Quarters. In Exercises 9–12, refer to the accompanying table o...

Question

Quarters. In Exercises 9–12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available in Data Set 44 “Weights of Minted Quarters” in Appendix B.

Quarters: R Chart Treat the five measurements from each day as a sample and construct an R chart. What does the result suggest?

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says a manufacturing company produces metal washers and measures the thickness to ensure consistency. The thickness measurements in millimeters are taken from 5 washers per day for 5 consecutive days. The data is presented below. and we're given a table with 7 columns. In the first column, it is labeled day and has values of 1234, and 5. The next column is labeled sample 1, and it has values of 2.31, 2.34, 2.40, 2.29, and 2.32. The next column is labeled sample 2, and it has values of 2.35, 2.38, 2.45, 2.35, and 2.36. The next column is labeled sample 3, and it has values of 2.29, 2.36, 2.43, 2.31, and 2.30. The next column is labeled sample 4, and it has values of 2.32, 2.37, 2.41, 2.30, and 2.34. The next column is label symbol 5, and it has values of 2.30, 2.32, 2.39, 2.33, and 2.29. And the final column is labeled range, and it has values of 0.06, 0.06, 0.06, 0.06, and 0.07. We're also given that the average range or bar for these samples is 0.062. The lower control limit for the R chart is equal to 0, the upper control limit for the R chart is equal to 0.131. And we need to answer the question, to treat the 5 measurements from each day as a sample, and construct an R chart. What does the chart suggest about the stability of the process? And below this question, we're given a blank chart with which to plot our our chart. Now, since we were given the upper control limit, the lower control limit, and our bar for our data, we'll go ahead and plot those on our chart. So, the first thing that we'll plot is the lower control limit, and we're told that it has a value of 0. So we'll plot a horse online. With a point at each of our 5 days at 0, and connect those points to create that horizontal line. And we're going to label this as LCL. For the lower control limit. Next, we'll plot our upper control limit, and the upper control limit has a value of 0.131. We'll plot a point with a value of 0.131. For each of our 5 days, and connect those points to create a horizontal line. And so, we're then going to label this. As our upper control limit. With the abbreviation of UCL. Next, we're going to Let our line for our bar. And the average range was 0.062. We'll plot a point at 0.062 at each of our five days. And we'll connect. All five of those points together, you create a horizontal line with a value of 0.062. And we will label this line as our bar. And so now we just need to plot our range data. And so, for day one, we had a range of 0.06. For day two, we had a range of 0.06. Likewise, for day 3, we had a range of 0.06. For day four, we had a range of 0.06. However, for day 5, we had a range of 0.07. And so now we just need to connect those 5 points together. And this will complete our graph. And so now we just need to actually interpret. This graph in order to um determine what it says about the stability of the process. Now, if we look at our graph here, we see that all ranges fall within the control limits. That means that the variation in washer thickness is under control. And since the process variation is under control, no corrective actions are needed. So that's going to be the answer for this question. So, I hope that this explanation has been useful, and I'll see you in the next video.

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Key Concepts

R Chart

Sample Size

Control Limits

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