1. The smallest defect in a computer chip will render the entire chip worthless. Therefore, tight quality control measures must be established to monitor these chips. In the past, the percentage of defective for these chips has been 3%. The sample size is 100. Calculate the upper and lower control limits of a P-chart to monitor this process. Also determine whether the process is in control if a sample of 100 chips indicated 7 defectives.
2. Cool Technologies produces refrigeration units for food producers and retail food establishments. The overall average temperature that these units maintain is 49 ºF. The average range is 4 ºF. Samples of size 7 are taken to monitor the process. Calculate the control limits for X-bar and R charts. Also determine if the process is in control if the next sample taken results in 47, 48, 50, 52, 51, 57, and 56.
3. An electronic component has design specification limits of 215±25 mhz. Due to variation in the parts that goes into this component, the actual yield varies. A sample of 100 indicated a mean of 220 mhz and standard deviation of 7 mhz.
a. Find the Process Capability Index (Cpk) for this process. Is this process capable? Why?
b. Find the process capability if we adjust the process mean to 217 and reduce variability by 15%. Is this modified process capable? Why?
4. A random sample of 200 cars observed after paint jobs performed by robots indicated a total of 785 blemishes. Find the upper and lower control limits for a C-chart with alpha risk of 6% to monitor the number of blemishes per car. If a car has 10 blemishes, should any action be taken?
5. Sampling seven (n=7) pieces of precision-cut parts every hour for the past 14 hours has produced the following results.
|
Sample
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
|
X-bar
|
3.05
|
3.02
|
3.04
|
3.01
|
3.07
|
2.99
|
2.98
|
3.05
|
3.07
|
3.12
|
3.11
|
3.12
|
3.14
|
3.15
|
|
R
|
0.31
|
0.28
|
0.26
|
0.37
|
0.48
|
0.32
|
.23
|
0.37
|
0.32
|
0.56
|
0.71
|
0.79
|
0.88
|
0.92
|
a. Find the 3-sigma control limits for X-bar and R charts.
b. Draw the X-bar and R-charts and comment on the state of the process.