APPLICATION TIPS
(How to Plan, Design and Analyze
Taguchi Experiments)
Description of
FIVEPHASE (5P's)
Application Process
(Select project that can give you high return on investment.
Identify project that can produce the most customer satisfaction.
Review
warranty and rejection data. Look for a project which can show immediate
improvement in cost.)
For additional tips review the following
discussions:
Experiment Planning Tips Experiment Design Tips
Analysis
Tips
Presentation
Tips Application Tips
P1. Plan 
Arrange for the planning/brainstorming session. If it's your own project, you
may consider asking some one else to
facilitate. Work as a team when possible. Use common sense principles of working
as a team. Decide things by consensus.
Determine:
* Evaluation criteria and define a method to combine them
* Control factors and their levels.
* Interaction (if any)
* Noise factors (if any)
* Number of samples to be tested.
* Experiment logistics.
P2. Prescribe 
Design experiment
& prescribe recipes of the trial conditions.
* Determine the order of running the experiment
* Describe noise conditions for testing samples if the design
includes an outer array
P3. Perform
 Carry out experiments and collect results
* Note readings,
calculate and record averages if
multiple readings of the same criteria
are taken.
* Calculate OEC using
the formula defined in the
planning session.
P4. Predict
 Analyze results and Predict performance expected
* Determine factor
influence (Main Effect)
* Identify significant
factors (ANOVA)
* Determine optimum
condition and estimate performance
* Calculate confidence
interval of optimum performance
* Adjust design
tolerances based on ANOVA
P5. Prove
 Prove and verify predictions by running
confirmation tests
* Test multiple
samples at the optimum condition
* Compare the average
performance with the confidence
interval determined from DOE


Experiment Design Tips
Notations:
32LF = Three 2level
factors, 14LF = One 4level factor,
AxB = Interaction between two 2level factors A and B, etc.
AxB = 4 x 8 => 12 should be read as "Assign factors A to col. 4, B to col. 8, and
reserve col. 12 for interaction AxB", etc.
Design solutions
for a number of experimental situations are presented below. Using the notations described
above, the experimental requirements are first stated, followed by a common experiment
design strategy. The design shown are not necessarily unique, alternative solutions may
exist. Notations A, B, C, etc. represent factor descriptions.
For most convenient use
of the design recommendations, list your factors and interactions by first
assigning the character notations to each factor, then selecting the
REQUIREMENTS that best match your situation. As always double check your
interaction and upgraded columns with the applicable TRIANGULAR TABLE.
Recommended
Array Selection and Column Assignments
EXPERIMENT DESIGNS USING STANDARD ARRAYS
(no interaction or column upgrading)
 REQUIREMENTS: 22LF or 32LF
DESIGN: L4, factors assigned to columns arbitrarily
 REQUIREMENTS: 4, 5, 6 or 7 2LF
DESIGN: L8, factors cols. 1, 2, 4 & 6.Remaining columns left empty.
 REQUIREMENTS: 8, 9, 10 or 11 2LF, interaction present but ignored
DESIGN: L12, assign factors to columns arbitrarily (DO NOT USE L12 TO STUDY INTERACTION)
 REQUIREMENTS: 12, 13, 14 or 15 2LF
DESIGN: L16, assign factors to columns arbitrarily
 REQUIREMENTS: 16, 17, .... or 31 2LF
DESIGN: L32, assign factors to columns arbitrarily.
 REQUIREMENTS: 32, 33, ..... or 63 2LF
DESIGN: L64, assign factors to columns arbitrarily.
 REQUIREMENTS: 2, 3 or 4 3LF
DESIGN: L9, factors assigned arbitrarily
 REQUIREMENTS: 1 or 22LF and 23LF
DESIGN: L9, Dummy treat columns for 2level factors.
 REQUIREMENTS: 12LF and 4, 5, 6 or 7 3LF
DESIGN: L18, assign the 2level factor to col. 1 and all other factors to cols. 2  8.
(DO NOT USE L18 TO STUDY INTERACTIONS)
 REQUIREMENTS: 2 2LF(A & B) and 4, 5 or 6 3LF
DESIGN: L18, assign factor A to col. 1, dummy treat and assign factor B to col. 2. Assign
other factors to cols. 3  8.
 REQUIREMENTS: 8, 9, 10, 11, 12 or 13 3LF
DESIGN: L27, assign factors to columns arbitrarily.
 REQUIREMENTS: 3, 4 or 5 4LF
DESIGN: Modified L16, assign factors to columns arbitrarily.
 REQUIREMENTS: 6, 7, 8 or 9 4LF
DESIGN: Modified L32, Leave col. 1 empty and assign factors to the other columns
arbitrarily.
 REQUIREMENTS: 12LF and 5, 6, 7, 8 or 9 4LF
DESIGN: Modified L32, assign 2level factor to col. 1 and assign other factors to the
remaining columns arbitrarily.DESIGNS WITH MULTIPLE
INTERACTIONS (dependent and independent pairs)
 REQUIREMENTS: 22LF(A&B) and AxB
DESIGN: L4, factors A in col. 1,B in col. 2 and interaction AxB in col. 3
 REQUIREMENTS: 3, 4, 5 or 6  2LF and one interaction, AxB
DESIGN: L8, factor A in col.1, B in col. 2 and interaction AxB in col. 3. Other 2level
factors in the remaining column.
 REQUIREMENTS: 3, 4 or 5 2LF and two dependent interactions, AxB and BxC
DESIGN: L8, Factors A in col. 1, B in col. 2 and C in col. 4, Interactions AxB in col. 3
and BxC in col. 6
 REQUIREMENTS: 3 or 4 2LF and 3 dependent interactions AxB, BxC and CxA
DESIGN: L8, Factors A in col. 1, B in col. 2 and C in col. 4. Interactions AxB in col. 3,
BxC in col. 6, and CxA in col. 5.
 REQUIREMENTS: 4  2LF and 3 interactions AxB, AxC and AxD
DESIGN: L8, Factors A in col. 1, B in col. 2, C in col. 4 and Din col. 7. Interactions
AxB in col. 3 and AxC in col. 5 and AxD in col. 6
 REQUIREMENTS: 22LF(A&B) and interaction (AxB)
DESIGN: L9, assign factors A to col. 1, and reserve cols. 3 & 4 to study interaction
between the two 3level factors, AxB.
 REQUIREMENTS: 4 or 5 2LF and 2 interactions AxB and CxD
DESIGN: L16, factor A in col. 1, B in col. 2 and int. AxB in col. 3. Factors C in col. 4,
D in col. 8 and int. CxD in col. 12.
 REQUIREMENTS: 8, 9, 10,.... or 14 2LF and 1 interaction (AxB)
DESIGN: L16, assign factors A to col. 1, B to col2, and AxB to col. 3.
 REQUIREMENTS: 8, 9, 10,.... or 13 2LF and 2 interactions (AxB and BxC)
DESIGN: L16, assign factors A to col. 1, B to col. 2, C to col. 4, AxB to col. 3 and BxC
to col.6. Assign other factors to the remaining columns.
 REQUIREMENTS: 8, 9, 10,.... or 13 2LF and 2 interactions (AxB and AxC)
DESIGN: L16, assign factors A to col. 1, B to col. 2, C to col. 4, AxB to col. 3 and AxC
to col.5.
 REQUIREMENTS: 8, 9, 10,.. or 13 2LF and 2 interactions (independent, AxB and CxD)
DESIGN: L16, assign factors A to col. 1, B to col. 2, C to col. 4, D to col. 8, AxB to
col. 3 and CxD to col.12.
 REQUIREMENTS: 8, 9, 10, 11 or 12 2LF and 3 interactions ( AxB, BxC and CxA)
DESIGN: L16, assign factors A to col. 1, B to col. 2, C to col. 4, AxB to col. 3, BxC to
col. 6 and CxA to col. 5.
 REQUIREMENTS: 8, 9, 10, 11 or 12 2LF and 3 interactions ( AxB, AxC and AxD)
DESIGN: L16, assign factors A to col. 1, B to col. 2, C to col. 4, D to col. 7, AxB to
col. 3 and AxC to col. 5 and AxD to col. 6.
 REQUIREMENTS: 8, 9, 10, 11 or 12 2LF and 3 interactions ( AxB, AxC and CxD)
DESIGN: L16, assign factors A to col. 1, B to col. 2, C to col. 4, D to col. 8, AxB to
col. 3 and AxC to col. 5 and CxD to col.12.
 REQUIREMENTS: 8, 9, 10, 11 or 12 2LF and 3 interactions ( AxB, BxC and CxD)
DESIGN: L16, assign factors A to col. 1, B to col. 2, C to col. 4, D to col. 8, AxB to
col. 3 and BxC to col.6 and CxD to col.12.
 REQUIREMENTS: 8, 9, 10, 11 or 12 2LF and 3 interactions ( AxB, CxD and ExF)
DESIGN: L16, assign factors A to col. 1, B to col. 2, C to col. 4, D to col. 8, E to col.
7, F to col. 9, AxB to col. 3, CxD to col.12 and ExF to col. 14.
 REQUIREMENTS: 10 or 11 2LF(A,B,C,...J) and 4 interactions ( AxB, BxC, CxA and DxE )
DESIGN: L16, assign factors A to col. 1, B to col. 2, C to col. 4, D to col. 7 and E to
col. 9. Place interactions AxB to col. 3, BxC to col. 6 CxA to col. 5 and DxE to col. 14.
 REQUIREMENTS: 10 or 11 2LF(A,B,C,...J) and 4 interactions ( AxB, BxC, CxD and ExF )
DESIGN: L16, assign factors A to col. 1, B to col. 2, C to col. 4, D to col. 8, E to col.
7 and F to col. 9. Place interactions AxB to col. 3, BxC to col. 6 CxD to col. 12 and ExF
to col. 14.
 REQUIREMENTS: 10 or 11 2LF(A,B,C,...J) and 4 interactions ( AxB,AxC, AxD and ExF )
DESIGN: L16, assign factors A to col. 1, B to col. 2, C to col. 4, D to col. 8, E to col.
7 and F to col. 9. Place interactions AxB to col. 3, AxC to col. 5, AxD to col. 9 and ExF
to col. 14.
 REQUIREMENTS: 10 or 11 2LF(A,B,C,...J) and 4 interactions( AxB,AxC, AxD and AxE )
DESIGN: L16, assign factors A to col. 1, B to col. 2, C to col. 4, D to col. 8 and E to
col. 15. Place interactions AxB to col. 3, AxC to col. 5, AxD to col. 9 and ExF to col.
14.
 REQUIREMENTS: 10 or 11 2LF(A,B,C,...J) and 4 interactions ( AxB, CxD, ExF and GxH )
DESIGN: L16, assign factors A to col. 1, B to col. 2, C to col. 4, D to col. 8, E to col.
7, F to col. 9, G to col. 5 and H to col. 10. Place interactions AxB to col. 3, CxD to
col.12, ExF to col. 14 and GxH to col. 15.
 REQUIREMENTS: 10 2LF(A,B,C,...J) and 5 interactions ( AxB, CxD, ExF, GxH and IxJ)
DESIGN: L16, assign factors A to col. 1, B to col. 2, C to col. 4, D to col. 8, E to col.
7, F to col. 9, G to col. 5, H to col. 10, I to col. 6 and J to col. 11. Place
interactions AxB to col. 3, CxD to col.12 and ExF to col. 14, GxH to col. 15 and IxJ to
col13 (Note: the five interacting groups in L16 are 1x2=>3, 4x8=>12, 7x9=>14,
5x10=>15 and 6x11=>13) .
 REQUIREMENTS: 10 2LF(A,B,C,.. ) and 5 interactions ( AxB, BxC, CxA, DxE and DxF)
DESIGN: L16, assign factors A to col. 1, B to col. 2, C to col. 4, D to col. 7, E to col.
9 an F to col. 8. Place interactions AxB to col. 3, BxC to col.6, CxA to col. 5, DxE to
col. 14 and DxE to col. 15.
 REQUIREMENTS: 10 2LF(A,B,C,.. ) and 5 interactions ( AxB, AxC, AxD, AxE and AxF)
DESIGN: L16, assign factors A to col. 1, B to col. 2, C to col. 4, D to col. 8, E to col.
10 an F to col. 12. Place interactions AxB to col. 3, AxC to col. 5, AxD to col. 9, AxE to
col. 11 and AxF to col. 13. MIXEDLEVEL FACTOR DESIGNS (2, 3 and 4level factors only)
 REQUIREMENTS: 42LF and 14LF(A)
DESIGN: L8, assign factor A in col. 1, all other factors in cols. 4, 5, 6 & 7
 REQUIREMENTS: 1, 2, or 3 2LF and 14LF(A)
DESIGN: L8, assign factor A in col. 1, all other factors in cols. 4, 5, 6 & 7 as
appropriate
 REQUIREMENTS: 1, 2, 3 or 4 2LF and 13LF(A)
DESIGN: L8, assign factor A in col. 1, all other factors in cols. 4, 5, 6 & 7 as
appropriate
 REQUIREMENTS: 22LF(A & B) and 33LF (AxB is considered absent)
DESIGN: L9 used for COMBINATION DESIGN. Assign the two 2level factor combinations(3
levels) to any of the four columns of the array.
 REQUIREMENTS: 12, 11, 10 ..or 5 2LF, 14LF(A)
DESIGN: L16. Upgrade the interacting groups of cols., 1 2 3 to a 4level columns(1).
Assign factor A to col. 1 and the 2level factors to the remaining columns.
 REQUIREMENTS: 12, 11, 10 ..or 5 2LF, 13LF(A)
DESIGN: L16. Upgrade the interacting groups of cols., 1 2 3 to a 4level columns(1).
Dummy treat this 4level columns to a 3level (col. 1 ). Assign factor A to col. 1 and the
2level factors to the remaining columns.
 REQUIREMENTS: 9, 8, 7,..or 5 2LF, 13LF(A) and 14LF(B)
DESIGN: L16. Upgrade two interacting groups of cols., 1 2 3 and 4 8 12 to two 4level
columns(1 and 4). Dummy treat the first 4level columns to a 3level (col. 1 ). Assign
factor A to col. 1, B to col. 4 and the 2level factors to the remaining columns.
 REQUIREMENTS: 9, 8, 7, ..or 2 2LF, 23LF(A & B)
DESIGN: L16. Upgrade two interacting groups of cols., 1 2 3 and 4 8 12 to two 4level
columns(1 and 4). Dummy treat the two 4level columns to 3level (cols. 1 and 4). Assign
factor A to col. 1, B to col. 4 and the 2level factors to the remaining columns.
 REQUIREMENTS: 6, 5, 4, 3 or 2 2LF, 24LF(A & B) and 14LF(C)
DESIGN: L16. Upgrade two interacting groups of cols., 1 2 3 and 4 8 12 to two 4level
columns(1and 4). Assign factor A to col. 1, B to col. 4 and the 2level factors to the
remaining columns.
 REQUIREMENTS: 6, 5, 4, 3 or 2 2LF, 23LF(A & B) and 14LF(C)
DESIGN: L16. Upgrade three interacting groups of cols., 1 2 3, 4 8 12 and 7 9 14, to
three 4level columns(1, 4 and 7). Dummy treat the first two 4level columns to 3level
(cols. 1 and 4). Assign factor A to col. 1, B to col. 4 and C to col. 7. Assign the
2level factors to the remaining columns.
 REQUIREMENTS: 6, 5, 4, 3 or 2 2LF, 13LF(A) and 24LF(B & C)
DESIGN: L16. Upgrade three interacting groups of cols., 1 2 3, 4 8 12 and 7 9 14, to
three 4level columns(1, 4 and 7). Dummy treat the first 4level column to a 3level (col.
1 ). Assign factor A to col. 1, B to col. 4 and C to col. 7. Assign the 2level factors to
the remaining columns.
 REQUIREMENTS: 6, 5, 4, 3 or 2 2LF and 34LF(A,B & C)
DESIGN: L16. Upgrade three interacting groups of cols., 1 2 3, 4 8 12 and 7 9 14, to
three 4level columns(1, 4 and 7). Assign factor A to col. 1, B to col. 4 and C to col. 7.
Assign the 2level factors to the remaining columns.
 REQUIREMENTS: 6, 5, 4, 3 or 2 2LF and 33LF(A,B & C)
DESIGN: L16. Upgrade three interacting groups of cols., 1 2 3, 4 8 12 and 7 9 14, to
three 4level columns(1, 4 and 7). Dummy the upgraded 4level columns to 3level columns.
Assign factor A to col. 1, B to col. 4 and C to col. 7. Assign the 2level factors to the
remaining columns. OUTER ARRAY DESIGN FOR ROBUSTNESS (Static System win noise factors)
 REQUIREMENTS: 22LF or 32LF Noise factors
DESIGN: L4, Noise factors assigned to columns arbitrarily
 REQUIREMENTS: 4, 5, 6 or 7 2LF Noise factors
DESIGN: L8, Noise factors cols. 1, 2, 4 & 6.Remaining columns left empty.
 REQUIREMENTS: 8, 9, 10 or 11 2LF, interaction present but ignored
DESIGN: L12, assign factors to columns arbitrarily (DO NOT USE L12 TO STUDY INTERACTION)
 REQUIREMENTS: 12, 13, 14 or 15 2LF Noise factors
DESIGN: L16, assign factors to columns arbitrarily
 REQUIREMENTS: 2, 3 or 4 3LF Noise factors
DESIGN: L9, Noise factors assigned arbitrarily
 REQUIREMENTS: 1 or 22LF and 23LF Noise factors
DESIGN: L9, Dummy treat columns for 2level Noise factors.
 REQUIREMENTS: 12LF and 4, 5, 6 or 7 3LF Noise factors
DESIGN: L18, assign the 2level Noise factor to col. 1 and all other factors to cols. 2 
8.
 REQUIREMENTS: 2 2LF(A & B) and 4, 5 or 6 3LF Noise factors
DESIGN: L18, assign factor A to col. 1, dummy treat and assign factor B to col. 2. Assign
other factors to cols. 3  8. (Click here to review: Products and
Services Menu  List of Nutek Clients)
(Look for More Design Tips in Future Updates)


Application
Steps
(How
to apply the DOE/Taguchi technique):
[For expanded guidelines on experiment planning, follow:
Follow
Recommended Experiment Planning Steps]
 Select Project: Identify a design optimization or production
problem solving project . Define project clearly based on function you intend to improve.
For complex systems/process, review subsystems/subprocesses and select activities
responsible for the function. Lead if it's your own project, suggest DOE if it's some one
else's.
 Plan Experiment: Conduct or Arrange the planning/brainstorming session.
If it's your own project, you will benefit more if some one else facilitated the session.
Determine:
 Evaluation criteria and establish a scheme to combine them
 Control factors and their levels.
 Interaction (if any)
 Noise factors (if any)
 Number of samples to be tested.
 Experiment resources and logistics
 Designing experiments: Design experiment & describe trial
conditions. Also:
 Determine the order of running the experiment
 Describe noise conditions for testing samples if the design includes an outer array
 Conduct Experiments: Carry out experiments by selecting the trial
condition in random order, and:
 Note readings, calculate and record averages if multiple readings of the same criteria
are taken.
 Calculate OEC using the formula defined in the planning session.
 Analyze Results: Reduce observations (in case of multiple objectives)
into results and perform analysis to:
 Determine factor influence (Main Effect)
 Identify significant factors (ANOVA)
 Determine optimum condition and estimate performance
 Calculate confidence interval of optimum performance
 Adjust design tolerances based on ANOVA
 Confirm Expected Performance: Test one or more samples at the optimum
condition to:
 Establish performance at the optimum condition
 Compare the average performance with the confidence interval determined from DOE


Experiment Planning
BRAINSTORMING FOR TAGUCHI EXPERIMENTS
Brainstorming is an essential step in the Taguchi experimental design. Many issues
regarding the scopes and objectives of the experiment are resolved in this planning
session:
* Identify factors, levels and derive other pertinent
information about
the experiment, collectively with all involved in the experiment.
* Develop team effort and achieve the maximum participation from
the team members.
* Determine all experiment related items by consensus decisions.
WHO SHOULD CONDUCT?  The session should be facilitated by a person who has a good
working knowledge of the Taguchi methodologies. Engineers or statisticians dedicated to
helping others apply this tool will make better facilitators. The project leader should
only facilitate his/her own project only when none is available.
WHO SHOULD HOST THE SESSION?  The team/project leader should host the brainstorming
session.
WHO SHOULD ATTEND?  All those who have firsthand knowledge and/or involvement in
the subject under study should be included. For an engineering design or a
manufacturing process, both the design and the manufacturing personnel should
attend. If cost or supplier knowledge are likely factors, then persons from these
disciplines should be encouraged to attend (group size permitting).
HOW MANY SHOULD ATTEND?  The more the better. The upper limit should be
around 15. It can be as low as 2.
WHAT IS THE AGENDA FOR THE SESSION?  The facilitator should guide the group and maintain
her own schedule (follow guidelines given below). The meeting agenda need not be published
to the participants.
TOPICS OF DISCUSSIONS:
The following topics should be included in the agenda for the brainstorming session.
1. ESTABLISH OBJECTIVE OF THE STUDY (What are you after? 2  4 hours)
i. What is the characteristic of quality? How do we evaluate the
objective?
ii.. How do we measure the quality characteristic? What are the units
of measurement?
iii. What are the criteria (attributes) of evaluation for the quality
characteristic?
iv. How to combine criteria of evaluation, when there are more than one (OEC)?
v. How are the different quality criteria weighted?
vi. What is the sense of the quality characteristic? Lower is better,
nominal is the best, etc.
2. DETERMINE DESIGN FACTORS AND THEIR LEVELS (1  2 hours)
i. What are all the possible factors?
ii. Which ones are more important than others (pareto diagram)?
iii. How many factors should be included in the study?
iv. How to select levels for the factors? How many levels?
v. What is the trade off between levels and factors?
3. "NOISE" VARIABLES of (How to make a robust design? 1/2 hour)
i. What factors are likely to influence the objective function,but cannot be
controlled in real life.
ii. How can the product under study be made insensitive to the noise factors?
iii. How are these factors included in the study?
4. INTERACTION STUDIES (Which factors are likely to interact? 1/2 hour)
i. Which are the factors most likely to interact?
ii. How many interactions can be included?
iii. Should we include an interaction or an additional factor?
iv. Do we need to study the interaction at all?
5. TASK ASSIGNMENT AND DESCRIPTION (Who will do what, how and when? 1/2 hour)
i. What steps are to be followed in combining all the quality criteria into
an OEC?
ii. What to do with the factors not included in the study?
iii. How to simulate the experiments to represent the customer/field
applications?
iv. How many repetitions and in what order will the experiments be run?
v. Who will do what and when? Who will analyze the data?
Overall Evaluation Criteria (OEC)
Whenever you encounter multiple objectives in your project under study, you will have
the option to analyze your results by using performance of one objective at a time, or use
the overall evaluation criteria (OEC) obtained by combining all criteria of evaluations
into a single index. Follow the procedure for combining different
criteria into an OEC if desired. The OEC formulation capability is fully supported by Qualitek4 software.


Analysis
of Experimental Results
 Calculate Factor Average Effects
 Study factor influences
 Determine optimum condition
 Compute expected performance
 Find out if interaction is present
 Compute ANOVA Statistics
 Determine relative influence of factors to the variation of results
 Pool factors and interaction that are not significant
 determine if interaction is significant
 Calculate confidence interval (main effect and optimum performance)
 Estimate Savings Expected
 Determine improvement expected
 Calculated savings expected due to reduce variation


Project Presentation
Depending on your audience, organize and present your findings in three levels:
Level I: Management Briefing
Your presentation should include what you did, why you did it, what you found,
and what it is it going to be worth in terms of dollars:
 Describe project and its current performance
 Talk about the improvement
 Show a graph representing the improvement (Normal distributions of current and improved
performances)
 Estimate the savings in dollars
Level II: Team Presentation
This is more detailed presentation for your project team members and all others interested
in the project:
 Show details of factor influences, ANOVA, and optimum condition
 Explain how optimum is determined
 Discuss how different evaluation criteria affected your decision about optimum condition
 Share your plan for confirmation and future studies
Level III: Technical Session
Share with interested parties all issues related to experiment setup, data collection
& reduction, interaction studies, noise effects, etc.




