two out of three points that are on the same side of the centerline,īoth at a distance exceeding 2 sigma’s from the centerlineĮ. six successive points that increase or decreaseĭ. eight successive points on the same side of the centerlineĬ. one point outside the 3 sigma control limitsī. 19).Xbar and R chart are used to check whether the given process is under Control.These charts are used as tools of SPC(Statistical Process Control).Įach subgroup need to have two or more measurements/readings but less than or equal to nine measurements.Two or more subgroups but preferably less than or equal to twenty subgroups are needed.įirst, name the Process and enter number of measurements per subgroup(n),and enter number of subgroups(k). Since such tools often produce very little variation in the process and therefore allow a narrow control zone without the possibility of adjusting the tool, it may be better to cut the control limits loose from the process and lock them to a given distance from the tolerance limits instead (see Fig. One such case is where the process uses tools that are not easily adjustable, such as fixed reamers or punches. In some cases there may be difficulties about letting the control limits adapt to the process. If you let the control limits follow the process, you will react neither too early nor too late when the behaviour of the process changes. It is a widespread myth that this will cause the operator to adjust the process more often, but in practice the reverse is true the process is adjusted less often compared to operation without SPC. That way, a smaller spread in the process gives a narrower control zone, while a greater spread gives a wider control zone (see Fig. The correct way is to let the control limits adapt to the process. That also means that 0.27% of the outcome is not included in the normal distribution curve. These six account for 99.73% of the actual result. The normal distribution curve is thus derived from one standard deviation and consists of six of them. If you had gone on making measurements you could have plotted the curve, but now you have calculated it instead (see Fig. To calculate the normal distribution spread, you simply multiply the standard deviation by 6 to get the total width of the normal distribution curve. Instead you can calculate the spread using the standard deviation (see below). This means that you do not need to measure hundreds of components to find out how much the machine or process is varying. This distance constitutes one standard deviation (see Fig. The procedure is that you measure the distance from the mean value (highest point on the hump) to the point where the curve changes direction and starts to swing outward. This is a statistical function used to calculate the normal distribution curve, for example. If a point falls outside a control limit on the R graph, the spread of the process has changed (see Fig. If a point falls outside a control limit on the X graph, the position of the process has changed (see Fig. This means, in principle, that you have no reason to react until the control chart signals certain behaviour.Ī commonly used control graph is the XR graph, where the position and spread of the process are monitored with the help of sub groups and control limits. The function of control limits is to centre the process on the target value, which is usually the same as the middle of the tolerance width, and to show where the limit of a stable process lies. They have nothing to do with tolerance limits, because they are designed to call your attention when the process changes its behaviour.Īn important principle is that control limits are used along with the mean value on the control graph to control the process, unlike tolerance limits, which are used along with individual measurements to determine whether a given part meets specifications or not. Control limits are an important aspect of statistical process control.
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