Question

Six Sigma Problems 36. Analyze the following set of data in the table below. The target is 66 and the customer requirements are 60 and 72 respectively. A Defect costs $5 to rework. The control limits for averages are closest to the following: Sample 4/5 Average Range 67 62 6965 62 61 68 4/61 65 68 68 67 68 63 66 765 67 66 66 69 65 66 64.9 65.7 65.7 66.3 66.4 65 9 65.6 4/10 67 66 69 65 65 67 65 67 67 66 67 66 66 67 67 66 64 4/12 641 671 661 413 67 415 69165 64 67 68 417 66 62 66 71 65 64 67 66.3 65.9 4/18 64 66 68 68 66 65 68 65 4 4/20 64 66 64 68 66 66 67 4/2 66.1 66.3 66.1 65.7 4/23 | 65 | 65 | 66 | 70 | 67 | 64 | 66 66.3 4/28 66 65 68169 68 66 65 67.1 Ag = 66.00 4.92 68.06 and 63.94 66.08 and 64.36 69.46 and 60.64 None of the above 《 Prev Page

Answer 1

Sample size for set, n = 7

The constants d2 for n = 7 is 2.704

Standard deviation, $\sigma$ = $\bar{R}$ / d2 = 4.92 / 2.704 = 1.819527

Upper limit = $\bar{x}$ + 3 $\sigma$ / $\sqrt{n}$ = 66 + 3 * 1.819527 / $\sqrt{7}$ = 68.06

Lower limit = $\bar{x}$ - 3 $\sigma$ / $\sqrt{n}$ = 66 - 3 * 1.819527 / $\sqrt{7}$ = 63.94

Anser is,

68.06 and 63.94