مطالعه مدل پیش بینی گسسته خاکستری بر اساس منحنی مشخصه هزینه کیفیت Study of a discrete grey forecasting model based on the quality cost characteristic curve

1. Introduction In the 1950s, J.M. Juran presented a general discussion of quality cost in his Quality Control Handbook, in which the cost of poor quality was compared to “the gold in the mine” ( Juran, 1951). Over the next several years, Armand V. Feigenbaum first clarified the concept of quality cost and defined it as, “the costs incurred to ensure and guarantee the satisfaction of quality and the loss that did not achieve satisfactory quality”. Over the next few decades, there was a growing discussion of quality cost. The models of cost of quality (CoQ) for domestic and foreign scholars mainly included: the prevention-appraisal-failure (PAF) model (Baatz, 1992), the Crosby model (Bemowski, 1991), the opportunity cost model (Bohan and Horney, 1991), the process cost model (Burgess, 1997), the ABC model (Bottorff, 1997) and so on. These models of quality cost lay the foundations for further research on the subject. For the PAF model, E.B. Baatz divided the total quality cost into prevention cost (P), appraisal cost (A), internal failure cost and external failure cost. Then Juran presented a quality characteristic curve based on this model and he believed that the total mass cost curve was synthesised by the costs of conformance and the costs of non-conformance. The curve of costs of conformance and the curve of costs of non-conformance guaranteed the minimum position of total quality costs: it corresponded to the quality level P* – the best quality level, as shown in Figure 1. On the basis of the PAF model and Juran’s quality characteristic curve, other scholars have put forward the optimal exponential function model for researching cost optimisation, the best quality cost model based on Taguchi’s loss function, the cost optimisation model based on K.K. Govil’s function, the best quality cost model based on the Cobb-Douglas production function, etc. These have played a huge role in promoting the relationship between quality cost and quality management levels. All of these models have a large number of unknown parameters and the parameters in these models should be estimated according to regression methodology. When there is no more information and there are no more data about quality cost and quality level in practical application, all of these models cease to work. In this paper, we first discuss the modelling mechanism of several original cost control models, and then propose a new method for forecasting quality costs based on a discrete grey model (DGM). In order to eliminate the perturbation of a system’s behavioural data and improve the prediction accuracy of the model, we have introduced the weakening buffer operator to weaken the time series of quality cost and reduce its randomness. The DGM model and the exponential function model have also been compared in the context of a real case to verify their feasibility and rationality.