Your company operates a machine shop that fabricates cam rollers (see figure at right), and, having heard you had experience in statistics and design of experiments, consulted you for your opinion on an experiment they want to run. Management would like to run the grinding machine on its “High” setting to increase productivity, but workers suggest that would result in an increased amount of re-works necessary and actually reduce the number of cam rollers they could produce in a day. At the same time, a vendor has loaned the company a new machine that it says will increase productivity by 15%. The new machine also has a high setting, and it is not known whether the machine type (New or Old) has an effect on the productivity one could expect with the machine setting (High or Low). (Typically, it is expected that an operator could produce somewhere around 40 cam rollers per day.)

1) ) Identify the following: the factors, their levels, the independent variables, and the dependent variable. For each factor, assign it a Greek letter, such as τ, γ, δ, or θ.

2) Identify an appropriate statistical model for the experiment assuming you will be using ANOVA to analyze the data. (By statistical model, I mean the symbolic model discussed in class, e.g., y = µ + τi …, using the Greek letters you associated with each factor in #1.)