Dr. Patel is concerned about the long wait times in his office.The following table presents six random observations for thepatient waiting times over a period of 10 days.
| Observations (mins) |
Day | 1 | 2 | 3 | 4 | 5 | 6 |
1 | 30 | 17 | 18 | 21 | 19 | 33 |
2 | 17 | 11 | 33 | 33 | 39 | 11 |
3 | 19 | 25 | 40 | 17 | 38 | 13 |
4 | 29 | 31 | 29 | 25 | 22 | 21 |
5 | 15 | 34 | 26 | 14 | 14 | 18 |
6 | 8 | 11 | 29 | 33 | 39 | 17 |
7 | 24 | 24 | 26 | 37 | 28 | 20 |
8 | 14 | 33 | 23 | 16 | 40 | 13 |
9 | 27 | 18 | 30 | 11 | 20 | 17 |
10 | 37 | 35 | 12 | 38 | 29 | 8 |
- Dr. Patel is willing to use three-sigma limits. Use the givendata and the factors from Table 3.1 (page 110) to constructR-chart and -chart.
- Is the process in statistical control? Explain.
- If patient surveys indicate that they are willing to waitbetween 10 and 30 minutes before seeing Dr. Patel, is the processcapable of meeting this demand at the three-sigma level?
Table 3.1
Factors For Calculating Three Sigma Limits for the x¯x¯-Chart and R-Chart
Size of Sample (n) | Factor for UCL and LCL for x¯¯?Chart(A2)x¯-Chart(A2) | Factor for LCL for R-Chart (D3)(D3) | Factor for UCL for R-Chart (D4)(D4) |
|---|
2 | 1.880 | 0 | 3.267 |
3 | 1.023 | 0 | 2.575 |
4 | 0.729 | 0 | 2.282 |
5 | 0.577 | 0 | 2.115 |
6 | 0.483 | 0 | 2.004 |
7 | 0.419 | 0.076 | 1.924 |
8 | 0.373 | 0.136 | 1.864 |
9 | 0.337 | 0.184 | 1.816 |
10 | 0.308 | 0.223 | 1.777 |
