Nutek, Inc. Quality Engineering Seminar, Software, and Consulting ( Since 1987) Site: 5 Easy Steps 
(This simple approach is for solution of most desirable condition
with 4, 5, or 6 twolevel factors only. Feel free to copy, distribute, learn, and
apply without any cost or obligations.) 
Step 1: Describe factors and their levels as shown in the following example (4, 5, or 6 factors)
The first step is to describe factors A, B, C, etc. and their corresponding two levels for each factors. Lower case notations a1, a2, b1, b2, etc. are used for the levels. (An example descriptions shown below)
Factors
Level
 I
Level
 II
A: Tool Type
High Carbon
(a1) Carbide Tip (a2)
B: Cutting Speed 1500 rpm (b1)
2000 rpm (b2)
C: Feed Rate
2 mm/sec.
(c1)
5 mm/sec. (c2)
D: Type of Coolant Supplier 1(d1)
Supplier
2 (d2)
E: Part Support Absent
(e1)
Present
(e2)
F: Tool Holder Current Design (f1) New Design (f2)
Notations:
A, B, C, etc = Factor descriptions (descriptive), a_{1} b_{1,}
etc. = Levels of factors (descriptive)
R_{1,}R_{2,} etc. = Test results (Single or average of multiple samples,
numerical data)
A_{1} , B_{1,} etc. = Factor level effects (numeric)
The Factors and levels descriptions shown above are to be used as examples only. Descriptions applicable to your project will be different. You will need to define what A, B, C, a_{1}, b_{2}, R_{1}, R_{2}, etc. are for your situation before proceeding with the application.
The descriptions of the eight experiments (Tests) are described using the level notations. The actual test description will depend on your definitions. The results (or average of results of many samples) of the test samples are designated by notation R with corresponding subscripts. The numeric values, 8, 12, 10, etc. are shown as example values.
Test 1: [ a1 b1 c1 d1 e1 f1 ] Test result R1 = 8
Step 3: Calculate the Factor level effects for all
factors
Upper case letters with subscripts 1 and 2 ( A1, A2, B1, B2, etc.)
are used to denote numeric values of the average effects calculated using the test
results. For each factor two effects are calculated. These calculations are automatically
done by the program EASY5STP.EXE. You can freely download this software by just clicking
the descriptive line on top of this page.
Factor level effects
A_{1} = R_{1} + R_{2} + R_{3} + R_{4}
A_{2} = R_{5} + R_{6} +
R_{7} + R_{8}
B_{1} = R_{1} + R_{2} + R_{5} + R_{6}
B_{2} = R_{3} + R_{4} +
R_{7} + R_{8}
C_{1} = R_{1} + R_{3} + R_{5} + R_{7}
C_{2} = R_{2} + R_{4} +
R_{6} + R_{8}
D_{1} = R_{1} + R_{4} + R_{6} + R_{7}
D_{2} = R_{2} + R_{3} +
R_{5} + R_{8}
E_{1} = R_{1} + R_{4} + R_{5} + R_{8
} E_{2} = R_{2} + R_{3}
+ R_{6} + R_{7}
F_{1} = R_{1} + R_{3} + R_{6} + R_{8}
_{ }F_{2} = R_{2} + R_{4}
+ R_{5} + R_{7}
Calculation check: Totals of all factor levels must equal to the total of all results.
[ Total of all results (T) = R_{1} + R_{2} + R_{3} + R_{4} + R_{5} +R_{6} + R_{7} + R_{8} Optional calculation]
The table below is completed by using the calculations carried out above. No new calculations are needed. Users already familiar with the technique of determining the most desirable condition may skip this step in favor of establishing it by comparing the two factor average effects.
Solution Table (Most desirable factorlevel combination)
I Factor Descriptions 
II Effect of Level 1 
III Effect of Level 2 
IV
Most Desirable Complete this col. when BIGGER is desired 
Condition (solution)
V Complete this col. when SMALLER is desired 
A  A_{1} =  A_{2} =  *Select factor level  ** Select factor level

B  B_{1} =  B_{2} =  
C  C_{1} =  C_{2} =  
D  D_{1} =  D_{2} =  
E  E_{1} =  E_{2} =  
F  F_{1} =  F_{2} = 
<* Show level a_{2} (descriptive) if A_{2}>A_{1}
or a_{1} (descriptive) if A_{1}>A_{2}
** Show level a_{2} (descriptive) if A_{2}<A_{1} or a_{1}
(descriptive) if A_{1}<A_{2}
The most desirable condition identified must always be verified by running a few samples in the condition identified (column IV or V). The probability that the desirable condition will produce better performance than obtained before is over 95%.
Reference: Experiment design used for the solution above is accomplished by using using L8 Orthogonal Array forwarded by Dr. Genechi Taguchi as shown below. Notice that SIX 2level factors A, B, C, D, E, and F are assigned to columns 1, 2, 4, 7, 6, and 5 respectively. The third column of the array is left unused.
Test# A
B C F E
D Results
(assume Bigger)
1 1 1 1
1 1 1 1
R_{1} = 8 units (Results of your experiments will vary)
2 1 1 1
2 2 2 2
R_{2} = 12
3 1 2 2
1 1 2 2
R_{3} = 10
5 2 1 2
1 2 1 2
R_{5} = 15
6 2 1 2
2 1 2 1
R_{6} = 13
7 2 2 1
1 2 2 1
R_{7} = 9
EXAMPLE CALCULATIONS (automatically done by the DOS software EASY5STP.EXE)
Based on the experimental results shown above, the factor effects become:.
A_{1} = R_{1} + R_{2}
+ R_{3} + R_{4} = 8 + 12 + 10 + 11 = 41
A_{2} = R_{5} + R_{6} + R_{7} + R_{8} = 15 + 13 +
9 + 14 = 51
B_{1} = R_{1} + R_{2} + R_{5} + R_{6} = 8 + 12 +
15 + 13 = 48
B_{2} = R_{3} + R_{4} + R_{7} + R_{8} = 10 + 11 +
9 + 14 = 44
C_{1} = R_{1} + R_{3} + R_{5} + R_{7} = 8 + 10 +
15 + 9 = 42
C_{2} = R_{2} + R_{4} + R_{6} + R_{8 }= 12 + 11 +
13 +14 = 50
D_{1} = R_{1} + R_{4} + R_{6} + R_{7} = 8 + 11 +
13 + 9 = 41
D_{2} = R_{2} + R_{3} + R_{5} + R_{8} = 12 + 10 +
15 +14 = 51
E_{1} = R_{1} + R_{4} + R_{5} + R_{8 }= 8 + 11 +
15 + 14 = 48
E_{2} = R_{2} + R_{3} + R_{6} + R_{7} = 12 + 10 +
13 + 9 = 44
F_{1} = R_{1} + R_{3} + R_{6} + R_{8 }= 8 + 10 +
13 + 14 = 45
F_{2} = R_{2} + R_{4} + R_{5} + R_{7 }= 12 + 11 +
15 + 9 = 47
Solution Table (Most desirable factorlevel combination)
I Factor Descriptions 
II Effect of Level 1 
III Effect of Level 2 
IV
Most Desirable Complete this col. when BIGGER is desired 
Condition (solution) V Complete this col. when SMALLER is desired 
A  A_{1} = 41  A_{2} = 51  *Select factor level a_{2} (since A_{2} >A_{1} ) 
** Select factor level a_{1 }(since A_{1} < A_{2} ) 
B  B_{1} = 48  B_{2} = 44  b_{1}  b_{2} 
C  C_{1} = 42  C_{2} = 50  c_{2}  c_{1} 
D  D_{1} = 41  D_{2} = 51  d_{2}  d_{1} 
E  E_{1} = 48  E_{2} = 44  e_{1}  e_{2} 
F  F_{1} = 45  F_{2} = 47  f_{2}  f_{1} 
* Show level a_{2} (descriptive)
if A_{2}>A_{1} or a_{1} (descriptive) if A_{1}>A_{2}
** Show level a_{2} (descriptive) if A_{2}<A_{1} or a_{1}
(descriptive) if A_{1}<A_{2}
For BIGGER results, the most desirable condition is (col. IV): a2 b1 c2 d2 e1 f2
That is,
(a2) Carbide Tip – Tool, (b1) 1500 rpm, (c2) 5 mm/sec – Feed Rate, (d2) Supplier 2, (e1) Absent – Part Support and (f2) New Design – Tool Holder
FREE Software for Five Easy Steps to Solving Production Problems. Click here to download the DOS software: easy5stp.zip zipped file (Unzip and run the .EXE file)
If you tried this technique and found good results, I would appreciate hearing from you. Should you send me your completed problem solution and if you permit me, I would like to include it in one of my publication crediting you and/or your company. Good luck.
Ranjit K. Roy, Ph.D.,P.E. (Mech. Engr.), Trainer and Consultant (Founder & President of Nutek, Onsite seminars/workshops, Application Consulting, Structured Problem Solving, Qualitek4 Software Applications)
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