Question

Your company manufactures audio tapes for machinery markets. The thickness of the magnetic coating is an important characteristic. Random samples of size 4 are selected, and the thickness is measured using an optical instrument. Table 1 shows the mean and standard deviation for 25 samples. The specifications of its design are 38.0 ± 4.5 mm. If a coating thickness is less than the specifications call for, that tape can be used for a different purpose by running it through another coating operation.

Sample	Sample Mean	Std
1	36.4	4.6
2	35.8	3.7
3	37.3	5.2
4	33.9	4.3
5	37.8	4.4
6	36.1	3.9
7	38.6	5
8	39.4	6.1
9	34.4	4.1
10	39.5	5.8
11	36.7	5.3
12	35.2	3.5
13	38.8	4.7
14	39	5.6
15	35.5	5
16	37.1	4.1
17	38.3	5.6
18	39.2	4.8
19	36.8	4.7
20	37.7	5.4
21	36.5	4.7
22	38.7	4
23	37.3	5.1
24	34.7	4.2
25	39.1	5.4

A. Find the trial central line and control limits for the S-chart.

B. Find the trial central line and control limits for the X- bar chart.

C. Assuming the thickness of the coating to be normally distributed, what proportion of the product will not meet specifications?

D. Find the process capability indices of Cp, CPU, CPL, and Cpk.

Please show your work and Explain

Answer 1