The bore size on a component to be used in assembly is a critical dimension. Samples of size 4 are collected and the sample average diameter and range are calculated. After 25 samples, we have

The specifications on the bore size are 4.4 ± 0.2 mm. The unit costs of scrap and rework are $2.40 and $0.75, respectively. The daily production rate is 1200.
(a) Find the - and R-chart control limits.
(b) Assuming that the process is in control, estimate its standard deviation.
(c) Find the proportion of scrap and rework.
(d) Find the total daily cost of scrap and rework.
(e) If the process average shifts to 4.5 mm, what is the impact on the proportion of scrap and rework produced?

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Xi = 107.5 R, 12.5