Question

Data were collected on a quantitative measure with a subgroup size of seven observations. Thirty sub roups were collected X-47 and R Complete parts a rough below Click the icon to view a table of control chart factors. a. Determine the Shewhart factors that will be needed if x- and R-charts are to be developed The Shewhart factor for the i-chart is A2 (Round to three decimal places as needed.) The Shewhart factors for the R-chart are D3 and D4-D (Round to three decimal places as needed.) b. Compute the upper and lower control limits for the R-chart. UCL= (Round to three decimal places as needed.) LCL = (Round to three decimal places as needed.) c. Compute the upper and lower control limits for the x-chart. UCL Round to three decimal places as needed.) LCL (Round to three decimal places as needed.)Control Chart Factors Number of Obser vations in Subgroup 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078 3.173 3.258 3.336 3.407 3.472 3.532 3.588 3.640 3.689 3.735 3.778 3.819 3.858 3.895 3.931 0.853 0.888 0.880 0.864 0.848 0.833 0.820 0.808 0.797 0.787 0.778 0.770 0.763 0.756 0.750 0.744 0.739 0.733 0.729 0.724 0.720 0.716 0.712 0.708 0 0 0 3.267 2.575 2.282 2.114 2.004 1.924 1.864 1.816 0 0.076 0.136 0.184 0.223 0.256 0.283 0.307 0.328 0.347 0.363 0.378 0.391 0.404 0.415 0425 0435 0.443 0.452 0459 8 1.744 13 14 15 1.693 1.672 1.653 1.637 1.622 1.609 1.596 1.585 1.575 1.565 1557 1.548 1.541 17 18

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Answer #1

A.

Since the sample size is 7,

Then,

Value of A2 = .419

Value of D3 = .076

Value of D4 = 1.924

B.

For R chart,

UCL = D4*R Bar

UCL = 1.924*6.4

UCL = 12.314

LCL = D3*R Bar = .076*6.4

LCL =.486

C.

For X bar chart

UCL = X double bar + A2*R

UCL = 47.05 + .419*6.4

UCL= 49.732

LCL = X double bar - A2*R

LCL = 47.05 - .419*6.4

LCL = 44.368

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