Discuss the logic underlying the use of three-sigma limits on Shewhart control charts. How will the chart respond if narrower li
1 answer:
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Answer:
a)
b)
c) Figure attached
d) Figure attached
Explanation:
The proportional model on this case would be given by:
Where P is the population size, t the time on years and k a constant.
We can reorder this expression like this:
If we integrate both sides we got:
And using exponentials on both sides we got:
Where represent the initial amount for the starting year t=0.
The rate on this case is given , so then our model would be given by:
Part a
For this case we just need to replace t=100 and we got:
Part b
For this case we have the following:
Part c
The graph is on the first figure attached.
Part d
If we take a log-log scale we have the following values
We need to exclude the point t=0 since the natural log for 0 is not defined.
ln 1 =0 , ln 2= 0.693, ln 10=2.30, ln 25 =3.22, ln 50= 3.91
The result would be the figure 2 attached. And we see a better result for the graph.
