Control and optimization of quality cost based on discrete grey forecasting model

Abstract

With the deepening and evolution of quality concept, the economy of quality is becoming more and more important, and the analysis of economy of quality is becoming an important part of quality management. The purpose of carrying out quality management is to seek a balance between quality level, quality cost and economic benefits. Since 1930s, quality management has gone through quality inspection phase, statistical quality control phase, total quality management phase and supply chain quality management phase. The theoretical system has gradually matured. In Juran's quality cost characteristic curve, the horizontal axis represents quality level while the vertical axis represents quality cost, and the total mass quality cost is composed of costs of conformance and costs of non-conformance. When the curve of costs of conformance and curve of costs of non-conformance intersects, the total mass quality cost reaches its minimum, which is called the best quality cost. On the basis of Juran's quality cost characteristic curve, many scholars put forward a series of control and optimization models of quality cost, which can be divided into four categories: (1) Prediction of quality cost based on the optimal exponential function model. The optimal exponential function model regards costs of conformance as positive exponential function and costs of non-conformance as negative exponential function. The total mass quality cost is the sum of positive exponential function and negative exponential function. Through the derivation of total mass quality cost, we can get the best quality level and then get the best quality cost. (2) The best quality cost model based on Taguchi's loss function. In this quality cost prediction model, costs of conformance include prevention cost and appraisal cost. Both prevention cost and appraisal cost can be expressed by Cobb-Douglas production function. Costs of non-conformance can be expanded according to Taylor formula and high-order infinitesimal items can be omitted. Then we can get the total mass quality cost. In this model, the point of best quality level is not just at the intersection of costs of conformance and costs of non-conformance. (3) Prediction of quality cost based on K.K. Govil function. In this model, we use K.K. Govil function which contains four parameters to simulate costs of conformance and costs of non-conformance. Like the first situation, the total mass quality cost is the sum of costs of conformance and costs of non-conformance. After the derivation, the best quality level and the best quality cost can be gained. (4) Prediction of quality cost based on Cobb-Douglas production function. Both costs of conformance and costs of non-conformance have a representation according to Cobb-Douglas production function. Then we sum up costs of conformance and costs of non-conformance, and can get the total mass quality cost. Let the derivation of total mass quality cost be zero, we can also get the best quality level and the best quality cost. These four models have been widely used for prediction and optimizations of quality cost, but when face a real situation, we don't have much information and the numbers of data are rather little. As grey system theory is famous of solving problems with “less data” and “poor information”, we try to use discrete grey model (DGM) into the prediction and optimizations of quality cost. Because certain interference exists in raw data, weakening buffer operator are introduced to reduce the environmental interference. In a real case, we compare DGM with traditional optimal exponential function model to simulate quality cost. The sum of squares of residuals and the mean of the relative error show that the prediction accuracy of discrete grey model after operated by first order weakening buffer operator is improved obviously. If we mix DGM and traditional optimal exponential function model together, we'll get a better result. With the rise of various quality ideas such as total quality management (TPM) and zero defect management, the requirement of quality cost is getting higher and higher. What's more, traditional static model may no longer apply. At this time, we should use new theory to guide the quality cost management of enterprise.