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mat510_lecture_w8.pptxMAT510 Business Statistics
Using Process Experimentation to Build Models
Topics
Why Do We Need a Statistical Approach?
Examples of Process Experiments
Statistical Approach to Experimentation
Two-Factor Experiments: A Case Study
Three-Factor Experiments: A Case Study
Larger Experiments,
Blocking, Randomization, and Center Points
Why Do We Need a Statistical Approach?
Statistical design of experiment is an efficient method to identify key drivers in the process
Collect quality data
Provide systematic approach
Control nuisance variables
Quantify drivers’ effect on system output
Identify interactions among process variables
Measure experimental uncertainties
Increase chances to identify key drivers
Haphazard experiment
One-Factor-at-a-Time (OFAAT): vary one factor in the process and measure output response
OFFAT limitations:
One minimum or maximum
Process variables do not interact
Small output variation on process variables
Examples of Process Experiments
Find the best chocolate drink example
Key drivers are
Chocolate level (10: strongest chocolate flavor)
Creaminess (10: very creamy)
Thickness (10: very thick drink)
Held environmental factors constants
Temperature (150 to 170 deg F)
Consumer hunger level (test at lunch time)
Design test
Find the best levels on chocolate level, creaminess and thickness
Use 2 (creaminess) x 2 (chocolate) x 2 (thickness) factorial design
Examples of Process Experiments
Experiment #1
Choose two test levels for each key driver
Identify the best level combinations for all three drivers (Cream: 7, Chocolate: 7 and thickness: 5)
Experiment #2
Repeat the best test result from experiment #1 on test 9
Alter test levels on all three drivers around the best levels found in experiment #1
Best result (cream: 8, chocolate: 6, thickness: 4)
Experiment #3
Repeat the best result from experiment #2 on test 9
Identify the best combinations of all drivers
Repeat the best combination in the following experiment to confirm test result
Statistical Approach to Experimentation
Key steps in planning an experiment
Clear statement of the problem
What is the question needed to be answered
Available resources (20% of budgets used in the first experiment)
Time to complete the experiment
Collect background information
Literature search
Previous work done
Ideas proposed or published
Design the experiment
Get all interested parties
Design, review and revised the experiment
Plan and conduct the experiment
Clear instructions on the experiment
Collect experimental data
Analyze the data
Report and discuss experimental results
Two-Factor Experiments: A Case Study
Use an example to illustrate the two-level (yes/no) factorial (all possible combinations) design of experiment
Telemarketing company wants to make its sale’s force more effective. Approaches considered
Use script
Provide training
They want to design an experiment to verify the effectiveness of the approach
Gathered 4 group and 5 persons in each group shown in upper left table
Test group 1: all 5 sales gave no script nor training
Test group 2: given script but no training
Average experiment results of each group shown in lower left table
| Test Group | Script | Training |
| 1 | No | No |
| 2 | Yes | No |
| 3 | No | Yes |
| 4 | Yes | Yes |
| Test Group | Percentage of Successful sales calls |
| 1 | 10.8 |
| 2 | 15.2 |
| 3 | 20.6 |
| 4 | 41.8 |
Two-Factor Experiments: A Case Study (Continued)
We need to analyze our data
Effect of script and training on successful sales calls
-(average response without script)
script effect = (15.2 + 41.8)/2 – (10.8+20.6)/2 = 12.8
training effect = (20.6 + 41.8)/2 – (10.8+15.2)/2 = 18.2
Interaction effect = (10.8+41.8)/2 – (15.2+20.6)/2 = 8.4
Interactions may have positive or negative effects on results of experiment
Synergistic (positive interaction) means two factors involved generates larger effect than if the effects of the two factors were additive
Antagonistic (negative interaction) two factors is smaller than would be predicted by the additive of two factors
Two-Factor Experiments: A Case Study (Continued)
Regression analysis can be applied to design of experiment
Regression model
+++
: rate of successful sales call
: use script
: get training
: model residue error
= (10.8 + 15.2 + 20.6 + 41.8) / 4 = 22.1
= 12.8 / 2 = 6.4 (script effect)
= 18.2 /2 = 9.1 (training effect)
= 8.4 / 2 = 4.2 (interaction effect)
Regression model helps forecasting effects of individual factor
Three-Factor Experiments: A Case Study
Example for two-level three-factor design of experiment
Three factors and two levels are
Store size (large + or small -, x1)
Display type (shelf - or aisle end +, x2)
Package type (paper - or plastic +, x3)
Experiment results are summarized in the table shown in the left
| Store Size (x1) | Display Type (x2) | Package type (x3) | Average sales |
| Small (-) | Shelf (-) | Paper (-) | 51.5 |
| Large (+) | Shelf (-) | Paper (-) | 44.5 |
| Small (-) | Aisle End (+) | Paper (-) | 56 |
| Large (+) | Aisle End (+) | Paper (-) | 78 |
| Small (-) | Shelf (-) | Plastic (+) | 54 |
| Large (+) | Shelf (-) | Plastic (+) | 53 |
| Small (-) | Aisle End (+) | Plastic (+) | 67.5 |
| Large (+) | Aisle End (+) | Plastic (+) | 96.5 |
Three-Factor Experiments: A Case Study (Continued)
Data analysis is shown in the left table
Some calculations in the table are shown here
Sum+ on x1: add average sales on all large stores (44.5 + 78 + 53 + 96.5 = 272)
Sum- on x2: add average sales on all shelf display (51.5 + 44.5 + 54 + 53 = 203)
Avg+ on x3: average sales on all plastic package ((54 + 53 + 67.5 + 96.5)/4 = 67.75)
Avg- on x2 x3: average sales on all “-” entries on x2 x3 column ((56 + 78 + 54 + 53)/4 = 60.25)
Interaction x1 x2: multiply x1 and x2 (small store (-) x shelf display (-) = +)
Effect x2 x3: difference between Avg+ and Avg- on X2 and x3 (65 – 60.2 = 4.8)
t-ratio: indicate statistical significance of the effect (no calculation)
Three-Factor Experiments: A Case Study (Continued)
We can draw some important conclusions on process improvements using the experiment
Store size and display type interact strongly with each other
Package type has smaller effect on both store size and display type
All effects are positive (synergistic)
In large stores, we should use aisle end display and plastic package
Display type has minimum effect on small stores
Other factors such as cost-benefits should be considered
Regression model can be built based on effects
+++++
For examples, = 125.25, = 5.4
Larger Experiments
Large size experiment on number of levels or number of factors can increase costs and work required
Use smaller number of levels when large number of factors involved in the experiment
Use smaller number of factors when large number of levels required in the experiment
Blocking, Randomization, and Center Points
Blocking is a technique that reduce nuisance variables in the design of experiment
Nuisance factors can affect the validity of the experiment (e.g. tasters try too many drinks in a short period of time)
Properly choose samples in each block helps reduce bias in the experimental design
Randomization reduces nuisance factors
Complete randomization: randomize on population
Restricted randomization: randomize on local samples
Center Point is the middle levels of experimental design
Center point allows monitoring curvature of the response functions
Check Your Understanding
Directions: Choose the best answer to complete the following sentence from the list below, and then click the Submit button.
Question: How many test groups are necessary for conducting a three level (low, medium, and high) and two factor (temperature, pressure) design of experiment: ___________.
A. 5
B. 8
C. 9
Summary
Why Do We Need a Statistical Approach?
Examples of Process Experiments
Statistical Approach to Experimentation
Two-Factor Experiments: A Case Study
Three-Factor Experiments: A Case Study
Larger Experiments,
Blocking, Randomization, and Center Points
