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"Tiger Tools, a division of Drillmore Industries, was about to launch a new product.

"Tiger Tools, a division of Drillmore Industries, was about to launch a new product. Production Manager Michelle York asked her assistant, Jim Peterson to check the capability of the oven used in the process. Jim obtained 18 random samples of 20 pieces each. The results of those samples are shown in the following table. After the analyzed data, he concluded that the process was not capable based on a specification width of 1.44 cm.
Michelle was quite disappointed when she heard this. She had hoped that with the introduction of the new product her operation could run close to full capacity and regain some of its lost luster. The company had a freeze on capital expenditures of more than 10000, and a replacement oven would cost many times that amount. Jim peterson worked with the oven crew to see if perhaps different settings could produce the desired results, but they were unable to achieve any meaningful improvements.
chart sample mean range
1 45.01 .85
2 44.99 .89
3 45.02 .86
4 45 .91
5 45.04 .87
6 44.98 .90
7 44.91 .86
8 45.04 .89
9 45 .85
10 44.97 .91
11 45.1 .84
12 44.96 .87
13 45 .86
14 44.92 .89
15 45.06 .87
16 44.94 .86
17 45 .85
18 45.03 .88
Still not ready to concede, Michelle contacted one of her former professors and explained the problem. The professor suggested obtaining another set of samples, this time using a smaller sample size and taking more samples. Michelle then conferred with Jim and they agreed that he would take 27 samples of five observations each. The results are shown below.
sample mean range
1 44.96 .42
2 44.98 .39
3 44.96 .41
4 44.97 .37
5 45.02 .39
6 45.03 .4
7 45.04 .39
8 45.02 .42
9 45.08 .38
10 45.12 .4
11 45.07 .41
12 45.02 .38
13 45.01 .41
14 44.98 .4
15 45 .39
16 44.95 .41
17 44.94 .43
18 44.94 .4
19 44.87 .38
20 44.95 .41
21 44.93 .39
22 44.96 .41
23 44.99 .4
24 45 .44
25 45.03 .42
26 45.04 .38
27 45.03 .4
Consider the following questions.
1. How did Jim conclude that the process was not capable based on his first set of samples?(Hint estimate the process standard deviation using a2rbar
2.Does the second set of samples show anything that the first set doesn't? Explain what and why
3. Assuming the problem can be found and corrected, what impact do you think this would have on the capability of the process? Compute the potential process capability.
4.If small samples can reveal something that large samples might not, why not just take small samples in every sistuation?"

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