In: Statistics and Probability
Problem 4. A high-voltage power supply should have a nominal output voltage of 350 V. A sample of four units is selected each day and tested for process-control purposes. The data (see sheet Problem4 in Homework 4.xlsx) give the difference between the observed reading on each unit and the nominal voltage times ten; that is, ?? = (observed voltage on unit ? - 350)*10 (a) Set up ?̅ and ? charts on this process. Is the process in statistical control? (2 points) (b) If specifications are at 350 V ±5 V, estimate ? and ? , ? and ? ? (2 points) ? ??? ?? (c) What can you say about process capability ??? (2 points)
Sample | x1 | x2 | x3 | x4 | Xbar | R |
1 | 6 | 9 | 10 | 15 | 10 | 9 |
2 | 10 | 4 | 6 | 11 | 7.75 | 5 |
3 | 7 | 8 | 10 | 5 | 7.5 | 5 |
4 | 8 | 9 | 6 | 13 | 9 | 7 |
5 | 9 | 10 | 7 | 13 | 9.75 | 6 |
6 | 12 | 11 | 10 | 10 | 10.75 | 2 |
7 | 16 | 10 | 8 | 9 | 10.75 | 7 |
8 | 7 | 5 | 10 | 4 | 6.5 | 6 |
9 | 9 | 7 | 8 | 12 | 9 | 4 |
10 | 15 | 16 | 10 | 13 | 13.5 | 6 |
11 | 8 | 12 | 14 | 16 | 12.5 | 8 |
12 | 6 | 13 | 9 | 11 | 9.75 | 7 |
13 | 16 | 9 | 13 | 15 | 13.25 | 7 |
14 | 7 | 13 | 10 | 12 | 10.5 | 6 |
15 | 11 | 7 | 10 | 16 | 11 | 9 |
16 | 15 | 10 | 11 | 14 | 12.5 | 5 |
17 | 9 | 8 | 12 | 10 | 9.75 | 3 |
18 | 15 | 7 | 10 | 11 | 10.75 | 8 |
19 | 8 | 6 | 9 | 12 | 8.75 | 6 |
20 | 13 | 14 | 11 | 15 | 13.25 | 4 |
Yes, The Process is in Statistical Control.
Sample size | 4 | ||
Number of samples | 20 | ||
Mean | Range | ||
Upper Control Limit, UCL | 14.88 | 14.26 | |
Center | 10.33 | 6.25 | |
Lower Control Limit, LCL | 5.77 |
0.00 |
C-hatp = 5.49, so the process is capable.