Question

In: Statistics and Probability

The purpose of this project is to design an “optimal” paper airplane using a 2-factor factorial...

The purpose of this project is to design an “optimal” paper airplane using a 2-factor factorial experiment (2k) approach. Students will initially perform a 1/8 fractional factorial experiment on a paper airplane design that contains 6 design parameters, each design parameter containing two possible factors.

Using the interaction effects from the fractional factorial experiment, students will select the best combination of design parameters to create the “optimal” paper airplane. Experiments will be performed to assess the performance of this “optimal” design.

Your objective is to maximize the flight time. This will be assessed using maximum average distance traveled by the airplane in four trials.

Materials and Equipment:

  • • Paper of varying thickness
  • • Scissors
  • • Flat working surface
  • • Ruler

Design parameters / factors:

1) Paper Type

2) Length of Wing

3) Width of Body

4) Length of Body

5) Wing Type (Angled or Non-Angled)

6) Paper Clip

Recommended Protocol:

Part A : Assembling and testing initial airplane designs; results will be concluded out of class using Minitab, Excel, etc.

Part B: Develop and test the new airplane design using results of DOE from week 1.

Procedure:

Part A: Creation of Initial Airplane

Eight paper airplane designs will be created as defined below. The designs will vary based on the 6 design parameters. Trials will then be performed to assess the performance of each design. The performance measure of interest is the average distance traveled by the airplane in four trials.

Determine the Number of Trials Required:

Knowing that the experiment is a 2k fractional factorial design; and that 1/8 of the number of trials is acceptable; and that there are 6 factors and 2 responses; what is the number of required airplanes which need to be created?

Plane Design:

As stated before, this experiment is a 2-factor factorial experiment. The only factors for this experiment are high and low level values/characteristics.

Recording Distances:

Knowing that 4 trials is acceptable, complete 4 runs with each airplane, then find the average distance covered by the airplane. Record these distances in a table for each model.

Determining Effects of Control Parameters:

Which control parameter or parameters had the greatest effect? And why?

Complete the following table of the changes you made (include the table in your final report). Materials

New Design

Paper Type

Length of Wing

Width of Body

Length of Body

Wing Type (Angled or Non-Angled)

Paper Clip

Part B: Creation of Improved Airplane Design

Based on the most influential variables and the interaction effects, create the “ultimate” paper airplane. Re-run the experiment 4 times and note the distances. Conclude in the lab write-up the change you made to the airplane, and whether your resultant design effected the distance of your airplane.

Airplane Distance for New Design (include table and analysis in Final report): Runs

Distance (inches)

1

2

3

4

Average

Solutions

Expert Solution

I HOPE ITS HELPFULL TO YOU...IF YOU HAVE ANY DOUBTS PLS COMMENTS BELOW....I WILL BE THERE TO HELP YOU....PLS RATE THUMBS UP........!!

AS FOR GIVEN DATA....

2^k experiment involves an experiment which involves one or two factors, each having discrete values and the experiment is performed which takes all possible combination of values for the above-mentioned factors. Thus, a fractional experiment is simply where the possible number of combinations is too high and thus some are excluded. In the given case, as 1/4 fraction has to be used, meaning we will discard 75% of possible combinations.

I have taken the distance the plane goes when thrown as the sole factor underlying a design of a paper plane, thus every plane design can be checked on this factor and the following matrix can be designed.

Throw

PAPER AIRPLANE DISTANCE (meters)

Design 1 Design 2 Design 3 Design 4 Design5
Throw 1
Throw 2
Throw 3
Throw 4
Throw 5
Adjusted Average

I HOPE YOU UNDERSTAND...

PLS RATE THUMBS UP...ITS HELPS ME ALOT....

THANK YOU...!!


Related Solutions

A between-subjects factorial design has two levels of factor A and 2 levels of Factor B....
A between-subjects factorial design has two levels of factor A and 2 levels of Factor B. Each cell of the design contains n=8 participants. The sums of squares are shown in the table. The alpha level for the experiment is 0.05. Use the provided information and partially completed table to provide the requested values. Source SS df MS F p n2p Fcrit A 12 B 3 AxB 21 Within 84 Total 120 Specifically looking for the df total and F...
Consider a 2^5 factorial design. (a)How many factors and levels are considered in this factorial experiment?...
Consider a 2^5 factorial design. (a)How many factors and levels are considered in this factorial experiment? (b)Show all the 32 treatment combinations using a, b, c, d, and e. (c)Suppose you are not able to complete all 32 experiments in a day but you believe 16 experiments can be done in a day. How many blocks do you need under this situation? (d)Revisiting part (c), which interaction effect would be confounded with the blocks? Using the sign method, assign optimal...
Below is the data of a factorial experiment consisting of 2 levels of factor A, ie...
Below is the data of a factorial experiment consisting of 2 levels of factor A, ie levels 1 and 2, and 3 levels of factor B, ie levels 1, 2, and 3.                                                                                                 Factor B                                                                 Level 1                  Level 2                  Level 3                                 Level 1                  135                         90                           75 Factor A                                               165                         66                           93                                 Level 2                  125                         127                         120                                                                 95                           105                         136 Create an ANOVA table! And what can you conclude? α = 0.05 (Use manual...
What is meant by single-factor or one-way ANOVA? Please provide an example. What are factorial design...
What is meant by single-factor or one-way ANOVA? Please provide an example. What are factorial design ANOVAs? Can you give an example of a 2 × 2 design? What about a 3 × 2 design?
Problem 2. Purpose: practice algorithm design using dynamic programming. A subsequence is palindromic if it is...
Problem 2. Purpose: practice algorithm design using dynamic programming. A subsequence is palindromic if it is the same whether read left to right or right to left. For instance, the sequence A,C,G,T,G,T,C,A,A,A,A,T,C,G has many palindromic subsequences, including A,C,G,C,A and A,A,A,A (on the other hand, the subsequence A,C,T is not palindromic). Assume you are given a sequence x[1...n] of characters. Denote L(i,j) the length of the longest palindrome in the substring x[i,...,j]. The goal of the Maximum Palindromic Subsequence Problem (MPSP)...
a. Tom designed a complete factorial experiment with 2 factors. One factor had 4 levels, the...
a. Tom designed a complete factorial experiment with 2 factors. One factor had 4 levels, the other had 5 levels. For each combination of levels of factors, there were 6 replicates. In the ANOVA table associated with this design, what were the degrees of freedom of the interaction? a. 7, b. 12,   c. 20, d. 24, e. 30. b. In the above ANOVA table of the complete factorial experiment, suppose we want to test the significance of the main effect...
A 2^3 full factorial screening experimental design was performed to identify the important factors affecting the...
A 2^3 full factorial screening experimental design was performed to identify the important factors affecting the percent conversion in a chemical process. Two factors, temperature in C (x1) and reactant concentration (x2) were identified as the key process input variables and the method of steepest ascent was applied to identify the maximum percent conversion area. Create and analyze a central composite design using the data in the following table (in standard run order). Test the residuals assumption and comment on...
A 2 ^3 full factorial screening experimental design was performed to identify the important factors affecting...
A 2 ^3 full factorial screening experimental design was performed to identify the important factors affecting the percent conversion in a chemical process. Two factors, temperature in C (x1) and reactant concentration (x2) were identified as the key process input variables and the method of steepest ascent was applied to identify the maximum percent conversion area. Create and analyze a central composite design using the data in the following table (in standard run order). Test the residuals assumption and comment...
c++ The purpose of this project is to test your ability to use files, class design,...
c++ The purpose of this project is to test your ability to use files, class design, operator overloading, and Strings or strings effectively in program design Create a program which will read a phrase from the user and create a framed version of it for printing. For example, the phrase "hello world"would result in: ********* * hello * * world * ********* Whereas the phrase "the sky is falling"might be: *********** * the * * sky * * is *...
Consider a 2^8-3 fractional factorial design with design generators F=ABC, G=ABD, and H=BCDE a)Find the complete...
Consider a 2^8-3 fractional factorial design with design generators F=ABC, G=ABD, and H=BCDE a)Find the complete defining relation and generate the alias structure using the principle(positive) fraction. Second, determine the design resolution (you need to show your justification). b)List the basic variables and the design configuration (All 32 design points with the + and – signs. You should show the setting for all 8 factors by using the design generators) (Hint: Here there are 5 basic variables which you can...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT