14-1 Control Charts for Variation and Mean 709 Graph Points plotted: sample means Centerline: x = mean of all sample means Upper control limit 1UCL2: x + A2 R (where A2 is a constant found in Table 14-2) Lower control limit 1LCL2: x - A2 R (where A2 is a constant found in Table 14-2) Using the temperatures in Table 14-1 on page 701 with samples of size n = 10 for each of the 14 decades, construct a control chart for x. Based on the result, determine whether the process mean is within statistical control. CP YOUR TURN. Do Exercise 8 “Pepsi Cans: x Chart.” EXAMPLE 4 x Chart of Global Earth Temperatures SOLUTION Before plotting the 14 points corresponding to the 14 values of x, we must first find the values for the centerline and control limits. We get x = 13.819 + 13.692 + g+ 14.878 14 = 14.0802 R = 0.490 + 0.410 + g+ 1.210 14 = 0.4371 Referring to Table 14-2 on page 707, we find that for n = 10, A2 = 0.308. Knowing the values of x, A2, and R, we can now evaluate the control limits. Upper control limit 1UCL : x + A2R = 14.0802 + 10.308210.43712 = 14.2148 Lower control limit 1LCL2: x - A2R = 14.0802 - 10.308210.43712 = 13.9456 The resulting control chart for x will be as shown in the accompanying display. x Chart INTERPRETATION Examination of the x chart shows that the process mean is out of statistical control because there are points lying beyond the upper and lower control limits and there are at least eight consecutive points lying below the centerline. By analyzing the global Earth temperatures in Table 14-1 with a run chart, an R chart, and an x chart, we can see that the process is out of statistical control. It appears that the temperatures of Earth are increasing, so it appears that global warming is a real phenomenon.
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