1、PDF外文：http:/ 中文 3300字 出处： The International Journal of Advanced Manufacturing Technology, 2006, 27(5-6): 543-546 Sequential monitoring of manufacturing processes: an application of grey forecasting models Li-Lin Ku Tung-Chen Huang Abstract This study used statistical control charts as an
2、 efficient tool for improving and monitoring the quality of manufacturing processes. Under the normality assumption, when a process variable is within control limits, the process is treated as being in-control. Sometimes, the process acts as an in-control process for short periods； however, once the
3、 data show that the production process is out-of-control, a lot of defective products will have already been produced, especially when the process exhibits an apparent normal trend behavior or if the change is only slight. In this paper, we explore the application of grey forecasting models for pred
4、icting and monitoring production processes. The performance of control charts based on grey predictors for detecting process changes is investigated. The average run length(ARL) is used to measure the effectiveness when a mean shift exists. When a mean shift occurs, the grey predictors are found to
5、be superior to the sample mean, especially if the number of subgroups used to compute the grey predictors is small. The grey predictor is also found to be very sensitive to the number of subgroups. Keywords Average run length Control chart Control limit Grey predictor 1 Introductio
6、n Statistical control charts have long been used as an efficient tool for improving and monitoring the quality of manufacturing processes. Traditional statistical process control (SPC) methods assume that the process variable is distributed normally, and that the observed data are independent. Under
7、 the normality assumption, when the process variable is within the control limits, the process is treated as being in-control； otherwise, the process assumes that some changes have occurred, i.e., the process may be out-of-control. There are many situations in which processes act as in-control while
8、 in they are in fact out-of-control, such as tool-wear1 and when the raw material has been consumed. Sometimes the process acts as an in-control process for short periods； however, once the data show that the production process is out-of-control, a lot of defective products have already been produce
9、d, especially when the process exhibits an apparent normal trend behavior2 or if the change is only slight. Though these kinds of shifts in the process are not easy to detect, the process is nevertheless predictable. If the process failure costs are very large, then detecting these shifts as soon as
10、 possible becomes very important. In this paper, we explore the application of grey forecasting models for predicting and monitoring production processes. The performance of control charts based on grey predictors for detecting process changes is studied. The average run length(ARL) is used to measu
11、re the effectiveness when a mean shift exists. The ARL means that an average number of observations is required before an out-of-control signal is created indicating special circumstances. Small ARL values are desired. The performance of grey predictors is compared with sample means x . All procedur
12、es are studied via simulations. When a mean shift occurs, the grey predictors are found to be superior to the sample mean if the number of subgroups that are used to compute the grey predictors is small. The grey predictor is also found to be very sensitive to the number of subgroups. The advantage
13、of the grey methods is that the grey predictor only needs a few samples in order to detect the process changes even when the process shifts are slight. The number of subgroups(samples) can be adjusted so that the performance of grey predictors can be changed according to the desired criteria. In the
14、 next section, the grey forecasting models are introduced and an overview of the proposed monitoring procedure will be given. The details of the numerical analytical results and conclusions are then given in Sect. 3, in which the results of the grey predictors are compared with sample means. The Typ
15、e I error based on X-bar control charts for sample means and the grey predictors are also described. Finally, recommendations and suggestions based on the results are then discussed in Sect. 4. 2 Grey forecasting models and procedural steps The grey system was proposed by Deng 3. The grey syst
16、em theory has been successfully applied in many fields such as management, economy, engineering, finance 46, etc. There are three types of systems white, black, and grey. A system is called a white system when its information is totally clear. When a systems information is totally unknown, it is cal
17、led a black system. If a systems information is partially known, then it is called a grey system. In manufacturing processes, the operational conditions, facility reliability and employee behaviors are all factors that are impossible to be totally known or be fully under control. In order to control
18、 the system behavior, a grey model is used to construct an ordinary differential equation, and then the differential equation of the grey model is solved. By using scarce past data, the grey model can accurately predict the output. After the output is predicted, it can be checked if the process is u
19、nder control or not. In this paper, we monitor and predict the process output by means of the GM(1,1) model 7. Sequential monitoring is a procedure in which a new output point is chosen (usually it is a sample mean) and the cumulative results of the grey forecasts are analyzed before proceeding to t
20、he next new point. The procedure can be separated into five steps: Step 1: Collect original data and build a data sequence. The observed original data are defined as )0(ix , where i is i th sample mean. The raw sequence of k samples is defined as )0()0(3)0(2)0(1)0( , kxxxxx
21、 (1) Step 2: Transform the original data sequence into a new sequence. A new sequence )1(x is generated by the accumulated generating operation(AGO), where )1()1(3)1(2)1(1)1( , kxxxxx
22、; (2) The )1(ix is derived as follows: .,2,1,1)0()1( in nikixx (3) Step 3: Build a first-order differential equation of the GM(1,1) model. By transforming the original data sequence into a first-order differential equation, the time series can be approximated by an exponential function. The grey differential model is obtained as bxadtxd 11 (4)
