Research Of Game Modeling And Analysis Based On Quality-cost Trade-off In Auto-body Tolerance Design

Automotive body is a kind of complex product that has the large-scalemanufacturing characteristics. Part tolerance is a crucial factor affecting productperformance and manufacturing cost. Tight tolerances can ensure good part quality,but simultaneously pose a high investment stress on the manufacturers. On contrary,loose tolerances may cause a series of problems such as the rework rate increase orcustomer complaints. Consequently, it is significant to develop a reasonable tolerancescheme considering the demands and conflicts of quality and cost. Traditionaltolerance design methods for automotive body products consist of the trial-designand revision method, the least cost method under the quality constraint and thecomprehensive evaluating method combining several optimization objectives withdifferent weights. These approaches may not be desirable as it is difficult toeffectively evaluate the interactive influences and the conflict among differentdemands.Game theory is introduced into this research and a kind of auto-body tolerancedesign method based on game modelling and solving is established. The purpose is tobalance the quality and the cost demand and avoid the disadvantages of the traditionalmethods. This paper first describes the tolerance design problems and proposes thecorresponding theoretical models according to the research on the variation and thecost propagation. Then the engineering problem is converted to the game model.Further, the equilibrium points are calculated by the Shapley value method incooperative game. The solutions are also compared with the traditionalmulti-objective optimization methods. Finally, the feasibility of the procedure isdemonstrated through some engineering examples. Main research contents are shownas bellows.(1) Classification and description of the tolerance design problems ofautomotive body based on the “quality-cost” trade-offThe tolerance design problems of automotive body are divided into twocategories: the tolerance design problem of automotive body based on the specific process information and the tolerance design problem of automotive body based onthe historical data information. For the first tolerance design problem, themanufacturing variation model and the manufacturing cost model are presentedconsidering the variation propagation rules and the process cost of different tolerancegrades. For the second tolerance design problem, common quality, cost evaluationapproaches of parts&assemblies in the automotive body manufacturing process arepresented.(2) Establishment of the game models in the automotive body tolerancedesignFor the tolerance design problem of automotive body based on the specificprocess information, the quality and the cost requirement of the assembly product areconsidered as the game players. The corresponding game payoffs are established.Simultaneously, the tolerance design variables are divided into several groups usingthe fuzzy clustering theory. The game strategy belonging to each player is thendesigned. Finally, the game model (also described by a kind of game payoff matrix) isestablished. For the tolerance design problem of automotive body based on thehistorical data information, the game players, the game strategies and the gamepayoffs are defined by the common indicators that are used to evaluate the quality andthe cost level of parts&assemblies. A primary game payoff matrix is established.Then it is further transformed into a complete payoff matrix using the multipleregression analysis theory based on the measuring data.(3) Solving methods of the game models in the automotive body tolerancedesignThe Nash equilibrium theory is first proposed to solve the game model based onthe optimal individual payoff. Then the Shapley value theory is presented to solve thegame model based on the optimal collective payoff. The game solution is comparedwith the traditional multi-objective optimization solutions in order to show thetheoretical and the engineering advantage of the game method on solving thetolerance design problems of automotive body. It can be considered to be a kind ofimportance evaluation of each player based on their contribution to the profit of thewhole coalition. The game method is not dependent on the weights and has goodstability.(4) Application of the tolerance design of automotive body with game theory The software module for the tolerance design of automotive body based on“quality-cost” trade-off is developed and introduced. The water tank supportassembly and the front lamp assembly are analyzed with the game method. First thequality and the cost information that are relevant to the tolerances of parts&assemblies are converted to the game components in order to form the game model.Further, the equilibrium points are calculated by the non-cooperative and thecooperative game method. The solutions are also compared with the traditionalmulti-objective optimization methods. The optimization conclusion indicates that akind of reasonable and fair tolerance scheme is obtained and it is not dependent on theweights and has good stability. The whole process of the game analysis from thedescription of the design problem to the game modeling and solving is shown. It canbe effective and reliable for the tolerance design of automotive body with gametheory.