Question: Refer to the Hose Skiving case of in the Chap. 1 exercises. The plant works two shifts/day. Five hoses were sampled every two hours from each of three production lines and skive length, y measured. Specifications for skive length are target ± .032 in. The values (x = y - target) in the accompanying tables are in units of .001 in above target.
(a) Explain (possibly using the notions of "rational subgrouping" and "stratification") why it would not make good sense to combine data taken at a particular time period from the three different production lines to make a single "sample." (Particularly in cases where it is only possible to select a single item from each line at a given time period, the urge to make such a "sample" is strong, and this kind of error is a common one.)
(b) Compute the 48 sample means and ranges for the data given in Table. Then separately for lines 1, 2, and 3, make both x charts and R charts. Comment on what they indicate about the stability of the skiving process on the three lines over the two days of this study.
(c) One could think about plotting all 48 sample means on a single chart, for example, plotting means from lines 1, 2, and 3 in that order at a given time period. Discuss why that is not a terribly helpful way of summarizing the data. (Will it be easier or harder to see trends for a given production line on this kind of plot compared to the separate charts of part (b)?)
