Question

5. Use the given process data to construct a control chart for p.

A manufacturer monitors the level of defects in the television sets that it produces. Each week, 200 television sets are randomly selected
and tested and the number of defects is recorded. The results for 12 consecutive weeks are shown below.
4756831244562
Select the correct lower control limit.

Answer 1

To construct a control chart for p using the given process data, calculate the average proportion of defects (p-bar) and the standard deviation of proportions (s-bar). Then use p-bar-3*s-bar to find the lower control limit. The correct lower control limit for the control chart is 0.

Step-by-step explanation:

To construct a control chart for p, we first need to calculate the average proportion of defects (p-bar) and the standard deviation of proportions (s-bar).

1. Add up all the defects recorded for the 12 weeks: 4+7+5+6+8+3+1+2+4+4+5+6=55.
2. Calculate p-bar by dividing the total number of defects by the total number of television sets tested: 55/2400=0.0229.
3. Calculate s-bar using the formula: s-bar=√((p-bar(1-p-bar))/n), where n is the number of television sets tested. In this case, n=12*200=2400. So, s-bar=√((0.0229(1-0.0229))/2400)=0.0154.

Now that we have p-bar and s-bar, we can construct the control chart for p. The lower control limit is given by p-bar-3*s-bar. Substitute the values we calculated to find the lower control limit: 0.0229-3*0.0154=0.0229-0.0462=-0.0233.

Since the lower control limit cannot be negative, the correct lower control limit for the control chart is 0.