X-bar Chart

The X-bar chart uses sample means to monitor changes in the location of a process.

On the X-bar chart, the sample means (or averages) are plotted as points and connected with lines. The solid centerline is X-bar or the average of the sample means. The two inner dashed lines are the upper control limit (UCL) and the lower control limit (LCL). The control limits reflect the expected amount of variation in the sample means when only common causes of variation are present. The shape and color of the points indicate whether a point violates the specific control rules. Note that only the last point in each discovered pattern is marked.

The average is 4.9915, which is on target, but this plot shows the process is out of control. There are points outside the control limits at collection periods 2, 25, and 35. There is a trend of 6 increasing points from collection period 12 to 17. Moreover, there are several other near-trends, which suggests a cyclical pattern. Sure enough, the process peaks at collection periods 7, 17, 25, and 35. It bottoms out at periods 2, 12, 20, and 30. Looking back at the records, you find that the valleys all occur during the first shift, and the peaks occur during the third shift.

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