Minting Quarters Specifications for a quarter require that it ...

Question

Minting Quarters Specifications for a quarter require that it be 8.33% nickel and 91.67% copper; it must weigh 5.670 g and have a diameter of 24.26 mm and a thickness of 1.75 mm; and it must have 119 reeds on the edge. A quarter is considered to be defective if it deviates substantially from those specifications. A production process is monitored, defects are recorded and the accompanying control chart is obtained. Does this process appear to be within statistical control? If not, identify any out-of-control criteria that are satisfied. Is the manufacturing process deteriorating?
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Accepted Answer

Hello, everyone. Let's take a look at this question together. A factory produces bolts that must meet strict specifications. Each bolt must have a length of 50 millimeters, a diameter of 10 millimeters, and a weight of 15 g with a tolerance of plus or minus 0.2 millimeters for length and diameter, and plus or minus 0.5 g for weight. A bolt is classified as defective if it significantly deviates from the specified standards. The manufacturing process is monitored daily with defects recorded and analyzed using the following control chart. Does the control chart suggest that the process is within statistical control? If not, identify any out of control criteria that are met. Is the manufacturing process showing signs of deterioration? And here we have an image depicting our control chart for the bolt defects, and we have to determine, is it answer choice A, the process is within statistical control, as all points fall within control limits and show no deterioration. Answer choice B, the process is out of control because there is a run of more than 8 consecutive points on one side of the center line. Answer choice C, the process is out of control because of a consistent upward trend showing signs of deterioration, or answer choice D, none of these. So, in order to solve this question, we have to recall what we have learned about analyzing a control chart to determine if this control chart suggests that the process is within statistical control. And if it is not, identify the out of control criteria that are met. And so we have to recall the three standard out of control criteria to determine if the control chart is within or is out of statistical control, and the 3 standard out of control criteria are any point outside of the control limits, a run of consecutive points on one side of the center line. And a trend of increasing or decreasing values over several points. So looking at the control chart using our three standard out of control criteria, starting with number 1, we have to identify if the points are outside of the control limits. Well, from the control chart, we can see that the upper control limit is 28.31 defects. The lower control limit is 4.29 defects, and the center line is 16.3 defects. And looking at our control chart, we can identify that no points exceed the upper control limit or fall below the lower control limit, so we do not meet the criteria for the first standard, and then looking at our control chart to see if we Meet the criteria for our second standard, we know that if there are 8 or more consecutive points above or below the center line, this would indicate that we are out of statistical control. However, we can see from the control chart that no 8 or more consecutive points lie above or below the center line, though we do not meet the criteria for the second standard. And then lastly, Looking at our control chart to see if we meet the 3rd standard, which is a trend of increasing or decreasing values over several points. We know that a consistent upward or downward trend may indicate deterioration. However, looking at our control chart, we can identify that we do not meet the criteria for the 3rd standard. Therefore, based on the 3 standard out of control criteria, And our control chart, we know that no criteria is met and therefore, this process is within statistical control, which looking at our answer choices, we can identify that answer choice A is the correct answer, as based on the control chart that we are given, the process is within statistical control as all points fall within control limits and show no deterioration. So answer choice A is the only correct answer choice. I hope you found this video to be helpful. Thank you and goodbye.

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Key Concepts

Statistical Control

Defect Criteria

Control Chart Analysis

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