-stage in a battery production line in this work are shown. The efficiency in each workstation was also shown. Total production time to produce each part can be determined by adding the total task time in each workstation. To reduce the queuing time and increase the efficiency based on the analysis any probably improvement should be done. One probably action is by increasing the number of operators how manually operate this workstation.