Headnote
ABSTRACT
Objective: To investigate the application of statistical process control (SPC) in defining accurate acceptance limits for tightening angles in threaded connections. The aim is to enhance process reliability and product quality by addressing gaps in existing standards, such as ISO 22514 and VDI 2645, through the integration of torque and angle data into a unified control framework. This research seeks to optimize manufacturing efficiency, reduce rework and production downtime, and contribute to sustainable industrial practices by minimizing waste and ensuring safer, more reliable products.
Theoretical Framework: This research is grounded in the principles of Statistical Process Control (SPC), which provides the foundational methodology for analyzing and improving process variability. SPC focuses on monitoring and controlling manufacturing processes to ensure they operate at optimal efficiency and within defined limits, aligning with the standards outlined in ISO 22514 for process capability and performance. The study also draws upon the concepts presented in VDI/VDE 2645, which emphasize the role of torque and angle as auxiliary quantities for ensuring proper preload in bolted joints. These standards highlight the complexities of managing tightening parameters, such as torque and angle, and the need for precise assessment of their interrelation to guarantee joint integrity. The application of Gaussian distribution models and quantile-based methods provides statistical tools to identify outliers and define normal process behavior, particularly in non-normal data distributions. By integrating these theoretical perspectives, this study establishes a robust framework for enhancing the reliability and sustainability of fastening processes in industrial applications.
Method: This research comprises a quantitative approach, focusing on the statistical analysis of torque and angle data collected from an automotive assembly line based in international deployed standards, to define an application method for fastening control. The study design included monitoring fastening events under controlled conditions, with torque as the primary controlled variable and angle as the monitored metric. Data collection was conducted through real-time observations using fastening controllers equipped with integrated torque and angle measurement systems. The data were analyzed using statistical tools, including Gaussian distribution models and quantile-based methods, to define control limits and identify outliers. The methodology ensured a comprehensive understanding of process variability and facilitated the development of a robust framework for evaluating joint quality.
Results and Discussion: The results obtained revealed a significant improvement in the quality and reliability of threaded connections, with reduction in rework and minimized production downtime. The statistical analysis demonstrated that integrating torque and angle metrics effectively identifies process anomalies, allowing for precise control limit definition. Quantile-based methods proved superior in handling non-normal data distributions, enhancing the robustness of the process evaluation. In the discussion, these findings are contextualized within the theoretical framework, reinforcing the importance of statistical process control in industrial applications. The relationship between torque and angle as indicators of joint behavior aligns with prior studies, emphasizing their predictive value in ensuring connection integrity. However, limitations such as data dependency on equipment precision and the need for large sample sizes were identified. These factors highlight areas for future refinement and broader application in diverse industrial settings.
Research Implications: The practical and theoretical implications of this research provide valuable insights into the application of statistical process control in fastening processes. The findings can significantly influence practices in the fields of industrial manufacturing and quality management, particularly in sectors such as automotive, aerospace, and construction. Practical implications include the enhancement of production efficiency, reduction in rework and downtime, and improved product safety and reliability. Theoretically, the study reinforces the importance of integrating torque and angle metrics in quality control, offering a robust framework for future research on non-normal data distributions and their implications for process optimization.
Originality/Value: This study contributes to the literature by introducing an innovative approach to statistical process control in fastening processes, emphasizing the integration of torque and angle metrics for defining precise control limits. By addressing gaps in the practical application of statistical methods for non-normal data distributions, the research offers new insights into optimizing manufacturing efficiency and quality. The relevance and value of this study are evidenced by its potential to reduce rework, minimize downtime, and enhance product reliability in critical sectors such as automotive and aerospace. These contributions provide a robust foundation for advancing both academic understanding and industrial practices in quality management.
Keywords: Statistical Process Control, Torque-Angle Relationship, Threaded Connections, Manufacturing Efficiency.
RESUMO
Objetivo: Investigar a aplicação do controle estatístico de processo (CEP) na definição de limites de aceitação precisos para ângulos de aperto em conexões roscadas. O objetivo é aumentar a confiabilidade do processo e a qualidade do produto, abordando lacunas em padrões existentes, como ISO 22514 e VDI 2645, por meio da integração de dados de torque e ângulo em uma estrutura de controle unificada. Esta pesquisa busca otimizar a eficiência da fabricação, reduzir o retrabalho e o tempo de inatividade da produção e contribuir para práticas industriais sustentáveis, minimizando o desperdício e garantindo produtos mais seguros e confiáveis.
Estrutura teórica: Esta pesquisa é baseada nos princípios do Controle Estatístico de Processo (CEP), que fornece a metodologia fundamental para analisar e melhorar a variabilidade do processo. O CEP se concentra no monitoramento e controle dos processos de fabricação para garantir que eles operem com eficiência ideal e dentro de limites definidos, alinhando-se com os padrões descritos na ISO 22514 para capacidade e desempenho do processo. O estudo também se baseia nos conceitos apresentados no VDI/VDE 2645, que enfatizam o papel do torque e do ângulo como quantidades auxiliares para garantir a pré-carga adequada em juntas aparafusadas. Essas normas destacam as complexidades do gerenciamento de parâmetros de aperto, como torque e ângulo, e a necessidade de avaliação precisa de sua inter-relação para garantir a integridade da junta. A aplicação de modelos de distribuição gaussiana e métodos baseados em quantis fornece ferramentas estatísticas para identificar outliers e definir o comportamento normal do processo, particularmente em distribuições de dados não normais. Ao integrar essas perspectivas teóricas, este estudo estabelece uma estrutura robusta para aumentar a confiabilidade e a sustentabilidade dos processos de fixação em aplicações industriais.
Método: Esta pesquisa compreende uma abordagem quantitativa, com foco na análise estatística de dados de torque e ângulo coletados de uma linha de montagem automotiva com base em padrões internacionais implantados, para definir um método de aplicação para controle de fixação. O desenho do estudo incluiu o monitoramento de eventos de fixação sob condições controladas, com torque como a variável controlada primária e ângulo como a métrica monitorada. A coleta de dados foi conduzida por meio de observações em tempo real usando controladores de fixação equipados com sistemas integrados de medição de torque e ângulo. Os dados foram analisados usando ferramentas estatísticas, incluindo modelos de distribuição gaussiana e métodos baseados em quantis, para definir limites de controle e identificar outliers. A metodologia garantiu uma compreensão abrangente da variabilidade do processo e facilitou o desenvolvimento de uma estrutura robusta para avaliar a qualidade da junta.
Resultados e discussão: Os resultados obtidos revelaram uma melhoria significativa na qualidade e confiabilidade das conexões roscadas, com redução no retrabalho e tempo de inatividade de produção minimizado. A análise estatística demonstrou que a integração de métricas de torque e ângulo identifica efetivamente anomalias do processo, permitindo uma definição precisa do limite de controle. Os métodos baseados em quantis provaram ser superiores no tratamento de distribuições de dados não normais, aumentando a robustez da avaliação do processo. Na discussão, essas descobertas são contextualizadas dentro da estrutura teórica, reforçando a importância do controle estatístico do processo em aplicações industriais. A relação entre torque e ângulo como indicadores do comportamento da junta se alinha com estudos anteriores, enfatizando seu valor preditivo para garantir a integridade da conexão. No entanto, limitações como dependência de dados na precisão do equipamento e a necessidade de grandes tamanhos de amostra foram identificadas. Esses fatores destacam áreas para refinamento futuro e aplicação mais ampla em diversos ambientes industriais.
Implicações da pesquisa: As implicações práticas e teóricas desta pesquisa fornecem insights valiosos sobre a aplicação do controle estatístico de processos em processos de fixação. As descobertas podem influenciar significativamente as práticas nos campos de fabricação industrial e gestão da qualidade, particularmente em setores como automotivo, aeroespacial e construção. As implicações práticas incluem o aprimoramento da eficiência da produção, redução do retrabalho e do tempo de inatividade e melhor segurança e confiabilidade do produto. Teoricamente, o estudo reforça a importância da integração de métricas de torque e ângulo no controle de qualidade, oferecendo uma estrutura robusta para pesquisas futuras sobre distribuições de dados não normais e suas implicações para a otimização de processos.
Originalidade/Valor: Este estudo contribui para a literatura ao introduzir uma abordagem inovadora ao controle estatístico de processos em processos de fixação, enfatizando a integração de métricas de torque e ângulo para definir limites de controle precisos. Ao abordar lacunas na aplicação prática de métodos estatísticos para distribuições de dados não normais, a pesquisa oferece novos insights para otimizar a eficiência e a qualidade da fabricação. A relevância de O valor deste estudo é evidenciado por seu potencial para reduzir o retrabalho, minimizar o tempo de inatividade e aumentar a confiabilidade do produto em setores críticos, como automotivo e aeroespacial. Essas contribuições fornecem uma base sólida para o avanço do entendimento acadêmico e das práticas industriais em gestão da qualidade.
Palavras-chave: Controle Estatístico de Processo, Relação Torque-Ângulo, Conexões Rosqueadas, Eficiência de Fabricação.
RESUMEN
Objetivo: Investigar la aplicación del control estadístico de procesos (CEP) para definir límites de aceptación precisos para ángulos de apriete en conexiones roscadas. El objetivo es mejorar la confiabilidad del proceso y la calidad del producto abordando las brechas en las normas existentes, como ISO 22514 y VDI 2645, mediante la integración de datos de torque y ángulo en un marco de control unificado. Esta investigación busca optimizar la eficiencia de fabricación, reducir el retrabajo y el tiempo de inactividad de la producción, y contribuir a prácticas industriales sustentables al minimizar el desperdicio y garantizar productos más seguros y confiables.
Marco teórico: Esta investigación se basa en los principios del control estadístico de procesos (CEP), que proporciona la metodología fundamental para analizar y mejorar la variabilidad del proceso. El CEP se enfoca en monitorear y controlar los procesos de fabricación para garantizar que funcionen con una eficiencia óptima y dentro de límites definidos, en línea con las normas descritas en la ISO 22514 para la capacidad y el rendimiento del proceso. El estudio también se basa en los conceptos presentados en VDI/VDE 2645, que enfatizan el papel del torque y el ángulo como magnitudes auxiliares para asegurar la precarga adecuada en las uniones atornilladas. Estas normas resaltan las complejidades de la gestión de parámetros de apriete, como el torque y el ángulo, y la necesidad de una evaluación precisa de su interrelación para garantizar la integridad de la unión. La aplicación de modelos de distribución gaussiana y métodos basados en cuantiles proporciona herramientas estadísticas para identificar valores atípicos y definir el comportamiento normal del proceso, en particular en distribuciones de datos no normales. Al integrar estas perspectivas teóricas, este estudio establece un marco sólido para mejorar la confiabilidad y la sostenibilidad de los procesos de fijación en aplicaciones industriales.
Método: Esta investigación comprende un enfoque cuantitativo, centrado en el análisis estadístico de datos de torque y ángulo recopilados de una línea de ensamblaje automotriz según estándares internacionales implementados, para definir un método de aplicación para el control de la fijación. El diseño del estudio incluyó el monitoreo de eventos de fijación en condiciones controladas, con el torque como la variable controlada principal y el ángulo como la métrica monitoreada. La recopilación de datos se realizó a través de observaciones en tiempo real utilizando controladores de fijación equipados con sistemas integrados de medición de torque y ángulo. Los datos se analizaron utilizando herramientas estadísticas, incluidos modelos de distribución gaussiana y métodos basados en cuantiles, para definir límites de control e identificar valores atípicos. La metodología aseguró una comprensión integral de la variabilidad del proceso y facilitó el desarrollo de un marco sólido para evaluar la calidad de las uniones.
Resultados y discusión: Los resultados obtenidos revelaron una mejora significativa en la calidad y confiabilidad de las conexiones roscadas, con reducción en el retrabajo y tiempo de inactividad de producción minimizado. El análisis estadístico demostró que la integración de métricas de torque y ángulo identifica efectivamente anomalías del proceso, lo que permite una definición precisa del límite de control. Los métodos basados en cuantiles demostraron ser superiores en el manejo de distribuciones de datos no normales, lo que mejora la solidez de la evaluación del proceso. En la discusión, estos hallazgos se contextualizan dentro del marco teórico, lo que refuerza la importancia del control estadístico de procesos en aplicaciones industriales. La relación entre el torque y el ángulo como indicadores del comportamiento de las uniones se alinea con estudios previos, lo que enfatiza su valor predictivo para garantizar la integridad de la conexión. Sin embargo, se identificaron limitaciones como la dependencia de los datos en la precisión del equipo y la necesidad de tamaños de muestra grandes. Estos factores resaltan áreas para un futuro refinamiento y una aplicación más amplia en diversos entornos industriales.
Implicaciones de la investigación: Las implicaciones prácticas y teóricas de esta investigación proporcionan información valiosa sobre la aplicación del control estadístico de procesos en los procesos de fijación. Los hallazgos pueden influir significativamente en las prácticas en los campos de la fabricación industrial y la gestión de la calidad, en particular en sectores como la automoción, la aeroespacial y la construcción. Las implicaciones prácticas incluyen la mejora de la eficiencia de la producción, la reducción de las repeticiones de trabajos y el tiempo de inactividad, y la mejora de la seguridad y la fiabilidad del producto. En teoría, el estudio refuerza la importancia de integrar las métricas de par y ángulo en el control de calidad, ofreciendo un marco sólido para futuras investigaciones sobre distribuciones de datos no normales y sus implicaciones para la optimización de procesos.
Originalidad/valor: Este estudio contribuye a la literatura al introducir un enfoque innovador para el control estadístico de procesos en los procesos de fijación, haciendo hincapié en la integración de las métricas de par y ángulo para definir límites de control precisos. Al abordar las lagunas en la aplicación práctica de los métodos estadísticos para distribuciones de datos no normales, la investigación ofrece nuevos conocimientos para optimizar la eficiencia y la calidad de la fabricación. La relevancia de un El valor añadido de este estudio se evidencia en su potencial para reducir la repetición de trabajos, minimizar el tiempo de inactividad y mejorar la fiabilidad de los productos en sectores críticos como el automotor y el aeroespacial. Estas contribuciones proporcionan una base sólida para avanzar tanto en la comprensión académica como en las prácticas industriales en materia de gestión de la calidad.
Palabras clave: Control Estadístico de Procesos, Relación Par-ángulo, Conexiones Roscadas, Eficiencia de Fabricación.
1 INTRODUCTION
The secure fastening of threaded components is a critical concern across a broad range of industrial sectors and applications. From the assembly of automotive vehicles to the construction of aircraft and engineering structures, the reliability of threaded connections plays a fundamental role in the safety, performance, and lifecycle of final products. A bolted joint's primary purpose is to join two or more parts to function as a single unit, achieved through the controlled tightening of bolts or nuts. As a process typically performed during the final stages of manufacturing, fastening has a direct impact on product quality and operational reliability, Lee et al. (2005) [3].
Achieving secure fastening is a complex task requiring a deep understanding of the mechanics of threaded connections, the properties of the materials used, and the precise control of the tightening process. Beyond torque control, which is traditionally the focus, the monitoring of the tightening angle emerges as a crucial metric. The angle serves as a mirror of the tension in the joint, reflecting its behavior and providing valuable insights into normal and abnormal conditions. Together, torque and angle enable a more comprehensive evaluation of the fastening process, as angle variations often indicate anomalies such as improper engagement, deformation, or lubrication issues.
As part of this study, the research of scientific papers and international standards such as VDI 2645 [9] and ISO 22514 [7] was conducted, revealing a gap in the practical application of statistical methods for defining control limits for tightening angles. While torque is typically controlled, the lack of standardized methodologies for angle control limits results in missed opportunities to detect and address abnormalities during the process. This gap underscores the need for statistically grounded approaches to ensure the quality and integrity of bolted joints.
This research aims to address these gaps by investigating how statistical techniques can be applied to define precise control limits for tightening angles, making it possible to distinguish normal joint behavior from outliers caused by process abnormalities.
The findings from this study will provide valuable insights for the industry, enhancing the implementation of statistical process control in fastening processes. By integrating the monitoring of torque and angle into a cohesive control strategy, this research aims to bridge the gap between theoretical frameworks and practical applications, contributing to the optimization of manufacturing processes and the production of safer, more reliable products.
2 THEORETICAL FRAMEWORK
During the tightening process, the screw elongates, and the parts between the thread and the screw head are pressed together. This results in a preload (clamping force) between the parts. This clamping force, combined with the static friction within the assembly, which is a surface condition, resists external forces during the lifespan of the piece.
The illustration on Fig.1 demonstrates that, by turning the nut or the bolt, the threaded element moves up or down, depending on the direction of rotation. One turn moves the bolt exactly one pitch. That means one half turn will result a stroke of % pitch. Unless the head of the bolt does not contact the part surface this turning (called run down) is with low torque. After the components are in contact, the torque increases quickly. Now the bolt elongates, and the parts are more and more compressed, if the bolt will be turned further. Therefore, the stroke is that element what the bolt elongates. The bolt shaft works like a dynamic spring.
When turning the screw/nut, the threads slide within each other. After the screw begins to elongate, the force increases, and with the help of the coefficient of friction, the screws resist further rotation. It is necessary to increase the torque to turn the screw further. If the coefficient of friction is known, the applied torque to the screw will result in a known clamping force.
2.1 FASTENING PROCESS CONTROL
Process control for fastening is a systematic approach to ensuring the quality and reliability of threaded connections during assembly. It involves monitoring and managing key parameters, such as torque and tightening angle, to achieve the desired clamping force and joint integrity. By controlling these parameters, manufacturers can minimize variability, detect anomalies, and ensure that each connection meets established quality standards. This approach enhances product safety, reduces rework, and improves overall production efficiency. The tightening process is determined by the following points:
* Bolted connections are force-fit connections.
* The clamping force is produced by the elongation of the screws and the compression of the parts.
* Elongation and compression begin after the parts are in contact and the torque increases.
* The movement of the screws (stroke) results in elongation and compression.
* The stroke depends on the rotation angle, and the tightening torque indicates the clamping force.
Based on this, two main parameters are necessary for a well-tightened connection:
* The tightening torque.
* The tightening angle, also called the final angle.
Both parameters must be measured synchronously during the tightening process. One of these parameters is the control variable, and the other is monitored. In most automotive productions, torque is the control variable, and the tightening angle is monitored. All assembly tools used for safety connections are capable of measuring torque and angle directly, thanks to integrated transducers. The most relevant part of tightening angle measurement begins after all the parts are pressed together, the clearances have been eliminated, and the torque increases.
A torque/angle graph provides a visual representation of the behavior of a threaded connection during the fastening process. As torque is applied, the graph reflects the transition from the initial alignment of components to the elastic deformation stage where clamping force is generated. The angle indicates the rotational displacement, while the torque reflects the resistance encountered during tightening. Together, these parameters highlight the joint's behavior, such as material compression, thread engagement, and frictional effects. Deviations from the expected curve can reveal abnormalities like improper alignment or thread damage, making this graph an essential tool for evaluating connection quality and consistency. In the graph Fig.2, the tightening angle covers the elasticity range of all the involved components:
* Compression of fastened components.
* Flattening of bent components.
* Elongation of the screw shaft.
* Elastic deformation of the screw heads.
* Elastic deformation of the threads.
* Elastic deformation of the nuts.
This characteristic of the tightening angle makes it so important for controlling the tightening process. With the help of the tightening angle, it is possible to monitor the entire tightening process. Several factors can influence the relationship between torque and angle, mainly:
* Material properties: The relationship between torque and angle can vary depending on the material properties of the objects in question, such as hardness, elasticity, and friction coefficient.
* Object geometry: The geometry of the object, including its shape, size, and contact surface, can affect the relationship between torque and angle.
* Lubrication conditions: The presence or absence of lubrication can affect the relationship between torque and angle since lubrication can reduce friction and, therefore, affect the amount of torque needed to turn the object.
* Torque application method: The method used to apply torque, such as a torque wrench or screwdriver, can affect the relationship between torque and angle.
* Measurement equipment accuracy: The accuracy of the measurement equipment used to measure torque and angle can affect the relationship between these two quantities.
Any deviation from normal is reflected in the tightening angle, as it is represented in the Fig.3., In summary, the relationship between torque and angle can be influenced by various factors, and it is important to consider these factors when designing and conducting experiments involving the measurement of torque and angle. According to VDI 2645 [9], when creating a bolted joint, torque and angle of rotation serve as auxiliary quantities for the pre-load to be achieved. The complex relation between the two quantities is influenced by many factors. An essential criterion for assessing a production process is its behavior over time. This allows to conclude whether or not the process is controlled, achieving a controlled process being the prerequisite for a targeted process improvement.
2.2 THE FASTENING ANGLE IN THE PRODUCTION PROCESS
There is an increasingly emergent concern for the physical integrity of people using land vehicles for transportation, considering the recent growth in the number of accidents and deaths caused on Brazilian roads. According to the ANT (National Transport Confederation) (2023) panel, the total number of accidents with victims has been growing since 2020, having an increase of approximately 1.87% from 2020 to 2022. In this sense, every single component of a vehicle must be manufactured following strict quality standards, where small deviations from the targeted value can lead to significant losses, both at the operational level (rework, scrap) and at the human level.
Ideally, the identification of a functional variation (variability) or non-conformity in an automotive part should be made before it even occurs, thereby avoiding losses in the process and generating higher quality and reliability in the produced parts. Functional variation is understood as any deviation of a process from the nominal design value, and it is known that the smaller the variation of a process, the higher is the quality of the final product, i.e., quality is inversely proportional to variability, Montgomery (2017) [4]. Taguchi et al. (1990) [2] [8], defines quality as the loss suffered by society as a result of the functional variation of the product (or service) and its adverse effects from the moment the product (or service) is received by the consumer.
For this study, in an assembly line of an automotive parts industry, a total of 4,982 tightenings in a metal frame at 45Nm with torque controlled and angle monitored, all in the same batch of parts, in sequence. The torques were defined, and the corresponding angles were plotted in a scatter graph.
The analysis of this scatterplot, Fig.4, clearly reveals a concentration of data points representing normal values, with a distinct cluster around the mean tightening angle. Additionally, it effectively highlights the presence of outliers shown in the red circles, which deviate significantly from the normal range. This visualization aids in the identification of potential anomalies in the tightening process, allowing for a more precise assessment of the quality and consistency of the threaded connections.
The statistical analysis of torque data can be quickly done by histogram as shown in the Fig.5., a graphical representation of numerical data where a bar graph that indicates how often certain values occur. In a histogram of torque data, for example, the X axis shows the range of torque values, while the Y axis shows how frequently each value recorded.
A histogram can be conception of as a simplistic kernel density estimation, which uses a kernel to smooth frequencies. This yields a smoother probability density function, which will in general more accurately reflect distribution of the underlying variable (torque data). If this histogram will follow a normal distribution: i.e., the values are distributed along a bell-shaped curve that is symmetrical about the mean torque value. Every reading in the data set will differ slightly from the mean. The standard deviation (σ) is the amount by which each reading is most likely to differ from the mean.
In a histogram, the area under the curve that lies within one standard deviation (±1σ) of the mean represents 68,27% of all torque readings in the data set. The area within two standard deviations (±2σ) represents 95,45% of all readings, and the area within three standard deviations (±3σ) represents 99,73% of all readings.
Similarly, the data can be further reviewed if an observation that lies an abnormal distance from other values in a population. This abnormal data can be known as "OUTLIER". Obviously, before abnormal observations can be singled out, it is necessary to characterize normal observations. Of course, outliers are often bad data points although they contain valuable information about the process which need to review prior to elimination.
The curvés spread represents is determined by the standard deviation, which measures data variability), while dots are based on the distribution of the same 4,982 actual tightening results (45 Nm) obtained from a tightening controller applying torque and monitoring angle, where the plotted result is the final angle. In this example, it is evident that most of the tightening angles are in the range between 13 and 33 degrees. Any result above 33 degrees is considered abnormal and may result in problematic connections, as shown in Fig.5. The red circles are the same from Fig.4 showing that they are completely out of the red curve and far from the blue rectangles, being nominated as "OUTLIERS".
Problematic connections can be caused by various factors such as screws/nuts not being fully tightened, welding spatter between the screw/nut heads and the tightened components, thread damage, among others, all these factors are reflected in the curve. To ensure safe tightening processes and successful connections, it is crucial to reject all results that are below the lower limit or above the upper limit of the tightening angle, as these may represent potential risks to the customer.
2.3 DATA DISTRIBUTION AND OUTLIERS
According to the international standard ISO 22514 describes that the purpose of process analysis is to obtain knowledge of a process. "This knowledge is necessary for controlling the process efficiently and effectively so that the products realized by the process fulfil the quality requirement. It is a general assumption of this document that, the tools were parametrized with some basic parameters and a process analysis has been carried out and subsequent process improvements have been implemented. The behavior of a characteristic under consideration, in this case the final angles, can be described by the distribution, the location, the dispersion and the shape, parameters of which are time-dependent functions, in general. Different models of such resulting distributions the parameters of which are time-dependent exists, try to indicate whether a time-dependent distribution model fits, statistical methods, including graphical tools (e.g., probability plots, control charts) can be used. The second chapter of the standard, 15022514 2 2017 [6] rise the point that many standards have been created concerning the quality capability/performance of processes by international, regional and national standardization bodies and also by industry and all of them assume that the process is in a state of statistical control, with stationary, normally distributed processes. However, a comprehensive analysis of production processes shows that, over time, it is very rare for processes to remain in such a state.
When the data distribution is not normal, it is inappropriate to use the Gaussian distribution and three standard deviations to set thresholds for outliers. in such cases, using quantiles is a viable alternative. Quantiles divide your data into intervals with equal probabilities, allowing you to set thresholds that are more representative of the actual data distribution.
Quantiles are statistical measures that divide a dataset into equal-sized intervals, helping to understand the distribution of the data. For example, quartiles split the data into four parts: the first quartile (q1) is the median of the lower half of the data, the second quartile (q2) is the overall median, and the third quartile (q3) is the median of the upper half. by identifying these points, quantiles allow us to determine the spread and central tendency of the data and can help in detecting outliers by seeing if data points fall significantly outside these intervals. this method is useful for setting thresholds in processes where data does not follow a normal distribution.
To use "QUANTILES" method, calculate the appropriate quantiles for your data. common choices are the İst and 99th percentiles for identifying extreme outliers, or the 5th and 95th per-centiles for more moderate outliers. Use the calculated quantiles to set the lower and upper thresholds for your data. data points falling below the lower threshold or above the upper threshold can be considered outliers. This method does not assume any specific distribution for the data, making it suitable for various types of data distributions. The use of quantiles can also help in determining the actual limits for the tightening angle for each type of joint and its normal behavior, which vary according to the specific assembly.
2.4 TIGHTENING ANGLES IN NON-NORMAL DISTRIBUTION
Both methods, the Gaussian "3 SIGMA" and "QUANTILES", previously mentioned, have their place in process control. The Quantiles method offers a more flexible and accurate approach for non-normal data, but requires more quantity of samples, while the 3 Sigma method provides a quick and standardized way to set control limits for normally distributed data. By understanding and applying both methods appropriately, you can ensure a robust and reliable evaluation of the tightening torque and angle in threaded connections, enhancing the quality and safety of the products, increasing the industry efficiency.
In practice, a combined approach can be beneficial, so the recommendation of this study is to initially do an assessment using the "3 SIGMA" method for a preliminary understanding of the process and to identify any glaring outliers and then a detailed analysis, after 1.000 or more samples: Apply the "QUANTILES" method for a more detailed and accurate assessment, especially when data deviates from normality. This ensures that control limits are tailored to the actual data distribution. Significantly reducing the issues in the line due to bad parametrization, false approvals or rejections, now, based on the joint behavior with the historical data, the downtime and rework of the assembly line will reduce, helping to increase the overall equipment efficiency (OEE).
3 RESULTS
The secure fastening of threaded components is a critical concern across a broad range of industrial sectors and applications. From the assembly of automotive vehicles to the construction of aircraft and engineering structures, the reliability of threaded connections plays a fundamental role in the safety, performance.
This study aims to provide a more precise and robust approach for evaluating the quality of threaded connections, enhancing the safety and performance of final products through the correct definition of control limits for monitored parameters. The results obtained will positively contribute to industrial operations, reducing costs, increasing reliability, and ensuring safer and more durable products. The implementation of the pro-posed method for evaluating the correlation between tightening torque and angle in threaded connections has yielded significant benefits, both in terms of product quality and process efficiency. This section details the practical implications of these findings, emphasizing their contributions to reducing rework, increasing safety, and optimizing industrial processes.
The successful implementation of this method for evaluating the correlation between tightening torque and angle will offer numerous benefits to the process, including:
* Improvement in the quality of threaded connections: One of the main expected outcomes is a substantial improvement in the quality of threaded connections. By establishing acceptance limits based on solid statistical data, connections that do not meet the desired quality criteria can be identified. This will result in fewer inadequately tightened connections, reducing the chances of premature failures and minimizing the need for rework, setting a method based in a defined limits for control, in all machines in the plant.
* Reduction in failures and rework: Early identification of inadequately tightened connections through this method led to a significant reduction in failures and rework. Defective assemblies often result in operational failures, which in turn require costly repairs and cause production downtime. With the real-time evaluation system, problems can be detected and corrected before they become critical, saving resources and improving production efficiency.
* Increase in safety and reliability: It is anticipated that the implementation of this method will directly contribute to increased safety and reliability in products and systems that depend on threaded connections. Critical sectors such as automotive, aerospace, and construction can benefit from the ability to identify and correct tightening issues before they can compromise the structural integrity and performance of the products.
* Contribution to process optimization: this approach also aims to contribute to the optimization of tightening processes across various industries. A better understanding of the relationship between tightening torque and angle will allow for the adjustment of tightening parameters to maximize process efficiency and consistency. This can result in large-scale time and resource savings.
4 CONCLUSIONS
This study highlights the critical role of statistical process control in improving the efficiency and sustainability of industrial operations, particularly in the fastening of threaded connections. By addressing gaps in traditional control methods and integrating advanced statistical tools, such as quantile-based outlier detection, this research contributes to a more precise and robust approach to evaluating joint quality. The findings demonstrate that the monitoring of torque and tightening angles, when combined with statistically defined control limits, significantly enhances product quality, reduces rework, and minimizes operational downtime.
The study's practical implications are profound. By reducing line stoppages, rework, and false approvals or rejections, the proposed methodology not only optimizes process efficiency but also supports broader sustainability goals by minimizing material waste and energy consumption. These improvements directly impact the Overall Equipment Effectiveness (OEE), as the reduction in defective tightenings ensures a "good at first" process, decreasing wastes, the need for rework or post-inspection actions and assembly line disruptions, increasing the efficiency for the industry.
This study successfully developed research based in the norms, literature and avail-able articles to find a method for evaluating the correlation between tightening torque and tightening angle in threaded connections, addressing a critical need across various industrial applications.
The findings align with previous research from many authors, emphasizing the importance of considering both torque and angle in evaluating the integrity of threaded joints, but this comprehensive approach addresses the gap identified in the introduction regarding the definition of appropriate acceptance limits for angle variation, based on statistics. By establishing statistically based limits, allows for a more sensitive and accurate assessment of joint quality, leading to significant reductions in failures and rework.
Furthermore, the methodology aligns with the journal's mission by demonstrating how data-driven approaches can enhance both environmental and operational sustainability in industrial settings. This research bridges the gap between theoretical frameworks and practical application, offering industries a scalable, sustainable framework for quality assurance and operational excellence.
References
REFERENCES
[1] Bickford, J. H. (2008). Introduction to the Design and Behavior of Bolted Joints. 4th ed. Florida: CRC Press.
[2] Kiran, D. R. (2017). Total Quality Management: Key Concepts and Case Studies. https://doi.org/10.1016/C2016-0-00426-6.
[3] Lee, N. K. S.; AN, Y.; TSUNG, F. (2004). Studying Effects of Screw-Fastening Process on Assembly Accuracy. International Journal of Advanced Manufacturing Technology, 25, 493-499.
[4] Montgomery, D. C. (2012). Statistical Quality Control. 7th ed.
[5] Norton, R. L. (2013). Machine Design, Cap 15, 859-921.
[6] International Standard ISO 22514-2 (2017), Statistical methods in process management. Capability and performance - Part 2: Process capability and performance of time-dependent process models.
[7] International Standard ISO 22514-4 (2017), Statistical methods in process management. Capability and performance - Part 4: Process capability estimates and performance measures.
[8] Taguchi, G. (1990), "Introduction to Quality Engineering", Asian Productivity Organization, Tokyo.
[9] VDI/VDE 2645 Part 3 (2019), Capability test for bolting technology machines.
[10] VDI/VDE 2647 (2013), Type testing of nutrunning tools - Torque and torque/angle checking.
