I. Background
A steel mill has been asked to produce high strength low alloy steel (H.S.L.A.) that has a minimum yield
strength of 60,000 psi. You are the quality control supervisor for the steel mill. As the steel is produced,
each coil is tested for strength. The data shown at the end of the case study has been obtained.
The product is a thin sheet steel that is several feet wide and several thousand feet long. The strip has been
rolled into coils to make them easier to handle. The samples are taken from the outside ends of each coil.
The samples are nominally 0.5 in width, 0.030 in thick and 2.0 in length. The samples are tested to yield in
tension and the load at yield is read directly from the load displacement plot produced by the testing
machine. The yield point can normally be determined within +/- 3 pounds.
II. Your Task
Your job is to decide whether or not to ship any of the coils of steel A-E based on the sample tests and the
following applications:
• Aircraft manufacturer

• Unknown manufacturer

1. Decide which test method should be used for each application. You can use a different method for each
   application. Justify your answer with appropriate analysis and/or reasoning. Just picking one method
   because you think it is best is not sufficient! You cannot use the test data to decide which method to use!
   That would be like having data from 5 samples for all coils before you decided how many samples to
   actually test.
   There are three testing options you can pick from: Option #1 assumes that you only make one test per coil;
   option #2 assumes you make three tests per coil, but this increases the cost of each roll by 10%; and option

3 assumes you make five tests per coil, but this increases the cost of each roll by 20%.

Your selection of the number of tests and data analysis methods is not neutral, since it may change your
decision as to which coils can be shipped. Using the wrong methods could result in you shipping bad coils.
This could have safety implications, as well as damaging your own and your company's reputation. On the
other hand, if you do not ship coils that are actually good, then you are costing your company money and
not fulfilling your obligation to be a faithful trustee for your company's resources. The tests also take time
and have associated costs that should be considered.
Carry out any numerical calculations necessary to ensure that the steel shipped satisfies the minimum
requirements of 60,000 psi yield strength. The production control department has put you under pressure to
ship all of the coils, since they all were produced from the same heat of steel (same batch) and have all
been processed in the same manner, thus all should have the same nominal properties.

1. Decide which test method should be used for each application. You can use a different method for each
   application. Justify your answer with appropriate analysis and/or reasoning. Just picking one method
   because you think it is best is not sufficient! You cannot use the test data to decide which method to use!
   That would be like having data from 5 samples for all coils before you decided how many samples to
   actually test.
2. Once you have selected a test method, identify which coils should be shipped for each application based
   only on the data from the method(s) selected in question 1. Support your decisions using appropriate
   

Sample Solution