Chap06-SPC-2-solved

Sample (clerk) No. of errors (out of 100) p 1 6 0.06 2 5 0.05 3 0 0 4 1 0.01 5 4 0.04 6 2 0.02 7 5 0.05 8 3 0.03 9 3 0.03 10 2 0.02 11 6 0.06 12 1 0.01 13 8 0.08 14 7 0.07 15 5 0.05 16 4 0.04 17 11 0.11 18 3 0.03 19 0 0 20 4 0.04 p_bar= 0.04 How to plot charts: 1) Select data (p) 2) Insert, Charts, X Y (Scatter) 3) Click on the chart, Select +, Chart Elements, Axis Titles (fix the titles). Also add the chart title. 4) Right click on the chart, select Data, Add, Series X Values "={0,20}" and Series Y Values "={UCL,UCL}", OK right click on new data points, format data series, marker, marker options and chage the shap right click on new data points, and add trend line. Adjust trend line thickness (format trend lin 5) Repeat Step 4 for LCL and p_bar A control chart exhibits a state of control when: 1.Two-thirds of the points are near the center value. 2.A few of the points are on or near the center value. 3.The points appear to float back and forth across the centerline. 4.The points are balanced (in roughly equal numbers) on both sides of the centerline. 5.There are no points beyond the control limits. 6.There are no patterns or trends on the chart.

Control charts for mean-type measures of performance: Constructing Attribute Control Chart (p-Chart): Step 1: Determine the Sample Size and Number of Samples: Sample Size (n) = 100 Number of Samples (m) = 20 Step 2: Calculate the average percentage of the desired attribute (p_bar) using all available d p_bar= 0.04 Step 3: Construct the p-Chart: UCL= p_bar+3[(p_bar(1-p_bar))/n]^0.5= 0.10 LCL= p_bar-3[(p_bar(1-p_bar))/n]^0.5= -0.02 Step 4: If UCL is larger than 1 (100%), set it to 100%. If LCL is negative (smaller than 0%), set it to 0%. So UCL= 0.10 LCL= 0 Step 5: Plot the chart and check if the process is in control. Step 6: If the process is not in control, then we either need to perform corrective actions to bring it inder control, or we need to collect more samples and update our control chart. pe. ne). 0 5 10 15 20 25 0 0.02 0.04 0.06 0.08 0.1 0.12 p-Chart Sample Sample percentage of error

Day No. of defectives (out of 250) p Control charts for mean-type measures o 1 7 0.028 Constructing Attribute Control Chart (p-C 2 5 0.02 3 19 0.076 4 10 0.04 5 11 0.044 6 8 0.032 7 12 0.048 8 9 0.036 9 6 0.024 UCL= p_bar+3[(p_bar(1-p_bar))/n]^0 10 13 0.052 LCL= p_bar-3[(p_bar(1-p_bar))/n]^0 11 18 0.072 12 5 0.02 13 16 0.064 14 4 0.016 15 11 0.044 16 8 0.032 17 12 0.048 18 4 0.016 19 6 0.024 20 16 0.064 21 17 0.068 22 12 0.048 23 6 0.024 24 7 0.028 25 13 0.052 26 10 0.04 Is the process under control? 27 4 0.016 28 6 0.024 29 12 0.048 30 3 0.012 p_bar= 0.04 0 5 10 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Sample percentage of defectives

of performance: Chart): Sample Size (n) = 250 Number of Samples (m) = 30 p_bar= 0.04 0.5= 0.08 0.08 0.5= 0.00 0 Yes 15 20 25 30 35 p-Chart Day

Is the process still under control?

of performance: Chart): Sample Size (n) = 100 Number of Samples (m) = 10 p_bar= 0.06 0.5= 0.13 0.13 0.5= -0.01 0 Yes p 0.12 0.05 0.13 4 6 8 10 12 p-Chart Day 4 6 8 10 12 14 p-Chart Day

Day No. of irate passengers 1 3 2 0 3 8 4 9 5 6 6 7 7 4 8 9 9 8 c_bar= 6 How to plot charts: 1) Select data (c) 2) Insert, Charts, X Y (Scatter) 3) Click on the chart, Select +, Chart Elements, Axis Titles (fix the titles). Also add the chart title. 4) Right click on the chart, select Data, Add, Series X Values "={0,9}" and Series Y Values "={UCL,UCL}", OK right click on new data points, format data series, marker, marker options and chage the shape. right click on new data points, and add trend line. Adjust trend line thickness (format trend line) 5) Repeat Step 4 for LCL and c_bar A control chart exhibits a state of control when: 1.Two-thirds of the points are near the center value. 2.A few of the points are on or near the center value. 3.The points appear to float back and forth across the centerline. 4.The points are balanced (in roughly equal numbers) on both sides of the centerline. 5.There are no points beyond the control limits. 6.There are no patterns or trends on the chart.

Control charts for mean-type measures of performance: Constructing Attribute Control Chart (c-Chart): Step 1: Determine the Number of Samples: umber of Samples (m) 9 Step 2: Calculate the average number of defects per sampling unit (c_bar). c_bar= 6.00 Step 3: Construct the c-Chart: UCL= c_bar+3[c_bar]^0.5= 13.35 LCL= c_bar-3[c_bar]^0.5= -1.35 Step 4: If LCL is negative (smaller than 0), set it to 0. So UCL= 13.35 LCL= 0 ). Step 5: Plot the chart and check if the process is in control. Step 6: If the process is not in control, then we either need to perform corrective actions to bring it inder control, or we need to collect more samples and update our control chart. 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 c-Chart Day No. of irate passengers

27.66 27.66 3.84 3.84 10 12 14

Week No. of complaints Control charts for mean-type measures of performance: 1 5 Constructing Attribute Control Chart (c-Chart): 2 6 3 4 4 3 Number of Samples (m) = 10 5 7 6 4 c_bar= 4.80 7 5 8 2 UCL= c_bar+3[c_bar]^0.5= 9 7 LCL= c_bar-3[c_bar]^0.5= 10 5 c_bar= 4.8 Is the process under control? Yes Future samples: Week No. of complaints 11 13 12 14 13 12 0 2 4 6 0 1 2 3 4 5 6 7 8 c-Chart Week No. of complaints 0 2 4 6 0 2 4 6 8 10 12 14 16 c-C No. of complaints

11.37 11.37 -1.77 0 8 10 12 8 10 12 14 Chart Week

rform corrective actions to der control, or we need to collect more samples and update our art.