# Implementation of AHP Methodology for the Evaluation and Selection Process of a Reverse Engineering Scanning System

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

- MetraSCAN 70 (a
_{1}); - MetraSCAN 70-R (a
_{2}); - HandyPROBE (a
_{3}); - Nikon XC65Dx(a
_{4}); - Nikon LC60Dx (a
_{5}); - Nikon LC15Dx (a
_{6}); - Metronor DUO (a
_{7}); - ATOS Triple Scan (a
_{8}).

#### 2.1. Pairwise Comparison of Expert Evaluation Criteria

- Degree of education f
_{1}; - Practical experience with RE systems f
_{2}; - Theoretical knowledge in the field of quality inspection f
_{3}; - Economic knowledge f
_{4}.

_{1}.

#### 2.2. Pairwise Comparison of Experts According to Individual Criteria

_{1}) and economist (a

_{3}) have a university degree. Technician (a

_{2}) has secondary technical education. The individual comparisons are listed in Table 5.

_{Afi}) of individual matrices A

_{f}

_{i}we calculated their roots. According to Equation (4) we determined the parameters of lambda, and according to Equation (6) we assessed the consistency of the matrices, as follows:

## 3. Results

## 4. Discussion

Algorithm 1. MATLAB program |

[x,xn] = ahp(A), Where x is a proprietary vector of matrix A, xn is a proprietary vector of matrix A (x/sum x) and alfa is a level of consistence function [x,xn] = ahp(A,alfa) % Check that the matrix is entered correctly for i = 1:size(A,1) for j = 1:size(A,1) if i~= j if A(j,i) == A(i,j) & A(j,i) ~= 1; str=[‘The matrix is misspelled: element a_’… ,num2str(i),num2str(j),’ ‘,’=‘,’ ‘… ,’a_’,num2str(j),num2str(i)]; disp(str) return; elseif A(j,i) ~= 1/A(i,j) str = [‘The matrix is misspelled: element a_’… ,num2str(i),num2str(j),’ ‘,’a’,’ ‘… ,’a_’,num2str(j),num2str(i),’ ‘,… ‘ not in the desired shape a_ij = 1/a_ji’]; disp(str) return; end end end % Check of matrix A consistency. if eigs(A,1)<= size(A,1) + alfa*(1.7699*size(A) − 4.3513) % Calculation of eigenvector of matrix (x) and the eigenvalue vector % matrix (xn) according formula (A − lambda*J)x = 0 x = (A − eigs(A,1)*eye(size(A,1))); x = [1;inv(x(2:size(A),2:size(A)))*(−A(2:size(A),1))]; xn = x/sum(x); else str = [‘Matrix on level alfa=‘,num2str(alfa),’ ‘,’ is not consistent’ ]; disp(str) end |

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Parameter | MetraSCAN 70 | MetraSCAN 70R | HandyPROBE |
---|---|---|---|

Price (EUR) | 67,350 | 130,000 | 38,500 |

Weight (kg) | 1.85 kg | 1.85 kg | 0.45 kg |

Dimensions (mm) | 282 × 250 × 282 | 204 × 159 × 97 | |

Measuring speed (pts/s) | 36,000 | 30 | |

Volumetric accuracy (mm) | 0.075 | 0.022 | |

Spacing distance (mm) | 152 | N/A | |

Depth/width FOV (Field of View) (mm) | 50/2 × 70 | N/A | |

Operating humidity range (%) | 10–90% | 10–90% | |

Working temperature (°C) | 15–40 | 15–40 °C |

Parameter | XC65Dx | LC60Dx | LC15Dx |
---|---|---|---|

Price (EUR) | 97,130 | 65,110 | 64,850 |

Weight (kg) | 0.44 | 0.39 | 0.37 |

Dimensions (mm) | 155 × 86 × 142 | N/A | 100 × 104 × 58 |

Measuring speed (pts/s) | 75,000 | 75,000 | 70,000 |

Accuracy (mm) | 0.012 | 0.009 | 0.006 |

Spacing distance (mm) | 75 | 95 | 60 |

Depth/width FOV (mm) | 3 × 65/3 × 65 | 60/- | 15/- |

Operating humidity range (%) | 10–90% | 10–90% | 10–90% |

Working temperature (°C) | 10–40 °C | 10–40 °C | 10–40 °C |

Parameter | Metronor DUO | ATOS III Triple Scan |
---|---|---|

Price (EUR) | 41,700 | 98,540 |

Weight (kg) | 0.52 | 7.5 |

Dimensions (mm) | 500 × 200 × 30 | 155 × 86 × 142 |

Measuring speed (pts/s) | 35 | 75,000 |

Accuracy (mm) | 0.025 | 0.01 |

Spacing distance (mm) | 1500–15,000 | 490–2000 |

Depth FOV (Field of View) (mm) | 230 | |

Width FOV (Field of View) (mm) | 250 × 250 | |

Working temperature (°C) | 10–45 °C | 5–40 °C |

Operating humidity range (%) | <90% | 10–90% |

Criterion | f_{1} | f_{2} | f_{3} | f_{4} |
---|---|---|---|---|

f_{1} | 1 | 1/9 | 1/8 | 1/5 |

f_{2} | 9 | 1 | 3 | 5 |

f_{3} | 8 | 1/3 | 1 | 3 |

f_{4} | 5 | 1/5 | 1/3 | 1 |

Kr. | f_{1} | f_{2} | f_{3} | f_{4} | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

a_{1} | a_{2} | a_{3} | a_{4} | a_{1} | a_{2} | a_{3} | a_{4} | a_{1} | a_{2} | a_{3} | a_{4} | a_{1} | a_{2} | a_{3} | a_{4} | |

a_{1} | 1 | 3 | 1 | 3 | 1 | 2 | 9 | 6 | 1 | 3 | 9 | 5 | 1 | 2 | 1/7 | 3 |

a_{2} | 1/3 | 1 | 1/4 | 1/3 | 1/2 | 1 | 9 | 6 | 1/3 | 1 | 9 | 4 | 1/2 | 1 | 1/8 | 2 |

a_{3} | 1 | 4 | 1 | 4 | 1/9 | 1/9 | 1 | 1/4 | 1/9 | 1/9 | 1 | 1/5 | 7 | 8 | 1 | 8 |

a_{4} | 1/3 | 3 | 1/4 | 1 | 1/6 | 1/6 | 4 | 1 | 1/5 | 1/4 | 5 | 1 | 1/3 | 1/2 | 1/8 | 1 |

Criterion | Weight | Quality Manager | Technician | Economist | Engineer |
---|---|---|---|---|---|

Education degree | 0.0383 | 0.3535 | 0.0855 | 0.4103 | 0.1507 |

Practical experiences with RE systems | 0.5635 | 0.5083 | 0.3612 | 0.0376 | 0.0928 |

Theoretical knowledge from quality inspection | 0.2736 | 0.5525 | 0.298 | 0.0362 | 0.1133 |

Economic knowledge | 0.1246 | 0.1458 | 0.0892 | 0.7067 | 0.0583 |

Weighted sum | 0.4693 | 0.2995 | 0.1349 | 0.0963 |

Expert | Weight | f_{1} | f_{2} | f_{3} | f_{4} | f_{5} | f_{6} | f_{7} |
---|---|---|---|---|---|---|---|---|

Quality manager | 0.4693 | 0.0228 | 0.4286 | 0.1083 | 0.1293 | 0.1582 | 0.1170 | 0.0358 |

Technician | 0.2995 | 0.0232 | 0.4391 | 0.1958 | 0.0718 | 0.0597 | 0.1299 | 0.0805 |

Economist | 0.1349 | 0.3375 | 0.2646 | 0.0352 | 0.0667 | 0.0887 | 0.1499 | 0.0574 |

Engineer | 0.0963 | 0.0245 | 0.4574 | 0.1734 | 0.0943 | 0.0806 | 0.1170 | 0.0528 |

Weighted sum: | 0.0655 | 0.4124 | 0.1309 | 0.1003 | 0.1118 | 0.1253 | 0.0537 |

Criterion | Weight | a_{1} | a_{2} | a_{3} | a_{4} | a_{5} | a_{6} | a_{7} | a_{8} |
---|---|---|---|---|---|---|---|---|---|

Price (f_{1}) | 0.0655 | 0.0894 | 0.0204 | 0.2930 | 0.0497 | 0.1252 | 0.1252 | 0.2473 | 0.0497 |

Accuracy (f_{2}) | 0.4124 | 0.0266 | 0.0198 | 0.0526 | 0.1292 | 0.2216 | 0.3488 | 0.0640 | 0.1375 |

Portability (f_{3}) | 0.1309 | 0.2288 | 0.0326 | 0.3073 | 0.0310 | 0.0310 | 0.0310 | 0.3073 | 0.0310 |

Sensed area (f_{4}) | 0.1003 | 0.1163 | 0.1163 | 0.0156 | 0.2009 | 0.0910 | 0.0584 | 0.0157 | 0.3859 |

Depth of field (f_{5}) | 0.1118 | 0.0339 | 0.0339 | 0.2928 | 0.0516 | 0.0699 | 0.0204 | 0.2784 | 0.2190 |

Sensing rate (f_{6}) | 0.1253 | 0.1305 | 0.1174 | 0.0175 | 0.1714 | 0.0800 | 0.0567 | 0.0165 | 0.4100 |

Possibility to move with sensed object & ease of implement. (f_{7}) | 0.0537 | 0.2082 | 0.2082 | 0.2082 | 0.0334 | 0.0334 | 0.0334 | 0.2416 | 0.0334 |

Weighted sum: | 0.0898 | 0.0551 | 0.1288 | 0.1098 | 0.1324 | 0.1731 | 0.1306 | 0.1804 | |

Order: | 7 | 8 | 5 | 6 | 3 | 2 | 4 | 1 |

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**MDPI and ACS Style**

Beniak, J.; Šooš, Ľ.; Križan, P.; Matúš, M.
Implementation of AHP Methodology for the Evaluation and Selection Process of a Reverse Engineering Scanning System. *Appl. Sci.* **2021**, *11*, 12050.
https://doi.org/10.3390/app112412050

**AMA Style**

Beniak J, Šooš Ľ, Križan P, Matúš M.
Implementation of AHP Methodology for the Evaluation and Selection Process of a Reverse Engineering Scanning System. *Applied Sciences*. 2021; 11(24):12050.
https://doi.org/10.3390/app112412050

**Chicago/Turabian Style**

Beniak, Juraj, Ľubomír Šooš, Peter Križan, and Miloš Matúš.
2021. "Implementation of AHP Methodology for the Evaluation and Selection Process of a Reverse Engineering Scanning System" *Applied Sciences* 11, no. 24: 12050.
https://doi.org/10.3390/app112412050