In Exercises 5–8, use the following two control charts that re...

Question

In Exercises 5–8, use the following two control charts that result from testing batches of newly manufactured aircraft altimeters, with 100 in each batch. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 6000 ft. The Federal Aviation Administration requires an error of no more than 40 ft at that altitude.

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Is the process variation within statistical control? Why or why not?

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Is the process variation within statistical control? Why or why not?

Accepted Answer

Hello, everyone. Let's take a look at this question together. Refer to the control chart below, which represents the results of testing batches of newly manufactured pressure gauges with each batch containing 50 units. The recorded values indicate pressure deviations in PSI measured under controlled conditions. According to industry regulations, the pressure deviation must remain within plus or minus 2 PSI. And here we have our control chart that we have to determine. Does the control chart suggest that the process variation is within statistical control? Why or why not? Is it answer choice A, the process is within statistical control, as all points fall within control limits? Answer choice B, the process is statistically out of control because there are points lying outside the control limits. Answer choice C, the process is out of control because of a consistent upward trend showing signs of deterioration, or answer choice D, the process is within statistical control because none of The three out of control criteria are met. So in order to solve this question, we have to recall what we have learned about determining if a control chart is within or without statistical control to determine if this control chart for pressure gauge manufacturing does in fact suggest that The process variation is within statistical control, and we know that to determine whether the pressure deviation is within statistical control, we analyze the control chart based on the three standard out of control criteria, which are #1, any point outside of the control limits. Number 2, a run of consecutive points on one side of the center line, and number 3, a trend of increasing or decreasing values over several points. So looking at our control chart, we must first identify if there are any points outside of the control limits, which include the upper control limit of +2 PSI, a lower control limit of -2 PSI, and a center line. Of 0 PSI. So if any data point exceeds the upper control limit or falls below the lower control limit, the process is out of control, which looking at our control chart, we can identify that there are in fact points that exceed the upper control limit and fall below the lower control limit, so our control chart does in fact meet the criteria for the first standard of out of. criteria. And then for the second standard, which is a run of consecutive points on one side of the center line, we know that if there are 8 or more consecutive points above or below the center line, this would indicate an out of control situation. However, from our control chart, we see that no 8 or more consecutive points lie above or below the center line, so we do not meet the criteria for the second. Standard of out of control criteria. And lastly, the third standard says a trend of increasing or decreasing values over several points, such as a consistent upward or downward trend, which would indicate deterioration, however, our control chart does not show a trend of increasing or decreasing values, so we do not meet the criteria for the 3rd standard, and we only meet the criteria for the first standard. As there are points outside of the control limits. And so looking at our answer choices based on our observations, we can identify that the correct answer is answer choice B. As answer choice B says the process is statistically out of control because there are points lying outside of the control limits. So answer choice B is the correct answer, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

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Key Concepts

Control Charts

Process Variation

Statistical Control

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