5. Process Improvement
5.6. Case Studies
5.6.3. Catapult Case Study

5.6.3.1.

Background and Data

Background

This experiment was conducted on a catapult, a table-top wooden device used to teach design of experiments and statistical process control. The catapult has several controllable factors, and a response easily measured in a class room setting. It has been used for over 10 years in hundreds of classes. Below is a small picture of a catapult that can be opened to view a larger version.

Catapult

The data set below represents one outcome of this experiment.

Variables

This experiment utilizes the following variables.

1. Response Variable (Y) = The distance in inches from the front of the catapult to the spot where the ball lands. The ball is a plastic golf ball.

2. Factor 1 (Z1) = The band height is the height of the pivot point for the rubber bands. The levels were 2.25, 3.5 and 4.75 inches.

3. Factor 2 (Z2) = The start angle is the location of the arm when the operator releases, i.e. starts the forward motion of the arm. The levels were 0, 10 and 20 degrees.

4. Factor 3 (Z3) = The number of rubber bands used on the catapult. The levels were 1 and 2 bands.

5. Factor 4 (Z4) = The arm length is the distance the arm is extended. The levels were 0, 2, and 4 inches.

6. Factor 5 (Z5) = The stop angle is the location of the arm where the forward motion of the arm is stopped and the ball starts flying. The levels were 45, 62 and 80 degrees.

The data set below enters each of the factor variables twice. The variables labeled as Z1, Z2 Z3, Z4, and Z5 are in the original units of the data. The variables labeled as X1, X2, X3, X4, and X5 are coded as -1, 0, and 1 where -1 represents the lowest level of the variable, +1 represents the highest level of the variable, and 0 represents the center point of the variable.

In addition, there are 2 addtional auxillary variables. The variable labeled SEQ identifies the run order of the observation and the variable labeled CENT POINT is set to 1 if the observation is a center point and to 0 otherwise.

This data set has 20 observations. It is a 2^5-1 resolution V design with 4 center points.

Purpose of the Experiment

This case study demonstrates the analysis of a 2^5-1 fractional factorial experimental design. The output and goals of this case study are:

1. Determine the significant factors that affect the distance the ball is thrown.

2. Predict the settings required to hit 3 different target values. The proposed target values are 30, 60, and 90 inches.

Data Used in the Analysis

The following is the data used for this analysis. This data set is given in Yates order.

                                                 RUN  CENT
     Y    Z1  Z2  Z3  Z4  Z5  X1  X2  X3  X4  X5 SEQ POINT  PATTERN
-------------------------------------------------------------------
 28.00  3.25   0   1   0  80  -1  -1  -1  -1   1   1     0    ----+
 35.00  4.75   0   1   0  45   1  -1  -1  -1  -1   6     0    +----
  8.00  3.25  20   1   0  45  -1   1  -1  -1  -1  10     0    -+---
 28.25  4.75  20   1   0  80   1   1  -1  -1   1   8     0    ++--+
 33.50  3.25   0   2   0  45  -1  -1   1  -1  -1  15     0    --+--
 84.00  4.75   0   2   0  80   1  -1   1  -1   1  17     0    +-+-+
 36.00  3.25  20   2   0  80  -1   1   1  -1   1  16     0    -++-+
 28.50  4.75  20   2   0  45   1   1   1  -1  -1  14     0    +++--
 33.00  3.25   0   1   4  45  -1  -1  -1   1  -1  12     0    ---+-
 85.00  4.75   0   1   4  80   1  -1  -1   1   1   9     0    +--++
 45.00  3.25  20   1   4  80  -1   1  -1   1   1  18     0    -+-++
 36.50  4.75  20   1   4  45   1   1  -1   1  -1  11     0    ++-+-
106.00  3.25   0   2   4  80  -1  -1   1   1   1  20     0    --+++
126.50  4.75   0   2   4  45   1  -1   1   1  -1   4     0    +-++-
 45.00  3.25  20   2   4  45  -1   1   1   1  -1   5     0    -+++-
126.50  4.75  20   2   4  80   1   1   1   1   1   3     0    +++++
 99.00  4.00  10   2   2  62   0   0   1   0   0   2     1    00+00
 45.00  4.00  10   1   2  62   0   0  -1   0   0   7     1    00-00
 84.50  4.00  10   2   2  62   0   0   1   0   0  13     1    00+00
 37.50  4.00  10   1   2  62   0   0  -1   0   0  19     1    00-00

Note that the independent variables are coded as 0, +1 and -1. The +1 and -1 represent the low and high settings for the levels of this variable and 0 represents a center point. This is a convenient scaling for purposes of the analysis. The factor variables can be scaled back to their original units for presentation purposes.