$4\mathrm{.}7\mathrm{.}2$ At a metal$-$working machine shop, small metal parts are produced for assembly into pieces of heavy equipment. The parts are currently being run in lot sizes of $200$ parts. After fabrication, any excess metal is machined off of the parts and the parts are deburred. To study the behavior of the process over time, two lots of parts are randomly selected and inspected at the end of each process for the existence of rough edges, excess metal, and burrs. The number of nonconformities found during the inspection of these parts has been recorded for the two shifts over a period of $10$ days. The data are provided in Table $4\mathrm{.}8,$ and a plot of the number of nonconformities is provided in Figure $4\mathrm{.}17.$

a$.$ Calculate the upper and lower control limits for the chart in Figure $4\mathrm{.}17.$

b$.$ Does the process appear to be operating in a stable and predictable manner over time?

C Are shift$-$to$-$shift differences captured within subgroups or between subgroups? Do differences exist between the two shifts? How is this conclusion reached?