Deriving A Mathematical Model Of A Paint Shop From Data Analysis

The authors deal with the optimization of production planning in the mixed-model assembly production. Modern paint shops are highly complex facilities with a multitude of interdependent process steps. In order to describe the occurring throughput and processing times, the behavior of these times is of great interest for production planning, a modeling of the paint shop is necessary. The disruptions appearing here, which are a major source for delays and reorganizations within the car plant, are due to the complex structure and various rework. In this work, an alternate formulation of a long term reliable model is discussed: The description of the paint shop based on a stochastic model which is directly derived from data analysis of the production data. COMPLEX STRUCTURE OF A PAINT SHOP Due to the many successive steps the production process of painting a body can be viewed as a multi stepped flow production (Spieckermann, 2002): Figure 1 gives a schematic overview over the major technological steps of a paint shop. In general this is reduced to the following steps: Pre-treatment: Arriving from the body shop, the body gets degreased and all metal fragments that are remnants of the production process in the body shop get cleaned away. Also some corrosion protective substances are applied. Base coat: At the base coating, the body is immersed in a bath of electrostatic particles that coat the body due to electrostatic forces. This is predominantly for protection from corrosion and for optimizing the color application. At the end of this step the body is heated in an oven to permanently fix the coating particles on the body. Underbody seam sealing: In this process step overlapping of the metal sheeting and gaps are sealed to prevent water intrusion. Additionally the underbody gets an extra coating against stone impact. Filler coating: After the surface of the body has been cleaned of dust again, the filler coating is applied. The brightness of the filler coating is adjusted concerning the brightness of the final color. This is an additional protection against stone chip. Top coating: The top coat is the layer of color that is determining the final color of the product. Clear finish: After the top-coating the whole body is painted with a clear paint. Clear finish is used in order to protect the color against scratches and other environmental influences. Final inspection and rework: In these steps the color is investigated for quality problems. In case of quality failures the painted body is transferred to the reworking, otherwise the painted body is clear and subsequently transferred to a storage unit. The reworking unit consists of several steps. In the inspection the severity of the problem and the specialized workstation for the repair is assessed. There are several work stations depending on the severity of the problem. The three major stations are paint removal, spot repair and extended completion. After a re-assessment of the quality of the repair work the bodies are re-introduces into the line at the appropriate position. The detailed description of each of these production steps is very difficult. Parallel process steps and the building of uniquely-colored batches have to be described. Furthermore, the paint shop of a car manufacturer is a place of continuing change. So the Proceedings 28th European Conference on Modelling and Simulation ©ECMS Flaminio Squazzoni, Fabio Baronio, Claudia Archetti, Marco Castellani (Editors) ISBN: 978-0-9564944-8-1 / ISBN: 978-0-9564944-9-8 (CD) formulation of long-term reliable model is nearly an impossible task. PROBABILISTIC NATURE OF PAINT SHOP PROCESSES Modern car production is organized by the pearl chain principle (Meyr, 2004; Weyer, 2002): The individual orders are lined up like pearls on a chain fixed in their sequence position relative to each other. Complex processes in the final assembly are based on the production order planned. For the delivery processes just-in-time (JIT) and just-in-sequence (JIS) the stability of the production order is of central importance. As a consequence the description of the behavior of a paint shop is essential for optimal production planning and for using production control systems. Parallelization of lines, processing of bodies in batches and rework due to system failures or violation of quality parameters cause turbulences of the preplanned order. Especially, painted bodies which have to be reworked are separated from the assembly line and are reworked on specialized work stations. A simulation model describing this process has to take into account this stochastic throughput. From an abstract point of view, the paint shop can be regarded as a so called “black-box”. Bodies in white are entering the paint shop and colored bodies are leaving it. Each body has an individual throughput time depending on its path through the paint shop. The individual throughput times of the bodies can be easily obtained from data analysis. DISTRIBUTION OF TROUGHPUT TIMES The throughput time of a body i is defined as the time it takes to successfully pass through a workstation or a group of workstations (Arnold and Furmans, 2009). In this case we are interested in the throughput time through the paint shop which is defined as the timestamp a body leaves the paint shop minus the timestamp the body has entered the paint shop. The manufacturing information system of a car manufacturer stores for each produced car many production timestamps. By using the timestamps from the input and the output of the paint shop a top-down analysis is applied. Through extensive data analysis, working time models and production interruptions have to be removed from the data set. By counting the bodies with defined throughput times random variables and corresponding distributions can be used to describe the throughput time. But, what is the correct distribution function? To answer this question several distribution functions where fitted to the distributions from data analysis. To obtain the parameters of the distributions, on the one hand maximum likelihood estimators and on the other hand moments estimators have been used. In general, empirical distributions of processing times are often skewed to the right, which is a result of the already mentioned production delays. So we have to concentrate on nonsymmetrical density functions. A commonly used distribution is the exponential distribution. Figure 1: Basic Layout of a paint shop