Question: Consider a situation where fatigue life testing of steel bar stock is to be done. Bar stock can be ordered from several different vendors and it can be ordered to several different sets of specifications with regard to each of the factors "dimensions," "hardness," and "chemical composition." There are several different testing machines in a lab and several different technicians could be assigned to do the testing. The response variable will be the number of cycles to failure experienced by a given test specimen. Assume that each factor has two levels.

(a) Describe the three-factor full factorial study that might be carried out in this situation (ignoring testing machine differences, technician differences, etc.). Make out a data table that could be used to record the results. For each "run" of the experiment, specify the levels of each of the 3 factors to be used. What constitutes "replication" in your plan?

(b) Suppose that attention is restricted to steel bar stock from a single vendor, ordered to a single set of specifications, tested on a single machine by a single technician. Suppose further, that either 10 specimens from a single batch or 1 specimen from each of 10 different batches can be used. Under which of the two scenarios would you expect to get the larger variation in observed fatigue life? Under what circumstances would the first test plan be most appropriate? Under what circumstances would the second be most appropriate?