14-2 Control Charts for Attributes 715 YOUR TURN. Do Exercise 5 “Euro Coins.” SOLUTION The centerline for the control chart is located by the value of p: p = total number of defects from all samples combined total number of altimeters sampled , = 2 + 0 + 1 + g+ 7 12# 100 = 42 1200 = 0.035 Because p = 0.035, it follows that q = 1 - p = 0.965. Using p = 0.035, q = 0.965, and n = 100, we find the control limits as follows: Upper control limit: p + 3 Bpq n = 0.035 + 3B10.035210.9652 100 = 0.090 Lower control limit: p - 3 Bpq n = 0.035 - 3B10.035210.9652 100 = -0.020 Because the lower control limit is less than 0, we use 0 instead. Having found the values for the centerline and control limits, we can proceed to plot the control chart for proportions of defective altimeters. The Minitab control chart for p is shown in the accompanying display. INTERPRETATION We can interpret the control chart for p by considering the three out-of-control criteria listed earlier in this section. Using those criteria, we conclude that this process is out of statistical control for these reasons: There appears to be an upward trend, and there is point lying beyond the upper control limit. The company should take immediate corrective action. Minitab CAUTION Upper and lower control limits of a control chart for a proportion p are based on the actual behavior of the process, not the desired behavior. Upper and lower control limits are totally unrelated to any process specifications that may have been decreed by the manufacturer. Quality Control at Perstorp Perstorp Components, Inc., uses a computer that automatically generates control charts to monitor the thicknesses of the floor insulation the company makes for Ford Rangers and Jeep Grand Cherokees. The $20,000 cost of the computer was offset by a first-year savings of $40,000 in labor, which had been used to manually generate control charts to ensure that insulation thicknesses were between the specifications of 2.912 mm and 2.988 mm. Through the use of control charts and other quality-control methods, Perstorp reduced its waste by more than two-thirds.
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