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The search for variables allows us to identify the factor causing the problem.

## Introduction

The search for variables allows us to identify the factor causing the problem. This tool is used when we have more than 5 to 20 variables to study.

## Step 1

The principle is based on the comparison between the best cases and the less good cases. The objective of this first step is to validate that among the factors chosen, there is the Red X.

1. List the variables that have been asleep-and-already were filtered by the previous steps.
2. Classify them in descending order of influence.
3. Assign 2 levels for each of the variables: the first, which is noted 1, being the one that generates a quality product, the second one, which is noted-1, which generates a product with a defect (within reasonable limits).
4. Do 2 tests with all levels at 1, and 2 tries with their position at-1. If the ratio of 5 is reached or exceeded between the results obtained, then the red X is considered to be among the factors chosen. If not, 3 alternatives:
• If it is thought that one has the right factors but that the levels have been reversed, do the B vs. C test on each suspicious factor and validate the hypothesis.
• If we think that the wrong factors have been chosen, we take it again in step 1 with other factors.
• If doubt persists, make a complete experience plan.

## Step 2

At this point, we know that among the factors chosen, there is the Red X. Remains to be able to identify it.

1. Experiment with factor A, level-1 and the rest of the factors at level 1:

• If there is no change in relation to the best result of step 4, then A has no influence.
• If there is a partial change, from the best result to the least good, then a is not the only influential factor.
• If the result is inverse with best at least good result of step 4 then A is the red X.

2. Perform a second Test with a at level 1 and other factors at level-1:

• If there is no change in the worst results of the previous phase, then factor A is confirmed as irrelevant.
• If there is a partial change in the worst results compared to the previous phase, a is confirmed as a possible pink X.
• If there is a complete reversal, the best results of phase 1 are estimated and a is confirmed as the Red X.

3. Perform phases 1 and 2 for the rest of the factors to separate important factors from others.

4. If no factor is confirmed as Red X, but 2 or 3 pink X are identified, perform a validation experiment with the Pink X at level 1, the other factors at level-1. The results should be closer to the best results of Phase 1 step 4.

5. Perform a new experiment with the Pink X at level-1, the remainder at level 1. The results of the worst level of phase 4 of step 1 should be found roughly.

## Example

We want to study a folding operation. This shows high variability and low KPC. It is known to sometimes generate defect without us knowing why. The goal is to achieve a constant tolerance of 0.005 see less.

### Step 1, Phase 1 to 3

The 6 factors chosen in the priority order of importance are:

 Factor Level 1 Level-1 A Alignment Aligned Not aligned B Thickness Thick Thin C Hardness Hard Soft D Curvature Flat Very bent E Speed Fast Low F Hardware Maintenance Important Low

### Step 1, Phase 4

 All at 1 All at-1 Test 1 4 47 Test 2 4 61

We obtain d = (47 – 4) + (61 – 4) = 100 and D = (61 – 47) + (4 – 4) = 14

Hence: a ratio of 100/14 is greater than 7.

One of the factors of the experiment is the Red X.

### Step 2, Phase 1 to 3

Test and Results table

 Test number Combination Results Conclusion 1 A-1; … 1 3 A not important 2 A1 …-1 102 3 B-1; … 1 5 B not important 4 B1 …-1 47 5 C-1; … 1 7 C not important 6 C1 …-1 72 7 D-1; … 1 23 Pink X: Interaction with another factor 8 D1 …-1 30 9 E-1; … 1 7 ??? 10 E1 …-1 20 11 F-1; … 1 73 Probably the Red X with interaction 12 F1 …-1 18

### Step 2, Phase 4 and 5

 Validation Test 1 D-1 F-1… 1 70 Completely reverse effect Validation Test 2 D1 F1…-1 4

It is concluded that the F-factor is arguably the most influential, Red X and Factor D and Pink x. This can be confirmed and quantified their relative influences and interactions with a complete factorial experience plan. In our case, we get the following results:

 D1 D-1 F1 4,9 20,5 F-1 51,5 57,8

Calculating the effects of factors:

• D = ((20.5 + 57.8) – (4.9 + 51.5))/2 = 10.95
• F = ((51.5 + 57,8)-(4.9 + 20.5))/2 = 41,95
• DF Interaction ((20.5 + 51.5)-(4.9 + 57,8))/2 = 4.7

The F-factor is therefore the Red X since the effect is the most influential.

The D-factor is the Pink X.

The interaction is considered minor.

## Source

A. K. Bhote, K. R. Bhote (2000) – World class quality

S. Amster, K. L. Tsui (1993) – Counterexamples for the component search procedure

S. H. Steiner, R. J. MacKay (2005) – Statistical Engineering: an ALGORITM for reducing variation in manufacturing processes

K. S. Vinay, G. Praveena, H. Hamakrishna (2014) – Industrial scrap reduction using Shainin technique