# Analysis of the Use of Similarity Coefficients in Manufacturing Cell Formation Processes
###### Abstract
Software designers can select and combine building blocks to create customized subsystems, reducing design effort and simultaneously ensuring the quality of the product due to the use of previously tested modules [3]. Cellular layout is a modular and hierarchical approach to shop floor organization, streamlining industrial implementation by segmenting the workspace into independent cells, each dedicated to a specific stage of the production process. In practice, industrial facilities are organized to cluster machines, equipment, and workstations into autonomous but interconnected cells. This array ensures a fair distribution of production resources, such as raw materials, energy, and labor, which avoids bottlenecks [4]. As important as the distribution of machines into cells is the classification of parts into families based on convenient grouping criteria. The technique used to group similar parts into families is known as group technology (GT), a complementary technique to CM. While CM organizes machines into cells, GT organizes parts into families based on their similarities. GT is a systematic and structured approach to the design and production of moderately mass-produced products. Families are created based on shared characteristics, such as manufacturing process, machine requirements, production layout, materials used, or physical product attributes [5]. GT is not applicable to customized products, as it would be difficult to group unique products into families if the production strategy is product differentiation, as is the case in engineering to order (ETO). Additionally, GT is not suitable for serial products, as their product variety is low, and it does not make sense to group them. Therefore, GT is most effectively applied when a certain degree of product variety is present, but is not excessive [6]. Both CM and GT have a common element: the need for a multivariate technique to segregate elements of a set into subsets according to a multidimensional vector of attributes that describes the elements. A similarity function or a membership function for a subset is then determined. Similarity is applied to pairs of elements, while membership applies to individuals. Through heuristics or algorithms, individuals (machines in CM and parts in GT) are separated into subsets that have some similarity between them. In summary, given a universe of individuals \(S=\{A_{1}\U A_{2}\U A_{3}\ldots\U A_{n}\}\), if an individual belongs to set \(A_{i}\), where \(1\geq i\geq n\), it does not belong to any other subset \(A\
eq Ai\). In multivariate analysis, this technique is called cluster analysis and can be used to define both cells and families of parts [7]. This study focuses on the industrial use of cellular layout, particularly multicellular layout, where a manufacturing facility is organized into more than one cell that must produce at least two families of components. It is not unusual for multicellular manufacturing (MCM) to produce more than one family of parts in the same cell as long as the families are compatible and a large part of the tooling can be shared. Additionally, the number of families is usually greater than the number of cells, which implies that most cells must manufacture more than one family. Among the known cluster analysis techniques, this study is particularly interested in the use of the similarity coefficient, a quantitative measure that defines the similarity between parts or processes [1]. The coefficient is calculated based on criteria including technical characteristics of products or parts, process requirements, tools, material flow, setup time, and market demand, among others. The greater the similarity between parts, the more likely they will be grouped in the same cell. At least twenty types of similarity coefficients have been proposed in the literature [8].