Question: Refer to the Package Sorting case of. Budworth, Heimbuch, and Kennedy also investigated the performance of the package scanning equipment. Just as items at a cashier's scanner often are not read on the first scan, so too were bar codes on packages not necessarily read on the first or second scan. Label damage and incorrect orientation, erroneous codes, and some simply unexplained failures all produced "no-read" packages. If a package was not read on the first pass, it continued on the carousel until reaching a second scanner at the end of the carousel. Failure to read at this second scanner resulted in the package being dropped into a "no-read" bin and scanned manually with a substantial loss in efficiency. The team took data over 30 consecutive 1- min periods on the variables
The values they recorded are in Table.
(a) What constitutes a "subgroup" in this problem?
(b) Is this an attributes data or a variables data problem? Why?
(c) Make a retrospective control chart to assess consistency of the proportion of packages failing both scans, and comment on what it indicates.
(d) Make a retrospective control chart to assess consistency of the proportion of packages that are not read on the first scan, and comment on what it indicates.
(e) Make a retrospective control chart to assess consistency of the proportion of all packages in a given minute that are not read on the first scan and are read on the second scan. Comment on what it indicates.
(f) Calculate the proportions of those packages failing the first scan that also fail the second scan.
(g) Make a retrospective control chart to assess consistency of the proportions in (f). Comment on what it indicates.