Answer:
a) The chart tell us that all the point are between the upper and lower control limits, so the process is under control.
b) Since the process under control, the number of defects are controled and we know with a 99.3 % of certainty the average of them, so the program is effective.
Explanation:
In order to draw a C chart we should calculate the average test errors and the control limits of the chart
The average test errors is = (52+27+35+44+55)/5= 42.6 = c
This will be the middle line in the chart.
Then, the Upper and lower control limits are:
LCL= c-m *sqr(c) and UCL= c+ m *sqr(c)
In this case, since we are told to contain the 99,7% of random variation, this means that we are working with a 6 sigma.
So m will be 3 (3 sigma) for the upper limit control and 3 (3 sigma) for the lower limit control:
LCL= 42.6 -3*sqr(42,6) = 23.0
UCL= 42.6+3*sqr(42,6) = 62.2
(the graphic is attached)
As we can see, al the test error values are between the control limits, so the program is undercontrol
