Sankyo Vietnam Corporation has become a supplier for many major companies such as Canon, Mitsubishi, Toto, Brother, Kyocera, etc. Some of the company’s outstanding products are motors and drives, card readers, plastic injection processing, music boxes, JIG, hot stamping molds, steel molds, metal moulds, electronic components, computer accessories, moulding products, etc.
The company was about to launch a new product. Production Manager Nhu asked her assistant, Trinh, to check the capability of a machinery used in the process. Trinh obtained 20 random samples of 16 pieces each. The results of those samples are shown in the following table. After she analysed the data, she concluded that the process was capable based on a specification width of 1.56 cm. Nhu 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. The company had a freeze on capital expenditures of more than $500,000, and a replacement machinery would cost many times that amount. Trinh worked with the machinery workers to see if perhaps different settings could produce the desired results, but they were unable to achieve any meaningful improvements.
|
Sample |
Mean |
Range |
|
Sample |
Mean |
Range |
|
1 |
44.99 |
0.84 |
|
11 |
44.97 |
0.9 |
|
2 |
45.01 |
0.89 |
|
12 |
45.11 |
0.84 |
|
3 |
45.02 |
0.86 |
|
13 |
44.91 |
0.87 |
|
4 |
45.01 |
0.91 |
|
14 |
45.01 |
0.82 |
|
5 |
45.01 |
0.87 |
|
15 |
44.92 |
0.85 |
|
6 |
44.82 |
0.91 |
|
16 |
45.06 |
0.87 |
|
7 |
44.79 |
0.86 |
|
17 |
44.94 |
0.84 |
|
8 |
45.01 |
0.89 |
|
18 |
44.81 |
0.85 |
|
9 |
45.02 |
0.85 |
|
19 |
45.03 |
0.88 |
|
10 |
44.79 |
0.89 |
|
20 |
45.08 |
0.92 |
(values in centimetre)
Still not ready to concede, Nhu contacted one of her former professors and explained the problem. The professor suggested obtaining another set of samples, this time using different sample size. Nhu then conferred with Trinh, and they agreed that she would take 28 samples of nine pieces each. The results are shown in the following table (see next page).
|
Sample |
Mean |
Range |
Sample |
Mean |
Range |
|
|
1 |
44.95 |
0.43 |
15 |
45.02 |
0.39 |
|
|
2 |
44.99 |
0.39 |
16 |
44.95 |
0.41 |
|
|
3 |
44.96 |
0.41 |
17 |
44.94 |
0.43 |
|
|
4 |
44.97 |
0.35 |
18 |
44.94 |
0.45 |
|
|
5 |
45.03 |
0.39 |
19 |
44.88 |
0.36 |
|
|
6 |
45.03 |
0.4 |
20 |
44.95 |
0.41 |
|
|
7 |
45.04 |
0.39 |
21 |
44.93 |
0.39 |
|
|
8 |
45.02 |
0.42 |
22 |
44.96 |
0.41 |
|
|
9 |
45.08 |
0.38 |
23 |
44.99 |
0.39 |
|
|
10 |
45.12 |
0.41 |
24 |
45.01 |
0.45 |
|
|
11 |
45.07 |
0.41 |
25 |
45.03 |
0.42 |
|
|
12 |
45.02 |
0.39 |
26 |
45.03 |
0.37 |
|
|
13 |
45.02 |
0.41 |
27 |
45.03 |
0.48 |
|
|
14 |
44.98 |
0.41 |
28 |
45.11 |
0.41 |
Questions (each question 2.5 marks, a total of 10 marks for this case study)
Consider the following questions, and then write a brief report to Jane summarizing your findings.
1. How did Trinh conclude that the process was capable based on his first set of samples? (Hint: Estimate the process standard deviation,)
2. Does the second set of samples show anything that the first set didn’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 using the second data set.
4. If small samples can reveal something that large samples might not, why not just take small samples in every situation?
