Design of Experiments - Basic concepts
By Pier Giorgio DELLA ROLE - July 2003

Objectives

• Understand when and why to do experiments is useful
• Understand different strategies of experimentation
• Understand what a factorial experiment is and
• what kind of information it can provide
• Identify advantages and disadvantages of different strategies

Why to do experiments

• Verify if a relationship cause-effect cause-effect does exist.
• Relationship cause-effect between all potential causes of variation (Xs) and the system response (Y).
• Find the vital few causes of variation.
• Those that have a major effect on the response.
  (vital few vs. trivial many - parameter design).
• Define the target value target value for each parameter
  (Xs).
• Define the target value for each parameter in order to optimize the response:
  Maximized, minimized or centered on target value

Xs = causes o parameters o factors
Y = effect o response
Y = f(X) equation between input (Xs) and output (Y): empirical model

Experimental Strategies

• TRIAL & ERROR TRIAL & ERROR
• Introduce one or more changes at a time and to evaluate the effect on the system.
• ONE FACTOR AT A TIME - OFAT ONE FACTOR AT A TIME - OFAT
• Manipulate one factor at a time looking for the best value of each factor.
• FACTORIAL EXPERIMENTS FACTORIAL EXPERIMENTS
• Change all the factors in the same time looking for their effects - including also their interactions - on the response.

Experimental Strategies: Trial & Error


but.....
What actions are really useful?
Have you implemented useless expensive actions?
What will you do if the problem comes again?
..... Have you learned anything?
Experimental Strategies: One Factor At a Time (OFAT)
OFAT means:
to manipulate one factor at a time looking for the best value of each factor.

Experimental Strategies: One Factor At a Time (OFAT)

Experimental Strategies: One Factor At a Time (OFAT)

Expected Mean: 86
Lost Opportunity: Mean Above 95
Experimental Strategies: One Factor At a Time (OFAT)
ADVANTAGES:

• very simple to understand and to apply
• but ......

DISADVANTAGES:

• it uses lines to explore a space
  (bidimensional, in the previous example)
• you loose any opportunity to discover interactions between factors
• it is less ‘efficient’ compared to a factorial experiment: we have to do more trials

Experimental Strategies: Factorial Experiments
A Factorial Experiment is:

• change all the factors in the same time, running
  trials for particular combinations of a limited number
  of factor levels

ADVANTAGES:

• it is the more efficient (less trials) way to evaluate effects
• it is possible to evaluate interactions between factors
• it give you the risk in taking decisions

DISADVANTAGE:

• “work” with statistics ......

Effect of a Factor

• The effect of a factor on a response variable is the change in the response when the factor goes from its low level to its high level.

Factor Interactions

• When the effect of one factor is influenced by the level of another factor, we say there is an interaction effect between the two factors

Empirical Model

From the previous experiment you can get the empirical model showing the relationship between factors and output

DOE - Sequential approach

During the improvement of products and processes, there are different ‘knowledge levels’ starting from a scarce knowledge to a deep knowledge.

Strategies of dealing with Noise

• Keep it constant
  Known noise factors should be blocked during the experiment in order to enhance
  precision but then you MUST draw your conclusions only for the constant level of
  noise
• Block
  Treat noise as a factor, but in a way that you can understand only its main effect,
  not its interactions with other factors
• Randomization
  It is always better to randomize the run sequence in order to minimize the risk of
  correspondance between the sequence of a factor and the “sequence” of an
  unknown noise factor; in this case it is possible to attribute an effect to the factor
  while it must be attributed to the noise.
  A remark: sometimes randomization is unpractical (setups, transients....)
• Analysis of Covariance
  Measure all it is possible! Later you can decide to analyse the correspondance
  between the output and the noise factor you have measured

The logic steps to be followed in and implementing implementing a DOE

• Define the product/process to be studied
• Determine the response(s) - Y
• Validate the Measurement System for the response(s) - Gage R&R
• Generate candidate factors - Xs
• Determine the levels for the selected factors
• Select the experimental design
• Have a plan to control the noise factors
• Perform the experiment according to the design
• Analyze the results and draw conclusions
• Document the new settings and perform confirmation runs