Question: Metal rods are spray painted by a machine and a p-chart is to be used to monitor the proportion of rods that are not painted

Metal rods are spray painted by a machine and a p-chart is to be used to monitor the proportion of rods that are not painted correctly. These defective rods have either an incomplete coverage or a paint layer that is too thick in some places. The data set in DS 16.4.2 contains the number of defective rods found in random samples of n = 400 rods taken at k = 25 time points.
(a) Why does it appear that the process was out of control at certain times while this data set was collected?
(b) What p-chart would you recommend be used to monitor future samples of rods?
(c) How many defective rods would need to be discovered in a future sample for the process to be considered to be out of control?

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