A tomato farmer has been using an X-bar and R chart to control the yield per...

A tomato farmer has been using an X-bar and R chart to control the yield per plant on her highly-mechanized farm. The yield is table over time in both variability and location. The X-bar chart has a centerline value of 10.50 pounds and the upper control limit is 14.20 pounds.

Find the value of the lower control limit of the X-bar chart?
Find the value of the upper and lower one-sigma and two-sigma zones of the X-bar chart?
Find the estimate of the value of the standard deviation of the yield of the tomato plants if the sample size is six?
If it is known that the upper specification and lower specification limits of the tomato yield are, respectively, 8.5 and 15.5 pounds. Find all capability indices of the yield? Is the “tomato yield” process capable? Why?

Expert Solution

orchestra answered 2 years ago

Solve step-by-step the following: 1) X-bar and R control Chart Subgroup X1 X2 X3 X4 X-bar...

Solve step-by-step the following: 1) X-bar and R control Chart Subgroup X1 X2 X3 X4 X-bar R 1 1.2 1.1 1.1 2.3 2 3.2 1.3 1.3 3.3 3 1.3 1.4 1.3 1.1 4 3.2 1.1 3.3 2 5 2.1 3.2 2.4 2.3 6 3.1 3.1 3.2 3.3 7 3 1 2.2 2.1 8 2.3 1.3 3.1 2.4 9 4 3.3 4 4.3 10 1.2 3.1 1.3 1.3 11 2.2 1.4 1.1 3 12 3.2 2.3 3.1 1.2 13 1.1 3...

Given the data provided below, calculate the control limits (X-bar and r-chart, Capability Index, create a...

Given the data provided below, calculate the control limits (X-bar and r-chart, Capability Index, create a control chart, and calculate the percentage of units that are expected to be out of spec (z-value). Please show all work for how all calculations were computed. Filling Line Checks - ounces Specification: 12 ounces min; max - 15 ounces Sample Sample Times Number 1pm 2pm 3pm 4pm 5pm 6pm 7pm 8pm 1 12.5 12.4 12.4 12.8 13 12.8 12.8 13 2 12.4 12.4...

For following data: a. Construct an R-chart for this process. b. Construct an X-bar chart for...

For following data: a. Construct an R-chart for this process. b. Construct an X-bar chart for this process. c. Does the process appear to be in control? Why or why not? d. Why must the R chart be read before the x-chart? Hour Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Sample 7 Sample 8 1 98.2706 98.82376 101.8175 100.1819 102.9594 101.165 95.25957 98.97423 2 100.7166 101.8866 98.56813 98.77126 101.8273 98.20298 101.6975 99.63706 3 98.9922...

x bar and R control Charts A quality control inspector at the Company B has taken...

x bar and R control Charts A quality control inspector at the Company B has taken twenty-five samples with four observations each of the sample weight (g). The data are shown in the table. Construct x bar and R control charts for these data. Identify any out-of- control points. Assume these points (if any) are assignable. Remove them and recalculate the control limits. Construct the revised x bar and R control charts. Submit data (spreadsheet) and charts. Comment on the...

what is the type 1 error of an x bar chart with 1 - sigma control...

what is the type 1 error of an x bar chart with 1 - sigma control limits? what is the type 1 error of an x bar chart with 2 - sigma control limits? what is the type 1 error of an x bar chart with 3 - sigma control limits? what is the type 1 error of an x bar chart with 4 - sigma control limits?

A farmer wishes to test the effects of a new fertilizer on her tomato yield. She...

A farmer wishes to test the effects of a new fertilizer on her tomato yield. She has four equal-sized plots of land-- one with sandy soil, one with rocky soil, one with clay-rich soil, and one with average soil. She divides each of the four plots into three equal-sized portions and randomly labels them A, B, and C. The four A portions of land are treated with her old fertilizer. The four B portions are treated with the new fertilizer,...

Solve step-by-step: X-bar and S control Chart Subgroup X1 X2 X3 X4 X-bar S 1 1.2...

Solve step-by-step: X-bar and S control Chart Subgroup X1 X2 X3 X4 X-bar S 1 1.2 1.3 1.2 2.2 2 3.3 1.2 1.2 3.2 3 1.2 1.3 1 1.3 4 3.4 1.2 3.1 2.1 5 2.3 3.3 2.2 2.3 6 3.1 3.3 3 3.1 7 3.1 1.2 2.1 2.4 8 2.4 1.4 3 2.4 9 4.1 4.2 4.1 4.2 10 1.3 3 1.3 1.3 11 2.3 1 1.4 3.3 12 3.3 2.4 3.3 1.1 13 1.4 3.4 1.3 3.2 14...

MEAN CI x-bar (Grand Mean) LCL x-bar (CI-A2R-bar) UCL x-bar (CI+A2R-bar) Sample Range (Max-Min) R-bar (Mean)...

MEAN CI x-bar (Grand Mean) LCL x-bar (CI-A2*R-bar) UCL x-bar (CI+A2*R-bar) Sample Range (Max-Min) R-bar (Mean) UCL R (R-bar*D4) 1 68.51 68.46 68.54 68.34 68.46 68.46 2 68.94 68.2 68.54 68.56 68.7 68.7 3 68.66 68.44 68.55 68.77 68.7 68.64 4 68.49 68.94 68.56 68.62 68.69 68.56 5 68.64 68.63 68.62 68.32 68.34 68.24 6 68.34 68.42 68.99 68.02 68.03 68.47 7 68.99 68.94 68.95 68.95 68.94 68.97 8 68.92 68.91 68.97 68.93 68.96 68.95 GRAND MEAN n= A2= D4=

7. A farmer wishes to determine if a new fertilizer increases her tomato crop yield. She...

7. A farmer wishes to determine if a new fertilizer increases her tomato crop yield. She lays out seven plots and in each plot plants two tomato plants. One plant is given the new fertilizer and the other is given the fertilizer the farmer is currently using. The table below has the yield (in pounds). Plot 1 2 3 4 5 6 7 New 5.3 6.1 5.7 8.4 3.7 9.4 9.2 Old 4.9 5.9 6.0 6.9 2.8 8.2 7.2 Make...

Calculate the control limits for the X-bar chart with 0.005 probability limits (instead of 3-sigma limits)....

Calculate the control limits for the X-bar chart with 0.005 probability limits (instead of 3-sigma limits). That is, here the type I error rate (false alarm rate) is now set to α = 0.005. Use Excel for any calculations, not Minitab. Day x1 x2 x3 x4 x5 1 839 585 583 613 768 2 706 527 956 644 612 3 322 614 807 282 170 4 1001 904 419 522 430 5 259 811 847 603 572 6 681 523...

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