Statistical control charts are usually developed under the assumption that observations of quality characteristics being monitored are statistically independent. However, this assumption is frequently violated in practice. A typical example is tool wear process, which may present trends in the process mean level because of the nature of tool wear. Conventional control charts do not work well in such process, as they may lead to many out-of-control signals even when the wear process is normal. In this research, the double exponential smoothing technique (DES), which is suitable for modeling processes with some linear trend, is used to develop a control scheme. This is a joint research that is being carried out with researchers from University of Linkoping and University of Lulea in Sweden.

It is clear that observations from tool wear processes often exhibit a trend because of the gradual development of tool wear. A typical data set is displayed in Figure 1 and it is from one of five tool inserts on a face mill and measured manually. The wear of the inserts, mainly flank wear, was measured every 45 seconds of cutting by means of a measuring microscope. The difficulty in accurately monitoring tool wear has been identified as a key quality and productivity problem. This includes poor utilization of the equipment and frequent tool changes if the tool is changed too early, or damage to the work piece and/or machine tool damage if the tool is changed too late. As frequent replacement of tools will be expensive and time consuming, practitioners would like to tolerate a certain amount of wear until it reaches a point where an undesirable item is produced.

A general approach that can be used for trended process is time series modeling, in which data can be modeled as stochastic time series with residuals monitored by more advanced techniques such as cumulative sum (CUSUM) charts and moving average (MA) charts. In our research, Brown’s one-parameter DES technique is used to fit the observations from the tool wear process since EWMA values always lag the actual data when a trend exists, which is the main reason for using the DES technique in forecasting theory. Then, the control chart on the residuals can be developed. The properties of this chart will also be studied.

As Figure 1 shows, the data set presents an increasing trend in the process mean level during the whole range. There are many points out of the control limit if the traditional chart for individual is used. However, we are usually willing to tolerate the change in process within a certain level and up to a certain point for this type of process. When DES is used to model this data set based on the minimum squared prediction error estimate of , the control chart is shown in Figure 2. The DES centerline control chart indicates that the process is in control.

Process performance observations with a gradual trend in its mean level present interesting problems for research and application. A suitable approach to process monitoring in the presence of trend is to identify and remove the cause of the trend. Although EWMA centerline control chart can follow a systematic trend in the process, it will lag behind the trend. Specifically, a linear trend at the origin of time can result in EWMA lagging behind the signal by . Therefore, for a process with trend, DES is more suitable for modeling.

Figure 1: Actual data set. (work material: SS2541, tool:

SECO face mill of type 220.13, insert material: T25M)

Figure 2: DES center line control chart.