Example 1 The data shown here are x? and R values for 24 samples of size n=5 taken from a process producing bearings. The measurements are made on the inside diameter of the bearing. a) Set up x-bar and R charts on this process. Does the process seem to be in statistical control? If necessary, revise the trial control limits. b) Estimate the process standard deviation x? R 34.5 3 34.2 4 31.6 4 31.5 4 35.0 5 34.1 6 32.6 4 33.8 3 34.8 7 33.6 8 31.9 3 38.6 9 35.4 8 34.0 6 37.1 5 34.9 7 33.5 4 31.7 3 34.0 8 35.1 4 33.7 2 32.8 1 33.5 3 34.2 2
Added by Larry L.
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First, we need to calculate the average (X-bar) and range (R) for each sample. Show more…
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TABLE 6E.2 Bearing Diameter Data Sample Number x R Sample Number x R 1 34.5 3 13 35.4 8 2 34.2 4 14 34.0 6 3 31.6 4 15 37.1 5 4 31.5 4 16 34.9 7 5 35.0 5 17 33.5 4 6 34.1 6 18 31.7 3 7 32.6 4 19 34.0 8 8 33.8 3 20 35.1 4 9 34.8 7 21 33.7 2 10 33.6 8 22 32.8 1 11 31.9 3 23 33.5 3 12 38.6 9 24 34.2 2 inside diameter of the bearing, with only the last three decimals recorded (i.e., 34.5 should be 0.50345). (a) Set up x̄ and R charts on this process. Does the process seem to be in statistical control? If necessary, revise the trial control limits. (b) If specifications on this diameter are 0.5030 ± 0.0010, find the percentage of nonconforming bearings produced by this process. Assume that diameter is normally distributed.
Patha S.
1. [10 points] The data shown in the table below are x , R and S values for 10 samples of size n=5 taken from a process producing bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals recorded (i.e., 34.5 should be 0.50345). Sample number | x | R | S 1 | 34.5 | 3 | 0.5 2 | 34.2 | 4 | 0.67 3 | 31.6 | 4 | 0.67 4 | 31.5 | 4 | 0.67 5 | 35.0 | 5 | 0.83 6 | 34.1 | 6 | 1.00 7 | 32.6 | 4 | 0.67 8 | 33.8 | 3 | 0.67 9 | 34.8 | 7 | 1.75 10 | 33.6 | 8 | 1.33 (a) Setup the control charts to monitor the process variability based on the 10 samples drawn. Show the center line and the control limits (you don't need to draw the chart). Does the process appear to be in control? (b) If specifications on this diameter are 0.50300 ± 0.0001, find the percentage of nonconforming bearings produced by this process. Assume that diameter is normally distributed.
Madhur L.
A machining operation produces bearings with diameters that are normally distributed with mean 3.0005 inches and standard deviation. 0010 inch. Specifications require the bearing diameters to lie in the interval $3.000 \pm .0020$ inches. Those outside the interval are considered scrap and must be remachined. With the existing machine setting, what fraction of total production will be scrap? a. Answer the question, using Table 4, Appendix 3. b. Applet Exercise obtain the answer, using the applet Normal Probabilities.
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