TABLE E10SampleTERASATSOMAANGEPAS89101112131415161718192021222327282930Sample Values10.3 9.8 9.7 9.9 10.29.4 10.0 9.4 10.29.9 9.69.99.09.2 10.610.1 10.6 10.3 9.6 9.710.8 9.4 9.9 10.1 10.110.3 10.1 10.0 9.5 9.88.8 9.3 9.9 8.9 9.39.4 9.7 9.4 9.9 10.59.1 8.9 9.8 9.0 9.38.9 9.4 10.6 9.4 8.79.0 8.6 9.9 9.6 10.59.5 9.2 9.4 9.3 9.69.0 9.4 9.7 9.4 8.69.4 9.3 9.79.4 9.29.4 10.2 9.0 8.8 10.29.6 9.5 10.0 9.3 9.410.2 8.8 10.0 10.1 10.110.4 9.4 9.9 9.4 9.911.1 10.5 10.6 9.8 9.49.3 9.9 10.9 9.5 10.69.5 10.2 9.7 9.4 10.010.5 10.5 10.1 9.5 10.39.8 8.9 9.6 9.8 9.69.3 9.7 10.3 10.1 9.710.2 9.6 8.8 9.9 10.210.8 9.5 10.5 10.5 10.110.4 9.9 10.1 9.9 10.911.0 10.8 10.1 9.2 9.910.3 10.0 10.6 10.0 11.110.9 10.6 9.9 10.0 10.8X9.989.789.6610.06.10.069.949.249.789.229.409.529.409.229.409.529.569.849.8010.2810.049.7610.189.549.829.7410.2810.2410.2010.4010.44R0.60.81.61.01.40.81.11.10.91.91.90.41.10.51.40.71.41.01.71.60.81.00.91.01.41.31.01.81.11.0S0.260.360.630.420.500.300.430.450.360.740.750.160.430.190.660.270.590.420.680.690.340.410.370.390.580.500.420.720.460.46 3.A certain type of integrated circuit is connected toits frame by five wires. Thirty samples of five unitseach were taken, and the pull strength (in grams) ofone wire on each unit was measured. The data arepresented in Table E10 below.The means areX = 9.81, R = 1.14, and 3 = 0.4647.a. Compute the 30 limits for the R chart. Is the vari-ance out of control at any point? If so, delete thesamples that are out of control and recompute Xand R.b. Compute the 30 limits for the X chart. On the ba-sis of the 30 limits, is the process mean in control?If not, at what point is it first detected to be out ofcontrol?c. On the basis of the Western Electric rules, is theprocess mean in control? If not, when is it first de-tected to be out of control?d. Repeat (a-b) using the S chart instead of the R chart.TABLE E10Sample2Sample Values10.3 9.8 9.7 9.9 10.29.99.4 10.0 9.4 10.29.0 9.9 9.6 9.2 10.610.1 10.6 10.39.6 9.7X9.989.789.6610.06

Given Information: Consider the given means: X¯¯=9.81 , R¯=1.14, s¯=0.4647 a. The 3σ control limits for R-chart can be obtained as: LCL=D3R¯CL=R¯UCL=D4R¯ In the given question, n=5, thus, the value of constants D3 and D4 for R-chart is, Thus, the 3σ control limits for R-chart are, LCL=D3R¯=0CL=R¯=1.14UCL=D4R¯=1.14×2.114=2.41 Hence, the control limits for R-chart: LCL=0, CL=1.14, UCL=2.41 The step-by-step procedure to create a control chart using Excel is given below: Enter the data into the Excel sheet in column A. Select the data and go to the tab Insert > recommended Charts > All charts >Line Charts. Click ok. The R-chart is shown below: From the above plot, it can be clearly seen that the variance process is in control because there is no point beyond the Upper control line and lower control line.b. The 3σ control limits for the X-bar chart can be obtained as: LCL=x¯¯-A2R¯CL=X¯¯UCL=x¯¯+A2R¯ In the given question, n=5, thus, the value of constants A2 for X-bar-chart is, Thus, the 3σ control limits for the X-bar chart are, LCL=9.81-0.577×1.14=9.15CL=9.81UCL=9.81+0.577×1.14=10.47 Hence, the control limits for the X-bar chart: LCL=9.15, CL=9.81, UCL=10.47 The step-by-step procedure to create a control chart using Excel is given below: Enter the data into the Excel sheet in column A. Select the data and go to the tab Insert > recommended Charts > All charts >Line Charts. Click ok. The X-bar chart is shown below: From the above plot, it can be clearly seen that the mean process is in control because there is no point beyond the Upper control line and lower control line.C. The Western Electric rules state that: Any point which goes beyond the 3-sigma limit indicates a special cause variation. Two of the last three points fall beyond the 2-sigma limit. Four out of the last five points falling beyond the 1-sigma control limits. Nine consecutive points falling on the same side of the center line. 1-sigma control limits for the X-bar chart are, LCL=x¯¯-A2R¯3=9.81-0.577×1.143=9.59CL=X¯¯=9.81UCL=x¯¯+A2R¯3=9.81-0.577×1.143=10.03 2-sigma control limits for the X-bar chart are: LCL=x¯¯-2A2R¯3=9.81-2×0.577×1.143=9.37CL=X¯¯=9.81UCL=x¯¯+2A2R¯3=9.81-2×0.577×1.143=10.25 the 3σ control limits for the X-bar chart are, LCL=9.81-0.577×1.14=9.15CL=9.81UCL=9.81+0.577×1.14=10.47 The step-by-step procedure to create a control chart using Excel is given below: Enter the data into the Excel sheet. Select the data and go to the tab Insert > recommended Charts > All charts >Line Charts. Click ok. The chart is shown below: From the above plot, the process is in control.d. The 3σ control limits for the X-bar chart are, LCL=x¯¯-A3S¯CL=X¯¯UCL=x¯¯+A3S¯ The 3σ control limits for the X-bar chart are, LCL=9.81-1.427×0.4647=9.15CL=9.81UCL=9.81+1.427×0.4647=10.47 Hence, the control limits for the X-bar chart: LCL=9.15, CL=9.81, UCL=10.47 The step-by-step procedure to create a control chart using Excel is given below: Enter the data into the Excel sheet in column A. Select the data and go to the tab Insert > recommended Charts > All charts >Line Charts. Click ok. The X-bar chart is shown below: From the above plot, it can be clearly seen that the mean process is in control because there is no point beyond the Upper control line and lower control line. The 3σ control limits for S-chart can be obtained as: LCL=B3S¯CL=S¯UCL=B4S¯ In the given question, n=5, thus, the value of constants B3 and B4 for S-chart is, Thus, the 3σ control limits for S-chart are, LCL=B3S¯=0CL=S¯=0.4647UCL=B4S¯=2.089×0.4647=0.9708 Hence, the control limits for R-chart: LCL=0, CL=0.4647, UCL=0.9708 The step-by-step procedure to create a control chart using Excel is given below: Enter the data into the Excel sheet in column A. Select the data and go to the tab Insert > recommended Charts > All charts >Line Charts. Click ok. The S-bar chart is shown below: From the above plot, the process is in control.