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The control charts are used in many production areas because they give an idea about the quality characteristic(s) of a product. The control limits are calculated and the data are examined whether the quality characteristic(s) is/are within these limits. At this point, it may be confusing to comment, especially if it is slightly below or above the limit values. In order to overcome this situation, it is suitable to use fuzzy numbers instead of crisp numbers. The purpose of this paper is to demonstrate how to create control limits of X ¯ -R control charts for a specified data set of interval type-2 fuzzy sets.

There are methods in the literature, such as defuzzification, distance, ranking and likelihood, which may be applicable for interval type-2 fuzzy set. This study is the first that these methods are adapted to the X ¯ -R control charts. This methodology enables interval type-2 fuzzy sets to be used in X ¯ -R control charts.

It is demonstrated that the methods – such as defuzzification, distance, ranking and likelihood for interval type-2 fuzzy sets – could be applied to the X ¯ -R control charts. The fuzzy control charts created using the methods provide similar results in terms of in/out control situations. On the other hand, the sample points depicted on charts show similar pattern, even though the calculations are different based on their own structures. Finally, the control charts obtained with interval type-2 fuzzy sets and the control charts obtained with crisp numbers are compared.

Based on the related literature, research works on interval type-2 fuzzy control charts seem to be very limited. This study shows the applicability of different interval type-2 fuzzy methods on X ¯ -R control charts. For the future study, different interval type-2 fuzzy methods may be considered for X ¯ -R control charts.

The unique contribution of this research to the relevant literature is that interval type-2 fuzzy numbers for quantitative control charts, such as X ¯ -R control charts, is used for the first time in this context. Since the research is the first adaptation of interval type-2 fuzzy sets on X ¯ -R control charts, the authors believe that this study will lead and encourage the people who work on this topic.

Six Sigma within small and medium‐sized enterprises (SMEs) is rapidly emerging as the new wave of change in Six Sigma. The purpose of this paper is to review the implications of applying Six Sigma methodology over the SMEs, taking a specific case of a bicycle chain manufacturing unit. The study could be a paradigm initiative towards high quality products and services at low cost for every SME.

Based on the literature, this paper proposes a process flow chart to present a one‐shot picture of the Six Sigma application in a bicycle chain manufacturing unit which falls in an SME environment. The methodology adopted is DMAIC methodology of Six Sigma, which had been mostly successful so far in large‐scale industries. The methodology has been applied to reduce the bush rejection rate (bush is an important component of a cycle chain) by reducing defects inherent in the processes. The statistical techniques such as two sample t‐test and process capability analysis have been used to establish the process capability before and after the Six Sigma application.

This paper is an attempt to justify the highly useful role of quality management techniques like Six Sigma for SMEs which are normally presumed to be in the domain of large industries. In this paper, Six Sigma methodology has been applied to a small unit manufacturing bicycles chains with dwindling productivity levels. After applying Six Sigma it was found that the chain manufacturing firm can increase its profit by controlling high rejection rate of cycle chain bush. Application of Six Sigma project recommendation brought up the process sigma level to 5.46 from 1.40 by reduction in bush diameter variation in the process of bicycle chain bush manufacturing. This increase in sigma level is equivalent to monetary saving of Rs 0.288 million per annum, which is a noteworthy figure for an industry of such level. The success of this study paves the way to further extend the Six Sigma application to more such industries working in the SME environment.

This paper provides documented evidence of Six Sigma implementation in a bicycle chain manufacturing unit which has been taken as representative of a small and medium‐size industry. The study will yield a great value to academics, consultants, researchers and practitioners of Six Sigma.

The purpose of this paper is to illustrate the power of the Six Sigma methodology in improving the first pass yield of a high-precision grinding process in the manufacture of automotive products.

The paper follows a case study approach showing how theory has been put into practice. The case study was executed in a leading automotive company based in India.

The application of the Six Sigma methodology resulted in a reduction of tolerance-related problems and improved the first pass yield from 85 to over 99 per cent. A number of tools and techniques in the Six Sigma tool box have been utilised for data analysis and drawing valid and sound conclusions. The implementation of the Six Sigma methodology has demonstrated a saving of US$70,000 in addition to the customer-facing benefits of improved quality on returns and sales.

The results of the case study have provided greater stimulus within the production facilities for wider application of the methodology as a powerful problem solving methodology. Moreover, this case study sets the foundation for many other projects within the business.

The paper is valuable to many Six Sigma black belts, practitioners of Six Sigma and researchers in terms of understanding the systematic application of the methodology in a real world situation.

The purpose of this paper is to discuss the causes for the discrepancy between the utilization of statistical process control (SPC) in services and manufacturing. Furthermore, an approach for integrating customer demands and technical aspects of a service is presented. Services are very often characterized by a large number of characteristics, with relatively few observations. This research addresses a methodology based on Z and W charts, proposing it for the control of service features. An example associated with service provision is presented to illustrate the computation of Z and W as well as its interpretation.

The shortcomings of traditional control charts are stated and compared with the control charts for Z and W. An example illustrates how to utilize these charts, their ability to monitor several characteristics simultaneously, along with a continuous monitoring of process capability.

The proposed approach allowed the representation of several process characteristics in the same charts, even when those characteristics are not collected with the same periodicity. The Z and W charts are dimensionless and can be applied whenever it is possible to estimate process parameters, being an interesting approach to be utilized in Phase 2 of SPC. The difficulty for identifying the existence of non-random patterns emerges as the major shortcoming for these charts.

The proposed approach is a contribute to overcoming the discrepancy that persists between the utilization of SPC in services and manufacturing. Nevertheless, service production and consumption are frequently simultaneous, which constitutes an issue hard to deal with that is not fully addressed in this piece of research. Furthermore, the Z charts also present some disadvantages, notably an increased difficulty for analyzing the existence of non-random patterns, which worsens as increases the number of products/quality characteristics to be checked.

The proposed charts are very flexible and provide a rational utilization of resources. In fact, the representation of several processes is possible, along with the traditional analysis of patterns, thus providing an effective approach for controlling services processes.

Several quantitative approaches that have been utilized in manufacturing for a long time are still scarce in services. However, services play a major role in modern economies, being clear that improvements in service provision might have a direct impact on society.

The approach was based on the utilization of Z/W with samples, but it can be extended to individual observations or even to the control of discrete variables. Additionally, a methodology for process capability analysis in real-time is also proposed.

Statistical process control (SPC) is widely applied for control and improve processes in manufacturing, but very few studies have reported on the successful application of SPC in the food industry, in particular. The purpose of this paper is to critically assess the status of SPC in the UK food manufacturing industry and to suggest future research avenues.

A research project was carried out in the UK food manufacturing sector through questionnaires. The results of the study were analysed using descriptive statistics and statistical tests to be applied in the hypothesis testing.

Findings revealed that 45 per cent of the respondents are SPC users and x ¯ -R and x ¯ -S charts are the most commonly applied SPC charts in this industry. It was determined that top management commitment is the most critical factor, while lack of SPC training is the most alarming challenge, and lack of awareness of SPC and its benefits are the main reasons for the food companies not implementing SPC.

The study considered only the food manufacturing companies. Future research could be addressed toward the food service and food supply chain.

The paper provides information to food companies in the UK on most common practiced and important quality tools, SPC charts and critical success factors in the food industry. Moreover, the most challenging factors of SPC implementation in the food industry are presented.

This study depicted the current state of SPC practices in the food industry and the process performance in SPC and non-SPC companies is compared.

The purpose of this paper is to develop a monitoring multiple-stream processes control chart with a finite mixture of probability distributions in the manufacture industry.

Data were collected during production of a wheat-based dough in a food industry and the control charts were developed with these steps: to collect the master sample from different production batches; to verify, by graphical methods, the quantity and the characterization of the number of mixing probability distributions in the production batch; to adjust the theoretical model of probability distribution of each subpopulation in the production batch; to make a statistical model considering the mixture distribution of probability and assuming that the statistical parameters are unknown; to determine control limits; and to compare the mixture chart with traditional control chart.

A graph was developed for monitoring a multi-stream process composed by some parameters considered in its calculation with similar efficiency to the traditional control chart.

The control chart can be an efficient tool for customers that receive product batches continuously from a supplier and need to monitor statistically the critical quality parameters.

The purpose of this paper is to explore the scope of robust dispersion control charts in a distribution-free environment, which is a specific case of non-normal control charts. These control charts are skewness-based structures designed to monitor skewed-type processes whilst equally performing under symmetric processes. Moreover, the choice of a suitable control chart for a particular non-normal situation is also suggested.

The probability control limits approach is considered as an alternative way to determine the skewness-based structure of dispersion control charts. The proposals of five robust and two conventional Shewhart-type dispersion control charts are suggested as efficient competitors of skewness correction (SC) dispersion control charts. The evaluation of robust proposals and competing dispersion control charts is done through false alarm rate (FAR) and probability to signal (PTS) measures.

The proposed dispersion control charts are found robust and efficient alternatives of SC dispersion control charts in both normal and non-normal distributions. The FARs and PTS properties of proposed control charts are impressive in all studied cases, and a real-data example also verifies the dominance of proposed control charts.

Conventional dispersion control charts quickly lose their efficiency as underlying process distribution deviates from normality; however, robust control charts emerge as most suitable candidates in such situations. This paper proposes the idea of robust dispersion control charts under a distribution-free structure for the skewed-type process, which is not yet explored.

This paper aims to present a teaching approach to achieve the most personal support for students with different backgrounds and preferences in studying an Informatics course.

The presented methodology is based on the main principles of flexible and blended learning. The authors considered three main aspects: student’s background, the level of knowledge and the most suitable style of learning. At the beginning of the course, students were randomly divided into reference and test group. The test group students were continuously supported by different tools within an e-learning environment. The learning process for the reference group students was held in a traditional form.

The success of the experiment presented in this paper is demonstrated by comparing the results of the test group who were taught using the new strategy with the reference group who were taught in a common way. The statistical analysis shows that the test group students had better achievements compared to the reference group.

This presented study was carried out with non-IT first-year university students from social sciences, economics and technical faculties. Each year the number of students varied from 150 to 300.

Based on developed methodology, the model of individualization of the educational process in an e-environment was created and implemented in the course of Informatics in Tallinn University of Technology.

The purpose of this paper is to propose a robust iterative LIDAR-based pose tracking method assisted by modified visual odometer to resist initial value disturbance and locate a robot in the environments with certain occlusion.

At first, an iterative LIDAR-based pose tracking method is proposed. The LIDAR information is filtered and occupancy grid map is pre-processed. The sample generation and scoring are iterated so that the result is converged to the stable value. To improve the efficiency of sample processing, the integer-valued map indices of rotational samples are preserved and translated. All generated samples are analyzed to determine the maximum error direction. Then, a modified visual odometer is introduced for error compensation. The oriented fast and rotated brief (ORB) features are uniformly sampled in the image. A local map which contains key frames for reference is maintained. These two measures ensure that the modified visual odometer is able to return robust result which compensates the error of LIDAR-based pose tracking method in the maximum error direction.

Three experiments are conducted to prove the advantages of the proposed method. The proposed method can resist initial value disturbance with high computational efficiency, give back credible real-time result in the environment with abundant features and locate a robot in the environment with certain occlusion.

The proposed method is able to give back real-time pose tracking results with robustness. The iterative sample generation enables the robot to resist initial value disturbance. In each iteration, rotational and translational samples are separately generated to enhance computational efficiency. The maximum error direction of LIDAR-based pose tracking method is determined by principle component analysis and compensated by the result of modified visual odometer to give back correct pose in the environment with certain occlusion.

The purpose of this paper is to investigate the non-linear characteristics and stability of the rolling bearing–axle coupling system under the excitation of the axle/wheel speed of railway freight cars, so as to put forward a rationale for judging the vibration law and running stability of railway freight wagon.

Considering the effects of eccentric force of the railway wagon axle, the non-linear resistance of the wagon and non-linear support forces of axle box rolling bearings, a centralized mass model of rolling bearing-axle coupling system of railway freight wagon is presented on the basis of the theory of rotor dynamics and non-linear dynamics. Then the Runge-Kutta method is adopted to solve the non-linear response of the proposed system, and numerical simulation including bifurcation diagrams, axis trajectory curves, phase plane plots, Poincaré sections and amplitude spectras are analysed when the axle rotating speed is changed. Meantime, the relation curve between Floquet multiplier and axle rotating speed, which affects the stability of coupling system, is plotted by numerical method based on the Floquet theory and method.

The simulation results of the dynamic model reveal the abundant dynamic behaviour of the coupling system when the axle rotating speed changes, including single period, quasi period, multi-period and chaotic motion, as well as the evolution law from multi-period motion to chaotic motion. And especially, the bearing–axle coupling system is in stable state with a single period motion when the axle rotating speed changes from 410 rpm to 510 rpm, in which the running speed of railway freight wagon is changed from 62 km/h to 80 km/h, the vibration displacement of the coupling system in X direction is between 1.2 mm and 1.8 mm, and the vibration displacement of the coupling system in Y direction is between 1.0 mm and 1.45 mm. Meanwhile, the influence law of axle rotating speed on the stability is obtained by comparing the bifurcation diagram and Floquet multiplier graph of the coupling system.

The numerical simulation data obtained in this study can provide a theoretical evidence for designing the running speed of railway freight wagon, utilizing or controlling the non-linear dynamic behaviours of the proposed coupling system, and ensuring the stability of railway freight wagons.