1. Exercise Tool Life
An engineer is interested in the effects of four factors on y = life of a tool: A: Cutting speed B: Cutting angle C: Tool hardness D: Cutting tool angle
Two levels were selected for each factor; sixteen runs were planned. Because of the length of time involved in doing each test, four stations (=four blocks) were used.
Exercise: Allocate the sixteen runs to the four blocks. What is the alias structure?

2. Exercise Block Design
Factors A through D will be assigned to columns 1-4 and the blocks to columns ABC and ABD (or any other pair chosen from ABC, ABD, ACD, and BCD).

3. Four Blocks Table of Column-Allocations (Four-factor experiment in four blocks of four runs each)
The runs in each block are as shown below.

4. Four Blocks Alias Structure (Four-factor experiment in four blocks of four runs each)
The alias structure for two-way interactions is: