# A Time Correlation Based Clustering Method for a Design of a Transformable Product
## 1 Introduction  
A product has to meet diverse requirements of various users in order to be competitive in the market. Although different products have been developed to meet different user needs, many products provide only a single function, which cannot fully utilize capacity of product resources such as material and space for a variety of user needs. There are products with multiple functions in the market. Some of these products perform different functions through the structural reconfiguration, and some provide multiple functions using a fixed structure. Because of the importance of multi-functional products, different methods have been proposed for design of multi-functional products, such as the reconfigurable design, adaptive design, modular design, and product family design. There are two kinds of reconfigurable design applications: one is the reconfiguration of manufacturing system resources to meet different design requirements [1; 2; 3; 4], and the other is the reconfiguration of product function modules to form different design solutions [5; 6; 7]. The adaptive design was proposed by [PERSON] et al. [8] to design products that can meet different needs in product design and applications. Design adaptability refers to the ability of the existing design to create new or modified design to meet changeable requirements. Product adaptability refers to the ability of the product to meetchanging needs in applications [9]. The modular design is widely used to form a product by using independent function modules [10; 11]. The module refers to a unit composed of a component or a group of components to perform a function of the product. Each module can be easily attached, detached, modified, relocated, and replaced for upgrading, modifying, recycling and reusing of the product [12; 13]. Common modules of the product can be used as platforms [14; 15]. The concept of the product platform can be used to design flexible products with similar common function modules to meet different customer needs [16; 17]. These existing methods can effectively guide the design of multi-functional products. However, when there is a need for a product to change functions only through structural transformation without replacing components, the modular product will not be able to meet the requirement. A transformable product is necessary to meet the need. A product is called the transformable product that can change its physical structure to perform different functions or enhance existing functions. For example, the Osprey plane can be transformed between helicopter and aircraft, and Aquada can be formed as either a car or ship [18; 19]. There are also many transformable products applied in the architecture and furniture industry [20; 21; 22]. Transformable products can often be smaller and lighter than equivalent single-state products or a set of single-function products [23]. Transformation is an action of changing the physical structure of a product in order to perform different functions or enhance an existing function. In order to effectively design transformable products, transformation design methods are required [24]. Comparing with a general product, the transformable product uses less material and space to meet different use requirements. It is critical to determine product functions that a transformable product should have in the product design. Although many approaches have been proposed for design of the transformable product, there is a lack of the effective way to identify all potential functions and select the appropriate set of functions for a transformable product. This paper reviews the related work of the design method of transformable products, and proposes a new method to decide required functional components of a transformable product in the design process. This paper focuses on the conceptual design stage of transformable products as the early stage of design determines 80% of product lifespan cost [25]. This paper proposes an effective approach to improve the design for transformable products.