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 x-bar 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 x-bar and r-charts for this process, assuming the measurements on each casting form a rational subgroup. Show the xbar and r-charts 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 re-calculate 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 np-chart 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
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