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 Five Easy Steps to Solving Production Problems (This simple approach is for solution of most desirable condition with 4, 5, or 6 two-level 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), a1 b1, etc. = Levels of factors (descriptive)
R1,R2, etc. = Test results (Single or average of multiple samples, numerical data)
A1 , B1, 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, a1, b2, R1, R2, etc. are for your situation before proceeding with the application.

##### Step 2: Carry out eight tests as described below in random order and note results (R1, R2, etc)

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
Test 2: [ a1 b1 c2 d2 e2 f2 ]     Test result R2 = 12
Test 3: [ a1 b2 c1 d2 e2 f1 ]     Test result R3 = 10
Test 4: [ a1 b2 c2 d1 e1 f2 ]     Test result R4 = 11
Test 5: [ a2 b1 c1 d2 e1 f2 ]     Test result R5 = 15
Test 6: [ a2 b1 c2 d1 e2 f1 ]     Test result R6 = 13
Test 7: [ a2 b2 c1 d1 e2 f2 ]     Test result R7 = 9
Test 8: [ a2 b2 c2 d2 e1 f1 ]     Test result R8 = 14

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

A1 = R1 + R2 + R3 + R4         A2 = R5 + R6 + R7 + R8
B1 = R1 + R2 + R5 + R6         B2 = R3 + R4 + R7 + R8
C1 = R1 + R3 + R5 + R7         C2 = R2 + R4 + R6 + R8
D1 = R1 + R4 + R6 + R7         D2 = R2 + R3 + R5 + R8
E1 = R1 + R4 + R5 + R8           E2 = R2 + R3 + R6 + R7
F1 = R1 + R3 + R6 + R8            F2 = R2 + R4 + R5 + R7

Calculation check: Totals of all factor levels must equal to the total of all results.

[ Total of all results (T) = R1 + R2 + R3 + R4 + R5 +R6 + R7 + R8 Optional calculation]

##### Step 4: Complete columns II, III, and one of columns IV and V as applicable.

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 factor-level combination)

 IFactor Descriptions IIEffect of Level  1 IIIEffect of   Level  2 IV   Most Desirable Complete this col. when BIGGER is desired Condition (solution) VComplete this col. when SMALLER is desired A A1 = A2 = *Select factor level ** Select factor level B B1 = B2 = C C1 = C2 = D D1 = D2 = E E1 = E2 = F F1 = F2 =

<* Show level a2 (descriptive) if A2>A1 or a1 (descriptive) if A1>A2
** Show level a2 (descriptive) if A2<A1 or a1 (descriptive) if A1<A2

##### Step 5: Verify solution by running a test in the factor level condition described by column IV or V as  applicable.

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 L-8 Orthogonal Array forwarded by Dr. Genechi Taguchi as shown below. Notice that SIX 2-level 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          R1 = 8 units
(Results of your experiments will vary)
2          1   1  1     2   2  2   2          R2 = 12
3          1   2  2     1   1  2   2          R3 = 10
4          1   2  2     2   2  1   1          R4 = 11
5          2   1  2     1   2  1   2          R5 = 15
6          2   1  2     2   1  2   1          R6 = 13
7          2   2  1     1   2  2   1          R7 = 9
8          2   1  2     1   1  2    2          R8 = 14

EXAMPLE CALCULATIONS  (automatically done by the DOS software EASY5STP.EXE)

Based on the experimental results shown above, the factor effects become:.

A1 = R1 + R2 + R3 + R4 = 8 + 12 + 10 + 11    = 41
A2 = R5 + R6 + R7 + R8 = 15 + 13 + 9 + 14    = 51
B1 = R1 + R2 + R5 + R6 = 8 + 12 + 15 + 13    = 48
B2 = R3 + R4 + R7 + R8 = 10 + 11 + 9 + 14    = 44
C1 = R1 + R3 + R5 + R7 = 8 + 10 + 15 + 9     = 42
C2 = R2 + R4 + R6 + R8 = 12 + 11 + 13 +14   = 50
D1 = R1 + R4 + R6 + R7 = 8 + 11 + 13 + 9     = 41
D2 = R2 + R3 + R5 + R8 = 12 + 10 + 15 +14  = 51
E1 = R1 + R4 + R5 + R8 = 8 + 11 + 15 + 14   = 48
E2 = R2 + R3 + R6 + R7 = 12 + 10 + 13 + 9   = 44
F1 = R1 + R3 + R6 + R8 = 8 + 10 + 13 + 14   = 45
F2 = R2 + R4 + R5 + R7 = 12 + 11 + 15 + 9   = 47

Solution Table (Most desirable factor-level combination)

 IFactor Descriptions IIEffect of Level 1 IIIEffect of  Level 2 IV         Most Desirable Complete this col. when BIGGER is desired Condition (solution)   V  Complete this col. when SMALLER is desired A A1 = 41 A2 = 51 *Select factor levela2 (since A2 >A1 ) ** Select factor levela1 (since A1 < A2 ) B B1 = 48 B2 = 44 b1 b2 C C1 = 42 C2 = 50 c2 c1 D D1 = 41 D2 = 51 d2 d1 E E1 = 48 E2 = 44 e1 e2 F F1 = 45 F2 = 47 f2 f1

*    Show level a2 (descriptive) if A2>A1 or a1 (descriptive) if A1>A2
** Show level a2 (descriptive) if A2<A1 or a1 (descriptive) if A1<A2

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

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, On-site seminars/workshops, Application Consulting, Structured Problem Solving, Qualitek-4 Software Applications)

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