The diameter of the casting is an important quality characteristic. A coordinate measuring machine is used to measure the diameter of each casting at five different locations. Data for 20 castings are shown below
Problem 1:
The diameter of the casting is an important quality characteristic. A coordinate measuring machine is used to measure the diameter of each casting at five different locations. Data for 20 castings are shown below. Perform a process capability study using xbar and R charts. The specification limits are: Lower specification limit: 11.7; Upper specification limit: 11.8
Note: Provide your answer under each bullet
Measurements  
Casting  1  2  3  4  5 
1  11.7629  11.7403  11.7511  11.7474  11.7374 
2  11.8122  11.7506  11.7787  11.7736  11.8412 
3  11.7742  11.7114  11.753  11.7532  11.7773 
4  11.7833  11.7311  11.7777  11.8108  11.7804 
5  11.7134  11.687  11.7305  11.7419  11.6642 
6  11.7925  11.7611  11.7588  11.7012  11.7611 
7  11.6916  11.7205  11.6958  11.744  11.7062 
8  11.7109  11.7832  11.7496  11.7496  11.7318 
9  11.7984  11.8887  11.7729  11.8485  11.8416 
10  11.7914  11.7613  11.7356  11.7628  11.707 
11  11.726  11.7329  11.7424  11.7645  11.7571 
12  11.7202  11.7537  11.7328  11.7582  11.7265 
13  11.8356  11.7971  11.8023  11.7802  11.7903 
14  11.7069  11.7112  11.7492  11.7329  11.7289 
15  11.7116  11.7978  11.7982  11.7429  11.7154 
16  11.7165  11.7284  11.7571  11.7597  11.7317 
17  11.8022  11.8127  11.7864  11.7917  11.8167 
18  11.7775  11.7372  11.7241  11.7773  11.7543 
19  11.7753  11.787  11.7574  11.762  11.7673 
20  11.7572  11.7626  11.7523  11.7395  11.7884 
a) Set up the xbar and rcharts for this process, assuming the measurements on each casting form a rational subgroup. Show the xbar and rcharts for the stable process. Ensure you have a stable process.
b) Calculate the Cp and Cpk indices based on the stable process.
c) Do your capability analysis using Minitab and show Minitab output.
d) Is the process capable?
e) Is the process centered?
Problem 2:
A paper mill uses a control chart to monitor the imperfections in finished rolls of paper. Production output is inspected for twenty days, and the resulting data are shown below. Set up a control chart for nonconformities per roll of paper. Remove any out of control points, and recalculate the control limits and center line. Provide the final control chart center line and limits below. Show your equations
Day  Number of Rolls Produced  Total Number of Imperfections  Day  Number of Rolls Produced  Total Number of Imperfections 
1  18  12  11  18  18 
2  18  14  12  18  14 
3  24  20  13  19  8 
4  22  18  14  20  10 
5  22  15  15  20  14 
6  22  12  16  20  13 
7  20  11  17  24  16 
8  20  13  18  24  18 
9  20  12  19  22  20 
10  20  10  20  21  17 
Problem 3:
The number of nonconforming switches in samples of size 150 is shown below. Create an npchart with the following data and then remove the out of control points and provide the revised control charts. What are the final center lines, upper and lower control limits? Show your equations
Sample  
1  8 
2  1 
3  3 
4  0 
5  2 
6  4 
7  0 
8  1 
9  10 
10  6 
11  6 
12  0 
13  4 
14  0 
15  3 
16  1 
17  15 
18  2 
19  3 
20  0 
Problem 4
Bath concentrations are measured hourly in a chemical process. Data (in ppm) for the last 32 hours are shown in the table below. (Read down from left)
The process target uo=175 ppm
a. Construct a tabular Cusum for this process using h=5 and k=1/2
b. Provide your interpretation based on the chart
Sample#  Conc.  Sample#  Conc.  Sample#  Conc.  Sample#  Conc. 
1  160  9  186  17  190  25  206 
2  158  10  195  18  189  26  210 
3  150  11  179  19  185  27  216 
4  151  12  184  20  182  28  212 
5  153  13  175  21  181  29  211 
6  154  14  192  22  180  30  202 
7  158  15  186  23  183  31  205 
8  162  16  197  24  186  32  197 
Problem 5:
The following data are temperature readings from a chemical process in degrees Celsius, taken every two minutes. Read the observations down from the left. The target value for the mean is 950.
a) Set up an EWMA control chart with lambda = 0.2 for this process. Show the EWMA chart.
b) Interpret the results
