Your company operates a machine shop that fabricates cam rollers (see figure at

ID: 3361566 • Letter: Y

Question

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 , , , or .

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 + i …, using the Greek letters you associated with each factor in #1.)

Explanation / Answer

Answer

It will be a 2-factor-2-level experiment or Randomised Block Design with machine type (Old/New) as treatments and machine settings (High/Low) as blocks. On each machine type-machine setting, more than one (preferred is 5) run is to be made to ensure replication.

The data sheet format would be as follows:

Machine Type

Machine Setting

High

Low

Old

x111

x112

x113

x114

x115

x121

x122

x123

x124

x125

New

X211

x212

x213

x214

x215

x221

x222

x223

x224

x225

Let xijk = number of cam rolls produced per day (taking into consideration the rework also, if any) in the kth run at jth machine setting on ith machine type, i = 1, 2; j = 1, 2; k = 1, 2, …, 5.

Model: xijk = µ + i + j + ij + ijk, where

µ = common effect

i = effect of machine type

j = effect of machine setting

ij = interaction effect

ijk = error which is assumed to be N(0, 2).

Independent Variables: machine type, machine setting

Dependent Variable: number of cam rolls produced per day (taking into consideration the rework also (xijk)

Analysis Tool: ANOVA – two way with equal number of observations per cell.

DONE