1. HW 9
Key

2. 14:34
Door Seam. A truck manufacturer monitors the width of the door seam as vehicles come off its assembly line. The seam width is the distance between the edge of the door and the truck body, in inches. These data are 62 days of measurements of a passenger door seam, with 10 trucks measured each day. It has been claimed that the process has average width .275 with sd=.1.

3. 14:34 a
If the seam widths at this assembly line are normally distributed, then what is the probability of finding a seam wider than .5 inch?
.0122

4. 14:34 b
b. If the process is under control, what is the probability of finding the mean of a daily sample of 10 widths more than 3 standard errors away from mean=.275? =.003

5. 14:34 c
c. Group the data by days and generate the X bar and S charts, putting the limits at +- 3 SE. Is the process under control? Yes

6. 14:34 d
d. If the process is under control, how does looking at both the X bar and S charts affect the chance for reaching an incorrect decision that the process is not in control, compared to looking at just the X bar chart? Looking at both let us compare means and standard errors. This was we can see if the variation is very spread out and irregular, which may be missed by just the X bar chart. There is only a possibility of Type II error since we’re not shutting it down.

7. 14:34 e
e. Ten measurements are average each day. Is this a large enough sample size to justify using a normal model to set the limits in the X bar chart? Do you recommend changes in future testing? N=10 10*|-.168|=1.68 N>1.68 It is large enough, the testing seems to be sufficient.

8. 14:35
Insulator. One stage in the manufacture of semiconductor chips applies an insulator on the chips. This process must coat the chip evenly to the desired thickness of 250 microns or the chip will not be able to run at the desired speed. If the coating is too thin, the chip will leak voltage and not function reliably; if the coating is too thick, the chip will overheat. The process has been designed so that 95% of the chips have a coating thickness between 247 and 253 microns. Twelve chips were measured daily for 40 days, a total of 480 chips.

9. 14:35 a
Do the data meet the sample size condition if we look at samples taken each day?
N=12
10*1.13=11.3
N>11.3
It meets the sample size condition.

10. 14:35 b
b. Group the data by days and generate X bar and S charts with the control limits +- 3 SE. Is the process under control? No, the variation is increasingly too large.

11. 14:35 c
c. Describe the nature of the problem found in the control charts. Is the problem an isolated incident (which might be just a chance event), or does there appear to be a more systematic failure? There appears to be a more systematic failure. About the first 15 days seem to be clustered fairly close but on an upward trend. The last 20 days sees an increase in variation, some of which exceeds the control limits.