# F and P-value in L9 Taguchi Design

J

Dear Friends,

I used a L9 (4 factor in 3 level) design with 2 repetition. But in ANOVA table there are any value for p and F. (only * instead any value). How can I solve this problem.

Thank you

#### Attachments

• 106.9 KB Views: 233

#### Miner

##### Forum Moderator
Staff member
You have a fully saturated model. This means that all degrees of freedom have been used by the terms in the model with none remaining for the residual error, which is used to calculate the F ratio and the p-value. In Taguchi designs, any time you assign a factor to all columns, you have a fully saturated design.

You must remove the weakest term from the model to solve this issue. This would be either Time or R. I usually look for the smallest Adj MS and remove that term from the model.

Also, remember that Taguchi OAs are resolution III, so your factors are aliased with 2-way interactions. Minitab does not display this alias structure, so you will have to look at the linear graphs for the L9 OA.

J

dear Miner
I'm not perfect in Minitab. If it possible for you to send your revision minitab file for me.

Thank you.

#### Miner

##### Forum Moderator
Staff member
This is saved in Minitab 16 format. If you are using an older version, I can save it as a Minitab 15 format also.

#### Attachments

• 233.7 KB Views: 188
J

Dear Miner

I agree with you. But in attached paper another way to solve F and p Value calculation. Is it right?

Thank alot

#### Attachments

• 2.2 MB Views: 209

#### Miner

##### Forum Moderator
Staff member
Please specify which paper and what page shows the method. I could not find details sufficient to support what appear to be serious flaws in their analysis.

The first paper uses an incorrect number for degrees of freedom and plots interaction graphs which should never be done when using a resolution III design except under special design considerations which were not followed.

The second paper also uses an incorrect number for degrees of freedom.

Neither paper explains where they obtain the variance used in the residual error to calculate F and P.

J

Thanks dear miner

You are right. Neither of paper don't explain how calculate DF, F and P. My question is this, how they obtained this parameters (F, P and DF)?
on the other hand, in my design, all of factors should be exist in ANOVA Table and S/R main effect plot.
In you proposed way, R removed in ANOVATable. So, with your idea, which ANOVA Table I should be report? A ANOVA Table after removing R or before removing of it? a paper similar to your way (paper 3) attached here. Is it correct paper? But in another paper that similar to paper 3, different DF was reported.
moreover in another paper (paper 5) different way (3rd way to calculate F, P, DF) was reported.

#### Attachments

• 462.5 KB Views: 277
• 239.7 KB Views: 203
• 1.1 MB Views: 242

#### Miner

##### Forum Moderator
Staff member
Okay. Good news / bad news.

Good News: I figured out what they must have done by dredging up something I learned 30 years ago from Yuin Wu.

When you have three levels, you can calculate a linear effect separate from the quadratic effect. Each analysis uses 1 degree of freedom. The authors apparently calculated and reported the linear effects and pooled the quadratic effects into residual error allowing calculation of F and p. The degrees of freedom would then add up correctly. See below for more information.

Bad News: Minitab cannot do this. You must calculate it by hand or use other software (don't ask which).

Main-effect linear/quadratic estimates. The Effect estimate for linear effects can be interpreted as the difference between the average response at the low and high settings for the respective factors. The estimate for the quadratic (non-linear) effect can be interpreted as the difference between the average response at the center (medium) settings and the combined high and low settings for the respective factors.

Regarding which ANOVA table to report, I would show the reduced model.

J

you are very expert in this regards. But I'm a novice in this area.

Your means is that I calculate F and P with the way that used in paper 1 and 2.
and what's your opinion about paper 5? Is have a correct way?

I don't understand your explanation about manual calculation linear and quadratic effect procedure. Please help me as you think it's right. I don't have any option except your help.

Thanks again.

#### Miner

##### Forum Moderator
Staff member
The problem is that none of these papers actually show or state how they did the analysis. I can only speculate on what they did based on the degrees of freedom shown and my 30-year old recollection of how Taguchi would separate the linear and quadratic (i.e., X^2, curvature) components.

The only source that I can find that demonstrates how this was done is System of Experimental Design by Genichi Taguchi. The method is covered in Volume 1, Chapter 1, Section 1.2.

Thread starter Similar threads Forum Replies Date
Determining a tolerance value for Measuring devices in-house inspection General Measurement Device and Calibration Topics 12
Improving low p-value Statistical Analysis Tools, Techniques and SPC 13
Registrars with VAR (Value Added Reseller) experience Registrars and Notified Bodies 8
Best approach to get a real value as average? Statistical Analysis Tools, Techniques and SPC 6
Missing value of Uncertainty B Measurement Uncertainty (MU) 10
Calibration certificate content - Average Value and True Value ISO 17025 related Discussions 6
In BAC5300 we have machining mismatch allowed is 3tau, what is the value of tau? Document Control Systems, Procedures, Forms and Templates 1
Change value of target during a batch Capability, Accuracy and Stability - Processes, Machines, etc. 0
Acceptance p-value for linearity and bias analysis in minitab results Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 0
Torque Value for Different types of Fasteners (Socket Head, Button Head, CSK) Manufacturing and Related Processes 2
IATF 16949 - 8.5.6.1.1 Providing a list of process controls: Does this requirement add value to QMS? IATF 16949 - Automotive Quality Systems Standard 4
Cycle times, value stream mapping, inventory, average values? Lean in Manufacturing and Service Industries 1
What are the criteria for setting a target KPI value against a quality objective? Benchmarking 7
S Adding Value prior to signing EASA Form 1 EASA and JAA Aviation Standards and Requirements 5
M Creating a Plant Level Value Stream Map Process Maps, Process Mapping and Turtle Diagrams 1
A IMDS - Changing the Locked Weight Value RoHS, REACH, ELV, IMDS and Restricted Substances 1
T Value Chain Map for Food Services Industry Service Industry Specific Topics 1
O P-Value less than 0.05. but everything else in control Statistical Analysis Tools, Techniques and SPC 19
P x I = Value interpretation for residual risk? ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 1
O CPK with a P value less than 0.005 Manufacturing and Related Processes 8
What degrees of freedom means in uncertainty budget and how do I set the value Measurement Uncertainty (MU) 2
Q Really do they add value (Vision, Mission, Values)? ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 1
What is the exact Temperature Coefficient Value to be set on a Conductivity Meter? General Measurement Device and Calibration Topics 2
M Value Stream Mapping Calculations Process Maps, Process Mapping and Turtle Diagrams 5
L How to interpret the average R bar Value shown in the R Chart Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 2
Non Value Added Corrective Actions IATF 16949 - Automotive Quality Systems Standard 15
R How To Calculate & Print CDF and Lower Bound CDF value for some t(time) with Minitab? Using Minitab Software 1
P Purpose of calculating Uncertainty value in calibration study Measurement Uncertainty (MU) 5
J Agenda of Value Stream Mapping workshop required Quality Tools, Improvement and Analysis 1
What is the value of documenting in-process rework for easily-detectable issues? Quality Manager and Management Related Issues 4
VSM - Value Stream Mapping (catheter manufacturing unit) Customer Complaints 10
W Quality for value adding or certification? ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 23
T Cpk for 0 as Ideal Value Statistical Analysis Tools, Techniques and SPC 1
Internal Audit Value - What is the point of conducting internal audits to a checklist Internal Auditing 40
L 5 minutes only for this Survey on the Value of PDCA and Your EMS Miscellaneous Environmental Standards and EMS Related Discussions 1
M How calculate P value for Linearity and Bias using Excel Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 8
S Value of Ppk or Cpk when targeting thinner material Statistical Analysis Tools, Techniques and SPC 4
B How to validate Microsoft Excel Spreadsheet Calculations for the Cpk value Capability, Accuracy and Stability - Processes, Machines, etc. 9
Analysis of 'Value Added' System & Process Steps - Inspection Pharmaceuticals (21 CFR Part 210, 21 CFR Part 211 and related Regulations) 2
P Which ISO 13485 clause(es) are applicable for Value Proposition Creation ISO 13485:2016 - Medical Device Quality Management Systems 1
R The Value and Effectiveness of In Process Inspection Quality Manager and Management Related Issues 17
D Value-Added Analysis - Staff (Employee) Satisfaction Quality Tools, Improvement and Analysis 11
T ISO Auditor Training - What online training is actually value added? ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 13
M Specific Capability case - Target Value is same as the Lower Limit Capability, Accuracy and Stability - Processes, Machines, etc. 9
S GR&R for an "R" value instrument installed on my 10K Horizontal Tester Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 5
S Value Stream Mapping for a Product Family Lean in Manufacturing and Service Industries 5
Are Inspection Operations Value Added? Lean in Manufacturing and Service Industries 50
How does Layout Inspection determine Reference Value? Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 1
S Labeling Medical/Health Value Claims with No Sources to Back Up EU Medical Device Regulations 1
DIN ISO 1101 - Show me the General Dimensioning Tolerance Value Other ISO and International Standards and European Regulations 3