Design of Experiments/Taguchi approach
Design of Experiments (Taguchi Approach)-Overview
Design of Experiments Applied to a Wave Soldering Process: A Case Study
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The DOE using Taguchi approach can economically satisfy the needs of problem solving and product/process design optimization projects in the manufacturing industry. By learning and applying this technique, engineers, scientists, and researchers can significantly reduce the time required for experimental investigations.
Overall application goals:
Optimize product and process designs
Study the effects of multiple factors (i.e.- variables, parameters, ingredients, etc.) on the performance
Solve production problems by objectively laying out the investigative experiments
Specific Objectives:
Influence of individual factors on the performance
Which factor has more influence, which ones have less
Which factor should have tighter tolerance, which tolerance should be relaxed
Which factor influences are significant and which are not
How to allocate quality assurance resources based on objective data
Whether a supplier's part causes problems or not (ANOVA data)
How to combine different factors in their proper settings to get the best results
How you can substitute a less expensive part to get the same performance
How much money you can save if you make the design improvement
How you can determine which factor is causing most of your problems
How you can set up your process such that it is insensitive to uncontrollable factors
Which factors have more influence on the mean performance
What you need to do to reduce performance variation around the target
How you can adjust factors for a system whose response varies proportional to signal factor (Dynamic response)
How to combine multiple criteria of evaluation into a single index
How you can adjust factor for overall satisfaction of criteria of evaluations
How the uncontrollable factors affect the performance
etc.,
Advantage of DOE Using Taguchi Approach
The application of DOE requires careful planning, prudent layout of the experiment, and expert analysis of results. Based on years of research and applications Dr. Genichi Taguchi has standardized methods for each of these DOE application steps. Thus, DOE using Taguchi approach has become a much more attractive tool to practicing engineers and scientists.
Experiment planning and problem formulation
Experiment planning guidelines are consistent with modern work disciplines of working as teams. Consensus decisions about experiment objectives and factors make the projects more successful.
Experiment layout
High emphasis is put on cost and size of experiments
Size of experiment for a given number of factors and levels is standardized
Approach and priority for column assignments are established
Clear guidelines are available to deal with factors and interactions (interaction tables)
Uncontrollable factors are formally treated to reduce variation
Discrete prescriptions for setting up test conditions under uncontrollable factors are described
Guidelines for carrying out the experiments and number of samples to be tested are defined
Data analysis
Steps for analysis are standardized (main effect, ANOVA and Optimum)
Standard practice for determination of the optimum is recommended
Guidelines for test of significance and pooling are defined
Interpretation of results
Clear guidelines about meaning of error term
Discrete indicator about confirmation of results (Confidence interval)
Ability to quantify improvements in terms of dollars (Loss function)
Overall advantage
DOE using Taguchi approach attempts to improve quality which is defined as the consistency of performance. Consistency is achieved when variation is reduced. This can be done by moving the mean performance to the target as well as by reducing variations around the target. The prime motivation behind the Taguchi experiment design technique is to achieve reduced variation (also known as ROBUST DESIGN). This technique, therefore, is focused to attain the desired quality objectives in all steps. The classical DOE does not specifically address quality .
WHAT'S NEW?
1. NEW PHILOSOPHY
- Building quality in the product design.
- Measuring quality by deviation from target (not by rejection).
2. NEW DISCIPLINE
- Complete planning of experiments and evaluation criteria before conducting experiments.
- Determining a factor's influence by running the complete experiment.
3. SIMPLER AND STANDARDIZED EXPERIMENT DESIGN FORMAT
- Orthogonal arrays for experimental design.
- Outer array design for robust product design.
- More clear and easier methods for analysis of results.
4. QUALITY: DEFINITION and OBJECTIVE
- Reduced variation around the target with least cost.
5. APPROACH: ROBUST DESIGN
- Reduce variation without actually removing the cause of variation. Achieve consistent performance by making product/process insensitive to the influence of uncontrollable factors.
WHAT DOES IT DO?
- Optimize design, solve problems, build robust products, etc.
WHY DO IT?
- Save cost (Reduce warranty, rejection and cost of development).
AREAS OF APPLICATION:
- Analytical simulation (in early stages of design).
- Development testing (in design and development).
- Process development.
- Manufacturing.
- Problem solving in all areas of manufacturing and production.
The Taguchi method is used to improve the quality of products and processes. Improved quality results when a higher level of performance is consistently obtained. The highest possible performance is obtained by determining the optimum combination of design factors. The consistency of performance is obtained by making the product/process insensitive to the influence of the uncontrollable factor. In Taguchi's approach, optimum design is determined by using design of experiment principles, and consistency of performance is achieved by carrying out the trial conditions under the influence of the noise factors.
1. PLANNING EXPERIMENTS (BRAINSTORMING )
This is a necessary first step in any application.
The session should include individuals with first hand knowledge of the
project. All matters should be decided based on group consensus,
(One person -- One vote).
- Determine what you are after and how to evaluate it. When there is
more than one criterion of evaluation, decide how each criterion
is to be weighted and combined for the overall evaluation.
- Identify all influencing factors and those to be included in the study.
- Determine the factor levels.
- Determine the noise factor and the condition of repetitions.
2. DESIGNING EXPERIMENTS
Using the factors and levels determined in the brainstorming session, the experiments now can be designed and the method carrying them out established. To design the experiment, implement the following:
- Select the appropriate orthogonal array.
- Assign factor and interaction to columns.
- Describe each trial condition.
- Decide order and repetitions of trial conditions.
3. RUNNING EXPERIMENT
Run experiments in random order when possible.
4. ANALYZING RESULTS:
Before analysis, the raw experimental data might have to be combined into an overall evaluation criterion. This is particularly true when there are multiple criteria of evaluation.
Analysis is performed to determine the following:
- The optimum design.
- Influence of individual factors.
- Performance at the optimum condition.
- Relative influence of individual factors. etc.
5. RUNNING CONFIRMATION EXPERIMENT(S)
Running the experiments at the optimum condition is the necessary final step.
Quality Characteristic
Quality Characteristic (QC) generally refers to the measured results of the experiment. The QC can be single criterion such as pressure, temperature, efficiency, hardness, surface finish, etc. or a combination of several criteria together into a single index. QC also refers to their nature of the performance objectives such as "bigger is better", "smaller is better" or "nominal is the best".
FACTORS AND LEVELS
Factors are:
- design parameters that influence the performance.
- input that can be controlled.
- included in the study for the purpose of determining their
influence and control upon the most desirable performance.
Example: time, temperature, etc.
Levels are:
- Values that a factor assumes when used in the experiment
Example:. Time : 5sec. 10sec. (Continuous level)
Part: type 1, type 2, etc. (Discrete level)
INTERACTION BETWEEN FACTORS
Two factors (A and B) are considered to have interaction between them when one has influence on the effect of the other factor respectively.
Interaction
- is an effect (output) and does not alter the trial condition.
- can be determined even if no column is reserved for it.
- can be fully analyzed by keeping appropriate columns empty.
- affects the optimum condition and the expected result.
NOISE FACTORS AND OUTER ARRAYS
Noise factors are those factors:
- that are not controllable.
- whose influences are not known.
- which are intentionally not controlled.
To determine robust design, experiments are conducted under the influence of various noise factors. An "Outer Array" is used to reduce the number of noise conditions obtained by the combination of various noise factors.
ORDER OF RUNNING EXPERIMENTS
There are two common ways of running experiments. Suppose an experiment uses an L-8 array and each trial is repeated 3 times. How are the 3x8=24 experiments carried out?
REPLICATION - The most desirable way is to run these 24 in random order.
REPETITION - The most practical way may be to select the trial condition in random order then complete all repetitions in that trial.
NOTE:
In developing conclusions from the results of designed experiments and assigning statistical significance, it is assumed that the experiments were unbiased in any way, thus randomness is desired and should be maintained when possible.
MINIMUM REQUIREMENT - A minimum of one experiment per trial condition is required. Avoid running an experiment in an upward or downward sequence of trial numbers.
ORTHOGONAL ARRAYS
The set of tables for determining: trial conditions and number of experiments (tool for designing experiments).
Standard Notations for Orthogonal Arrays:
L-8 (27), 8 = Number of experiments
2 = Number of levels
7 = Number of factors
Examples of Orthogonal Arrays:
L-4 L-8 L-12 L-16 L-32 L-64 ALL AT 2 LEVELS
L-9 L-18 L-27 AT 3 & 2 LEVELS
L-16 & L-32 Modified At 4 LEVELS
MSD AND S/N RATIOS
Recommendation: If you are not looking for a specific objective, then SELECT S/N ratio based on Mean Squared Deviation (MSD) for analysis of repeated results.
MSD expression combines variation around the given target and is consistent with Taguchi's quality objective.
RELATIONSHIPS AMONG OBSERVED RESULTS, MSD AND S/N RATIOS
MSD = ( (Y1-m)2 + (Y2-m)2 + .... (Yn-m)2 )/n for NOMINAL IS BEST
MSD = (Y12 + Y22 + ................... Yn2 )/n for SMALLER IS BETTER
MSD = ( 1/ Y12 + 1/ Y22 + ............. 1/ Yn2 )/n for BIGGER IS BETTER
S/N = - 10 x Log (MSD)................. for all characteristics
Loss Function
The Loss Function offers a way to quantify the improvement from the optimum design determined from an experimental design study.
Definitions:
L = k (Y - m)2 .... for a single sample.
L = k (MSD) ........ for the whole population.
where L = Loss in dollar.
k = Proportionality constant.
m = Target value of the quality characteristic.
Y = Measured value of the quality characteristic.
THE COST SAVINGS WHEN THE MEAN VALUE IS HELD AT A TARGET VALUE CAN BE CALCULATED WHEN THE FOLLOWING INFORMATION IS AVAILABLE :
- TARGET VALUE OF QUALITY CHARACTERISTIC.
- TOLERANCE OF QUALITY CHARACTERISTIC.
- COST OF REJECTION AT PRODUCTION(PER UNIT).
- UNITS OF PRODUCTION PER MONTH (TOTAL).
- S/N RATIO (MSD)OF THE OLD DESIGN.
- S/N RATIO (MSD)OF THE IMPROVED DESIGN.
Design of Experiments Applied to
a Wave Soldering process: A Case Study
This paper illustrates an application of Design of Experiments based on Taguchi approach for optimizing a certain wave soldering process. The study was carried out in a certain manufacturing company in Czech Republic. A certain manufacturer of assembled electronic circuit boards was suffering from severe quality problem in terms of high percentage of solder defects. The production consists of two stages: assembly of printed circuit boards and then followed by a wave soldering process. A Pareto analysis revealed that most of the defects occur due to bridges (i.e., short circuits between terminals) on microprocessors. A sample of 1000 under standard production conditions has shown a defect rate of 9.9%, which was quite unacceptable to the customers. In order to rectify the above problem, it was decided to perform an experimental design based on Taguchi approach with the objective of reducing the number of defects. The steps involved in the experiment are summarized as follows:
1.Nature of the problem: High defect rate due to bridging in a wave soldering process
2.Selection of the quality characteristic: Percentage of defects
3.Selection of the control and noise factors: Nine control factors were considered during the brainstorming session. No noise factors were considered for the experiment.
4.Number of interactions: The experimenter was interested to study one interaction between the factors.
5.Number of factor levels: It was decided to study five factors at 3-levels and four factors at 2-levels. The factors included both quantitative (continuous) and qualitative (discrete) type.
6.Choice of suitable experimental design: The number of degrees of freedom required for studying the nine effects was equal to 14. Similarly, the interaction between two three level factors consumed 4 degrees of freedom. In brief, the total degrees of freedom was equal to 18. Therefore the most desirable and suitable design was an L-27 Orthogonal Array.
7.Experimental execution: The experimental trials were conducted in a random order using the Software System Qualitek-4. Experiments were carried out on the night shifts, to avoid production breaks.
8.Experimental analysis and interpretation: Analysis of variance was performed to identify the most dominant factors and the interaction of interest. Pooling was done on the insignificant factors in order to obtain adequate degrees of freedom for the error term. Four main effects and the interaction effect were found to be statistically significant.
9.Determination of Optimal Condition: The optimal settings were determined and the percentage of defects were predicted. For better additivity, Omega Transformation proposed by Taguchi was utilized.
10.Confirmation runs: Confirmation runs have yielded zero defects. The optimum condition has been recommended for implementation.