Bottle | ||||||
Sample | 1 | 2 | 3 | 4 | X-bar | Range |
1 | 12.02 | 11.93 | 11.95 | 11.9 | 11.95 | 0.12 |
2 | 11.91 | 11.94 | 11.92 | 12.08 | 11.96 | 0.17 |
3 | 11.93 | 12.04 | 12.1 | 11.88 | 11.99 | 0.22 |
4 | 11.98 | 12.01 | 11.98 | 12.07 | 12.01 | 0.09 |
5 | 12.12 | 11.94 | 11.95 | 12.12 | 12.03 | 0.18 |
6 | 12.12 | 11.97 | 12.06 | 11.93 | 12.02 | 0.19 |
7 | 11.91 | 12.05 | 11.89 | 11.94 | 11.95 | 0.16 |
8 | 12.06 | 11.9 | 11.9 | 12.09 | 11.99 | 0.19 |
9 | 11.89 | 12.04 | 12.01 | 12.09 | 12.01 | 0.20 |
10 | 12.06 | 11.95 | 11.96 | 11.88 | 11.96 | 0.18 |
11 | 12.09 | 12.12 | 11.98 | 12.08 | 12.07 | 0.14 |
12 | 12.07 | 12.02 | 11.91 | 12.05 | 12.01 | 0.16 |
13 | 11.95 | 11.98 | 12.12 | 11.98 | 12.01 | 0.17 |
14 | 11.91 | 12.04 | 11.94 | 12.11 | 12.00 | 0.20 |
15 | 11.97 | 12.11 | 11.98 | 11.99 | 12.01 | 0.14 |
Averages | 11.998 | 0.167 | ||||
X_double-bar | R-bar |
For sample size n = 4,A2 = 0.729, D3 = 0, and D4 = 2.282
UCLR = D4 * R_bar = 2.282 * 0.167 =
0.382
LCLR = D3 * R_bar = 0 * 0.167 =
0
UCLX = X_double-bar + A2 * R_bar = 11.998
+ 0.729*0.167 = 12.120
LCLX = X_double-bar - A2 * R_bar = 11.998 -
0.729*0.167 = 11.876
a.
Process averages are in control. Process ranges are also in control.
b.
Estimate for process stdev = A2 * R_bar * √n / 3 = 0.729*0.167*√4 / 3 = 0.081
Cpu = (USL - mean) / 3.stdev = (12.10 - 11.998) / (3*0.081) =
0.420
Cpl = (mean - LSL) / 3.stdev = (11.998 - 11.90) / (3*0.081) =
0.402
So, Cpk = Min(Cpu, Cpl) = 0.402 and the process is not capable.
. The production manager at Sunny Soda, Inc., is interested in tracking the quality of the company's 12-ounce bottl...
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Sample 1|Sample 2 Sample 3 Sample 4 11.91 11.55 11.62 11.62 11.69 11.52 11.59 11.75 11.82 1.90 11.97 11.64 11.80 11.87 12.03 11.94 12.01 11.92 11.99 12.13 12.09 12.16 11.93 12.21 12.32 12.39 11.93 11.85 11.92 11.7611.83 11.7012.38 11.77 11 12.00 12.07 12.04 11.98 12.05 12.30 12.37 12.18 12.25 11.97 12.17 12.24 11.85 11.92 12.30 12.37 12.15 12.22 12.02 11.36 12.02 11.75 12.05 11.95 12.18 12.14 11.72 12.07 12.05 11.85 11.64 12.16 12.39 11.65 12.11 11.90 12.22 11.56 11.88 11.95...