Airco ships 1,000,000 hubs a year in lots of 1,000 to a foreign buyer. Airco’s current manufacturing process produces hubs whose mean smoothness follows a normal distribution 4 with a mean of 15 Rz and a variance of .01. Hubs are considered defective if their mean smoothness falls below 14.7 or above 15.3.

The foreign buyer is adopting a new acceptance sampling procedure that will increase Airco’s inspection costs. The buyer will receive lots of 1,000, and randomly sample 80 hubs for testing. If any of those 80 hubs is defective, the buyer will reject the entire lot and return it to Airco for
complete inspection (all 1000 hubs). This will cost Airco an additional $5000 per rejected lot.

One of Airco’s clever engineers has devised a modification for the manufacturing process that reduces the variance from 0.01 to 0.00826. What are the expected savings for Airco if they adopt this new manufacturing process (compared to the old process)? If the new process
involves a one-time switching cost of $500,000, is it worth switching?