Assignment – Statistical Quality Control
In this assignment, student will learn how to use Minitab in solving process variation by creating R chart, S chart, and X-bar chart. To understand concepts of process control chart, go to Unit Two/Supplement, folder “Minitab”, and read the handouts.
Some of this variation is due to a wide variety of causes that are inherent to the process like natural variation in the process. These causes are called common causes or chance causes. When common causes are the only source of variation, the process is said to be in a state of statistical control, or in control. These could be machines that are malfunctioning, operator error, fluctuations in ambient conditions, and variations in the properties of raw materials. These factors are called special causes or assignable causes. Special causes generally produce a higher level of variability than do common causes, this variability is considered unacceptable. When a process is operating in the presence of one or more special factors, it is said to be out of statistical control (Navidi, 2008).
Problem: Control chart for variables
The quality engineer in charge of a salt packaging process is concerned about the moisture content in packages of salts. Assume that five packages of salt are sampled every 15 minutes for eight hours (a total of 32 samples), and that the moisture content in each package is measured as a percentage of total weight. The data are presented below:
| Sample |
Sample Values |
|
|
|
Mean (x) |
Range |
SD (s) |
| 1 |
2.53 |
2.66 |
1.88 |
2.21 |
2.26 |
2.308 |
0.78 |
0.303 |
| 2 |
2.69 |
2.38 |
2.34 |
2.47 |
2.61 |
2.498 |
0.35 |
0.149 |
| 3 |
2.67 |
2.23 |
2.1 |
2.43 |
2.54 |
2.394 |
0.57 |
0.230 |
| 4 |
2.1 |
2.26 |
2.51 |
2.58 |
2.28 |
2.346 |
0.48 |
0.196 |
| 5 |
2.64 |
2.42 |
2.56 |
2.51 |
2.36 |
2.498 |
0.28 |
0.111 |
| 6 |
2.64 |
1.63 |
2.95 |
2.12 |
2.67 |
2.402 |
1.32 |
0.525 |
| 7 |
2.58 |
2.69 |
3.01 |
3.01 |
2.23 |
2.704 |
0.78 |
0.327 |
| 8 |
2.31 |
2.39 |
2.6 |
2.4 |
2.46 |
2.432 |
0.29 |
0.108 |
| 9 |
3.03 |
2.68 |
2.27 |
2.54 |
2.63 |
2.63 |
0.76 |
0.274 |
| 10 |
2.86 |
3.22 |
2.72 |
3.09 |
2.48 |
2.874 |
0.74 |
0.294 |
| 11 |
2.71 |
2.8 |
3.09 |
2.6 |
3.39 |
2.918 |
0.79 |
0.320 |
| 12 |
2.95 |
3.54 |
2.59 |
3.31 |
2.87 |
3.052 |
0.95 |
0.375 |
| 13 |
3.14 |
2.84 |
3.77 |
2.8 |
3.22 |
3.154 |
0.97 |
0.390 |
| 14 |
2.85 |
3.29 |
3.25 |
3.35 |
3.59 |
3.266 |
0.74 |
0.267 |
| 15 |
2.82 |
3.71 |
3.36 |
2.95 |
3.37 |
3.242 |
0.89 |
0.358 |
| 16 |
3.17 |
3.07 |
3.14 |
3.63 |
3.7 |
3.342 |
0.63 |
0.298 |
| 17 |
2.81 |
3.21 |
2.95 |
3.04 |
2.85 |
2.972 |
0.4 |
0.160 |
| 18 |
2.99 |
2.65 |
2.79 |
2.8 |
2.95 |
2.836 |
0.34 |
0.137 |
| 19 |
3.11 |
2.74 |
2.59 |
3.01 |
3.03 |
2.896 |
0.52 |
0.221 |
| 20 |
2.83 |
2.74 |
3.03 |
2.68 |
2.49 |
2.754 |
0.54 |
0.198 |
| 21 |
2.76 |
2.85 |
2.59 |
2.23 |
2.87 |
2.66 |
0.64 |
0.265 |
| 22 |
2.54 |
2.63 |
2.32 |
2.48 |
2.93 |
2.58 |
0.61 |
0.226 |
| 23 |
2.27 |
2.54 |
2.82 |
2.11 |
2.69 |
2.486 |
0.71 |
0.293 |
| 24 |
2.4 |
2.62 |
2.84 |
2.5 |
2.51 |
2.574 |
0.44 |
0.168 |
| 25 |
2.41 |
2.72 |
2.29 |
2.35 |
2.63 |
2.48 |
0.43 |
0.186 |
| 26 |
2.4 |
2.33 |
2.4 |
2.02 |
2.43 |
2.316 |
0.41 |
0.169 |
| 27 |
2.56 |
2.47 |
2.11 |
2.43 |
2.85 |
2.484 |
0.74 |
0.266 |
| 28 |
2.21 |
2.61 |
2.59 |
2.24 |
2.34 |
2.398 |
0.4 |
0.191 |
| 29 |
2.56 |
2.26 |
1.95 |
2.26 |
2.4 |
2.286 |
0.61 |
0.225 |
| 30 |
2.42 |
2.37 |
2.13 |
2.09 |
2.41 |
2.284 |
0.33 |
0.161 |
| 31 |
2.62 |
2.11 |
2.47 |
2.27 |
2.49 |
2.392 |
0.51 |
0.201 |
| 32 |
2.21 |
2.15 |
2.18 |
2.59 |
2.61 |
2.348 |
0.46 |
0.231 |
Using Minitab to perform R chart, S chart, and X-bar chart, and answer the following questions:
- Creating R chart with UCL, R-bar, and LCL
- Creating s chart with UCL, R-bar, and LCL
- From the above R chart and s chart, which sample is a signal of outside of the control limit? What should be a next step? Explain
- After deleting the out-of-control sample, re-compute the control limits and create a new R chart, s chart, and X-bar chart
- From the X-bar chart, explain the chart, if the process is not in control, what should be a next step?
Submit your assignment in Word Document as a file attachment in Discussion Board, under forum “Assignment Four- SQC”. The final product will include answers of these 5 questions and diagrams from Minitab.
Note:
To create R chart, S chart, X-bar chart in Minitab, follow these steps
- Open the data file (attached with this assignment), Assn-SQC
- Choose Stat > Control Chart > Variable chart for subgroup
- To work on R chart, move cursor down and select “R”
- In a box, click (then you will see the cursor), then click on the data set (C2), click on “select”
- In Subgroup sizes, enter 5
- Then click “OK”
- For s chart and X-bar chart, follow the above step
Definition and more details of SQC with examples are posted in Blackboard, Unit Two/Supplement, Minitab/SQC.
***********************************
