12.4 - Example 3 - Improving the Speed of Assembly

Example 12-3 Section

Click on the question mark for each question about the experiment to help un-pack clues toward understanding the appropriate design.

Improving the speed of Assembly

We are interested in evaluating the assembly process of three different machines. Each machine has two unique configurations of assembly. The machine can be operated at three power levels (low, medium, or high). For each of the two configurations of the assembly process within a machine, the assembly times of two replications are observed at each power level.

The sample data are as follows:

  Machine
1 2 3
Configuration 1 2 1 2 1 2
Power 1 10.2 1.2 12.0 4.1 13.1 4.1
13.1 5.2 13.5 6.1 12.9 6.1
2 16.2 8.0 12.6 4.0 12.9 2.2
16.9 9.1 14.6 6.1 13.7 3.8
3 13.8 2.5 12.9 3.7 11.8 2.7
14.9 4.4 15.0 5.0 13.5 4.1

Experimental Design

Treatment Design

 

How many treatments are there?

 

How many levels of each treatment are there?

 

If there is more than 1 treatment, how are they related?

Crossed: each level of treatments occur with all levels of other treatments. (Factorial)

Nested: levels of a treatment are unique to different levels of another treatment.

 

Are treatments fixed or random effects?

 

Are there continuous covariates? (ANOCOVA)

Randomization Design

 

What is the experimental unit?

An experimental unit is defined as that which receives a treatment, (e.g., plant, person, plot of ground, petri dish, etc.).

Is there more than one experimental unit? (Split Plot)

 

How are treatment levels assigned to experimental units?

Completely at random? CRD

Restriction or randomization?

one-dimension: RCBD

two-dimension: Latin Square

 

Are there sample units within experimental units? How many true replications are there?

 

Are there repeated measurements made on experimental units?


Solution

What is the experimental design?
A Cross-Nested treatment design in a Completely Randomized Design (CRD)