Question

15.06 25 Points) The data shown in table below are for ten samples of size 3. Sample Mean Range 18.58 11.52 2.85 8.70 7.38 11.26 2.81 6.94 5.06 10.38 3.09 / 9.71 2.53 10.65 4.85 7.65 2.44 18.64 1 1.83 a) Determine the appropriate control charts for this problem and find UCL and LCL b) Draw the charts. What conclusions can be drawn from the charts?

Answer 1

Below is the screenshot of the formula applied -

XC Chart Excel Abhishek Rai Help File Home Insert Page Layout Formulas Data Review View Tell me what you want to do Trace Precedents Define Name 5 Show Formulas fx Σ ? A Calculate Now Use in Formula Trace Dependents Error Checking Calculation Calculate Sheet Options Insert AutoSum Recently Financial Logical Text Date & Lookup & Math & More Name Watch Evaluate Formula Create from Selection Remove Arrows Time Reference Triq Functions Function Used Manager Window Function Library Defined Names Formula Auditing Calculation fx N11 X A В C D Е F Н J К L M A2 1.023 X-Chart R-Chart 1 X double bar Sample 2 UCL Center Line Х-Bar R R-bar Center Line LCL UCL LCL D4 2.574 - E3*SN$3 -E4*$N$3 -E5*SN$3 - E6* $N$3 -E7* $N$3 - E8*$N$3 - E9*$N$3 - E10*$N$3 - E11* $N$3 -E12*SN$3 -AVERAGE($B$3:$B$12)AVERAGE($C$3:$C$12)D3 -AVERAGE($B$3:$B$12)AVERAGE($C$3:$C$12)D4 -AVERAGE($B$3:$B$12)AVERAGE($C$3:$C$12)D5 -AVERAGE($B$3:$B$12)AVERAGE($C$3:$C$12)D6 -AVERAGE($B$3:$B$12)AVERAGE($C$3:$C$12)D7 -AVERAGE($B$3:$B$12)AVERAGE($C$3:$C$12)D8 -AVERAGE($B$3:$B$12)AVERAGE($C$3:$C$12)D9 -AVERAGE ($B$3:$B$12)AVERAGE($C$3:$c$12)D10 -AVERAGE ($B$3:$B$12)AVERAGE($C$3:$C$12) D11 -AVERAGE ($B$3:$B$12)AVERAGE($C$3:$C$12)D12 -F3+E3*SN$1 -F4+E4*$N$1 - F5+E5*$N$1 -F6+E6* $N$1 -F7+E7*$N$1 -F8+E8* $N$ 1 -F9+E9* $N$1 - F10+ E10* N$1 -F10-E10*SN$1 -F11+E11* $N$1 F11-E11*$N$1 - F12+ E12*SN$1 -F12-E12*SN$1 - F3-E3* $N$1 =F4- E4*$N$1 8.58 5.06 E13*$N$2 3 1 -E3 D3 0 14* $N$2 E 15*SN$2 16* $N$2 E17*$N$2 18*SN$2 19*SN$2 - 110* $N$2 E1 11* $N$2 E1 12*SN$2 4 2 11.52 2.85 -E4 5 3 -F5-E5*$N$1 - E5 8.7 7.38 6 4 - E6 11.26 =F6-E6*$N$1 -F7-E7*$N$1 2.81 7 5 - E7 6.94 5.06 -F8-E8* $N$1 10.38 3.09 2.53 -E8 8 6 9 7 9.71 - E9 =F9- E9* $N$ 1 10 8 10.65 4.85 E10 7.65 2.44 11 9 E11 1.83 12 10 8.64 -E12 13

Below is the screenshot of the result -

X C Chart Excel Abhishek Rai Chart Tools Page Layout Design File Home Insert Formulas Data Review View Help Format Tell me what you want to do Cut AutoSum General Calibri (Body) 10 A A aWrap Text Fill Copy Conditional Format as Formatting Table Styles Paste Insert Delete Format Merge & Center $% .0 ,00 00 0 A- BIU Clear Format Painter Clipboard Font Alignment Number Styles Cells Editim ffx Chart 2 A В C E F H K LM O P R S T v R-Chart 1.023 X-Chart A2. 1 X Chart X double Sam Cente Cente R-bar X-Bar R UCL LCL UCL LCL 2 ple bar r Line r Line 15.00 D4 2.574 8.58 5.06 3.79 D3 3 1 9.40 3.79 9.40 13.28 5.53 9.76 0.00 0 10.00 11.52 2.85 13.28 9.76 0.00 4 2 9.40 3.79 9.40 5.53 3.79 3.79 9.76 13.28 5.53 5 8.70 7,38 9.40 3.79 9,40 0.00 5.00 11.26 2.81 5.53 6 9.40 3.79 9.40 13.28 3.79 9.76 0.00 13.28 0.00 7 5 6.94 5.06 9.40 3.79 9.40 5.53 3.79 9.76 0.00 10.38 8 6 3.09 9.40 3.79 9.40 13.28 5.53 3.79 9.76 0.00 2 5 6 7 8 9 10 2.53 13.28 9.76 7 9.71 9.40 3.79 9.40 5.53 3.79 0.00 X-Bar UCL LCL 10.65 4.85 9.76 0.00 10 9.40 3.79 9.40 13.28 5.53 3.79 5.53 11 7.65 2,44 9.40 3.79 9.40 13.28 3.79 9.76 0.00 R Chart 3.79 9.76 9.40 12 10 8.64 1.83 9.40 3.79 13.28 5.53 0.00 13 15.00 14 10.00 15 16 5.00 17 0.00 18 2 4 5 6 7 9 10 19 UCL LCL 20 O 21