Question: Package Sorting. Budworth, Heimbuch, and Kennedy analyzed a company's package sorting system. As packages arrive at the sorting system, they are placed onto trays, and the bar codes affixed to the packages are scanned (in an operation much like the scanning process at a grocery store checkout). Bar code identification numbers begin with the zip code of the package destination. This permits packages to be sorted into 40 bins, each of which represents a different bulk mail center (BMC) or auxiliary service facility (ASF). All packages in a given bin are shipped by truck to the same mail center. The bulk transportation of these packages is much cheaper than if they were mailed directly by the nearest US Post Office. The large number of BMC packages handled daily by the company produces tremendous cost savings.
Initially, the team tackled the so-called "no chute open" problem. When one of the BMC bins is full, packages destined for that bin cannot be dropped into it. They end up in a "no chute open" bin. This eventuality produced many inefficiencies and even shutdowns of the entire system. In fact, the system was shut down about 10 min/day on average because of this problem. This lost time cost the company the ability to process about 400 packages/day, and accumulated over a year, this represents a serious loss.
The team decided to document the number of packages per shift dumped into the "no chute open" bin. The data they collected are in Table.
(a) Is this an attributes data problem or a variables data problem? Why?
(b) What constitutes a "subgroup" in the context of this problem?
(c) What probability model is a possible description of the number of packages routed to the "no chute open" bin during a given shift?
(d) Assuming the sorting process is stable, estimate the average number of packages routed to the "no chute open" bin during a particular shift. Estimate the standard deviation of the number of packages routed to the "no chute open" bin. These estimates should be consistent with your answer to (c).
(e) Was the number of packages in the "no chute open" bin apparently constant except for random fluctuation? Why or why not? Defend your answer using a control chart.