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Sampling four pieces of precision-cut wire (to be used in computer assembly) every hour for the past 24 hours has produced the following results: Develop appropriate control charts and determine whether there is any cause for concern in the cutting process. Plot the information and look for patterns.
Expert Answer
Please find UCL and LCL calculations:
| Mean(MM) | Range (MM) | Control-mean | Control- range | ||||||
| 1 | 3.25 | 0.71 | no | yes | |||||
| 2 | 3.1 | 1.18 | yes | yes | |||||
| 3 | 3.22 | 1.43 | no | yes | |||||
| 4 | 3.39 | 1.26 | no | yes | |||||
| 5 | 3.07 | 1.17 | yes | yes | |||||
| 6 | 2.86 | 0.32 | yes | no | |||||
| 7 | 3.05 | 0.53 | yes | yes | |||||
| 8 | 2.65 | 1.13 | no | yes | |||||
| 9 | 3.02 | 0.71 | yes | yes | |||||
| 10 | 2.85 | 1.33 | yes | yes | |||||
| 11 | 2.83 | 1.17 | yes | yes | |||||
| 12 | 2.97 | 0.4 | yes | no | |||||
| 13 | 3.11 | 0.85 | yes | yes | |||||
| 14 | 2.83 | 1.31 | yes | yes | |||||
| 15 | 3.12 | 1.06 | yes | yes | |||||
| 16 | 2.84 | 0.5 | yes | yes | |||||
| 17 | 2.86 | 1.43 | yes | yes | |||||
| 18 | 2.74 | 1.29 | no | yes | |||||
| 19 | 3.41 | 1.61 | no | no | |||||
| 20 | 2.89 | 1.09 | yes | yes | |||||
| 21 | 2.65 | 1.08 | no | yes | |||||
| 22 | 3.28 | 0.46 | no | yes | |||||
| 23 | 2.94 | 1.58 | yes | yes | |||||
| 24 | 2.64 | 0.97 | no | yes | |||||
| X( Mean) | 2.982 | ( add all means and divide by 24) | |||||||
| Range Mean | 1.024 | ( add all range and divide by 24) | |||||||
| UCL (Mean) | 3.143 | Mean+A2R | A2 value for 24 observations is 0.157 | ||||||
| LCL Mean | 2.821 | Mean -A2R | |||||||
| UCL Range | 1.585 | D4 * Range mean | D4 value for 24 observations is 1.548 | ||||||
| LCL Range | 0.454 | D3* Range mean | D3 value for 24 observations is 0.443 | ||||||
| Observations: | |||||||||
| 1. Mean control: 9 out of 24 are out of control | |||||||||
| 2. range control: 3 out of 24 are out of control | |||||||||
| clubbing one and two, the process needs to be controlled better so that variability in mean is decreased. | |||||||||
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