Reference no: EM132263452

Assignment Title - "In-class activity: Factorial designs"

Part 1: 2-level factorial design with replicates

In this activity you analyze the results of a study on computer monitor design with four factors:

- clearance under the base

- interface board height

- side vent size

- interface board angle

The response variable, Y, is defined as the failure rate. Lower values of Y correspond to higher product quality.

How many factor combinations are there for this study?

After downloading the data from Canvas, load them and perform a quick EDA to answer the questions below. You may want to use the sample code supplied to get you started.

1. How many replicates are there for each combination of factors?

2. Use the data to estimate the main effects without fitting a model.

Next fit the full model to these data. You will want to change the coding on the variables to -1 and +1 as described in lecture. You can use the code below to do this, but you need to have the dplyr package installed and loaded to do so.

Describe the model. Which main effects are significant? Which interactions are significant?

What do you notice about your estimates for the main effects and the estimates for the same effects in your model above?

For this example we had a relatively small number of factors and replicated data. This will not always be the case. Consider the next example dataset, pilot_training_data.csv.

Part 2: Unreplicated data

These data, pilot_training_data.csv, were collected to investigate the effects of five factors onthe learning rates of flight trainees when using flight simulators. The factors are:

- display type (-1 = symbolic, 1 = pictorial)

- display orientation (-1 = outside in, 1 = inside out)

- crosswind (-1 = no wind present, 1: crosswind present)

- command guidance (-1:constant guidance, 1:guidance only when trainee spreads far from best path)

- flight path prediction (-1: no prediction, 1: constant prediction)

The response, Y, is the average squared distance from the optimal flight path for 12 landing attempts by the trainee.

BEFORE you fit the model, answer the questions below (and don't change your answers after you fit the model!)

Which main effects do you think will be significant?

Do you think there will be any significant second-order interactions?

Now, fit the full model, including all possible interactions, and obtain estimates for all coefficients.

What is the most noticeable thing about the summary of the model you just fit?

Can you determine which effects and interactions are significant?

To produce the normal probability plot and Pareto chart on an lm object named 'full_model' you can use the code below:

'''{r}

qqnorm(full_model$coefficients[-1],pch=19);qqline(full_model$coefficients[-1])

paretoPlot(full_model)

'''

Part 3 (Complete after class)

The goal of this section of the lab is for you to make fractional factorial study designs using Minitab, and to give you practice analyzing one such set of trials in R.

First, navigate to Minitab 18 in WebApps. To explore factorial designs, go to Stat -> DOE -> Factorial -> Create Factorial Design

Click on 'Display Available Designs'. What levels of resolution are possible for a study with 8 factors?

Using all default options, have Minitab create a resolution 5 design with 8 factors (to choose resolution/fraction, click on the Design button in the factorial DOE dialog box).

Familiarize yourself with the output from Minitab, both in the Session window and in the worksheet.

Using this design, will any of the main effects be confounded with 2-way interactions?

Will any of the two-way interactions be confounded with each other?

Minitab has created a worksheet with values of -1 or +1 for the 8 factors, in addition to columns called 'StdOrder', 'RunOrder', 'CenterPt', and 'Blocks'. This worksheet is meant to be a guide for someone collecting data. 'StdOrder' indicates what the trial number would be for that combination of factors following the ordering conventions for 2-level designs. The variable 'RunOrder' indicates the order in which the data should be collected.

Why do you think taking the data in random order is important?

Now create a 1/8 fractional design.

What is the resolution?

Using this design, will any of the main effects be confounded with 2-way interactions?

Will any of the two-way interactions be confounded with each other?

Notice that the 1/16 fractional design has the same resolution as the 1/8 fractional design.

Describe the difference between these two designs.

Finally, we explore some data collected using these designs. Consider data from an industrial process. You are interested in which of the following 8 factors are active with respect to the outcome, Y, a measure of durability. In this case, larger values of Y are more desirable.

- temp1

- temp2

- reaction time

- cooling time

- altitude

- moisture

- acidity

- pressure

The company collecting data had a very tight budget and were only able to perform 16 trials, and did so following Minitab's advice for the resolution 4 model. The data is stored in 'DOE_industrial_process_data_sixteen.csv'. Fit an appropriate model using R and observe the normal plot or the Pareto Chart.

Which main effects and 2-way interactions seem to be active?

What other effects or interactions are they confounded with?

A competing company was able to carry out a resolution 5 study. Repeat your analysis with this data, "DOE_industrial_process_data_quarter.csv". Be sure to create both the Pareto plot and the normal probability plot.

Which main effects and 2-way interactions seem to be active?

What other effects or interactions are they confounded with?

What do you gain by using a resolution 5 design in place of a resolution 4 design? Be specific.

Note - Finish the part 3 of the Rmd file. You can follow the instruction.

Attachment:- Assignment Files.rar