# Reliable Method to Detect Alloy Soldering Fractures under Accelerated Life Test

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## Abstract

**:**

## 1. Introduction

#### Objective

## 2. Soldering Alloy

## 3. Accelerated Life Test (ALT)

## 4. Reliability Model

- ${\lambda}_{h}\left(t\right)$ = Failure rate
- ${f}_{h}\left(t\right)$ = Instantaneous failure speed function

- $TF$ = Failure rate.
- ${n}_{avg}$ = Average of units examined.

- $\beta <1$ is the risk rate decrease.
- $\beta =1$ is the remaining life of a stable system, and the failures are random.
- $\beta >1$ the risk rate increase indicating that the product is in the wear region.

## 5. Methodology

^{®}[24] made the corresponding calculations of the statistical analysis and the experiments design for calculating the accelerated factor of the temperature test. Arrhenius’s equation was used (Equation (4)). This mathematical equation allows escalation of the time of the test with the time of use [12].

- ${A}_{f}$ = pre-exponential factor or frequency factor.
- k = kinetic constant Boltzmann’s constant (physical constant that relates absolute temperature and energy).
- ${E}_{a}$ = activation energy.
- ${T}_{1}$ = Field-use temperature
- ${T}_{2}$ = Accelerated test temperature.

## 6. Results

- $GL$ = Degrees of freedom. Number of values that can be assigned arbitrarily, before the rest of the variables automatically take a value.
- $SC$ = Sum of squares, represents a measure of variation or deviation with respect to the mean.
- $MC$ = Square Medium, are used to determine if the terms of a model are significant.
- ${P}_{value}$ = probability corresponding to the test statistic.
- ${F}_{value}$ = is a value you get when you run an ANOVA test or a regression analysis to find out if the means between two populations are significantly different.
- $Adjust$ = Adjusted Value, indicates which comparisons between the levels of the factors within a family of comparisons are significantly different.

- S = Standard deviation.
- ${R}^{2}$ = Coefficient of determination.
- ${R}^{2}\left(adjust\right)$ = Adjusted coefficient of determination. Is the percentage of variation in the response variable that is explained by its relation to one or predictor variables, adjusted for the number of predictors in the model.
- ${R}^{2}\left(pred\right)$ = Predetermined coefficient of determination. Adjustments in model looking for an approach in the desired values.

- $Effect$ = There is a main effect when different levels of a factor affect the response differently.
- $Coef$ = Coefficient of determination.
- $SECoef$ = The standard error of the coefficient estimates the variability between the coefficient estimates that would be obtained if the samples were taken from the same population repeatedly. The calculation assumes that the size of the sample and the coefficients to be estimated would remain the same if the sample were taken repeatedly.
- ${T}_{Value}$ = Measure the relationship between the coefficient and its standard error.
- ${P}_{Value}$ = probability corresponding to the test statistic.
- $VIF$ = The variance inflation factor indicates how much the variance of a coefficient is inflated due to the correlations among the predictors in the model. Use the VIF to describe how much multicollinearity (which is correlation between predictors) exists in a regression analysis. Multicollinearity is problematic because it can increase the variance of the regression coefficients, making it difficult to evaluate the individual impact that each of the correlated predictors has on the response.

## 7. Discussion and Conclusions

#### 7.1. Discussion

- The observed degradation (change) is not reversible when tension is removed.
- There is a unique or dominant degradation process that can be studied (POF).
- Any degradation before the start of the accelerated test.

- The determination of the probability of failure, the product under conditions of use, means low life.
- Conditions of use and projected returns and guarantees.
- Costs can also be used to help in the detection of faults and process improvement
- Carrying out risk assessments, design, comparisons, etc.

- Application of Planned Statistical Techniques to expand the designer’s ability to draw conclusions from an ALT;
- Study of strengths and weaknesses in each ALT model presented and cross this study with current practices to determine the best test strategies;
- Reliability management practices, with definition of sequence, importance, allocation of resources and impact of ALT procedures in the product development cycle.

#### 7.2. Conclusions

## 8. Concluding Remarks

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Glossary

ALT | Accelerated Life Test. |

MTBF | Mean time between failure. |

TF | Failure rate. |

${A}_{f}$ | Pre-exponential factor or frequency factor. |

${E}_{a}$ | Activation energy. |

${f}_{h}\left(t\right)$ | Instantaneous failure speed function |

${l}_{h}\left(t\right)$ | Failure rate |

${R}_{h}\left(t\right)$ | Reliability function or survival function. |

${\lambda}_{h}t$ | Failure rate. |

k | Boltzmann’s constant (physical constant that relates absolute temperature and energy. Commonly for an LED 0.7 V is required). |

${T}_{1}$ | Field-use temperature |

${T}_{2}$ | Accelerated test temperature. |

$\beta $ | Weibull distribution form parameter |

$\eta $ | Scale parameter or Weibull distribution life parameter |

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**Figure 1.**Electronic component assembly. Type Diode-LED. (

**a**) shows SnPb Alloy. (

**b**) shows SnAg Alloy.

**Figure 2.**SEM image of biphasic composition of the tin and lead alloy taken at 2000×. (

**a**) corresponds SnPb alloy. (

**b**) corresponds SnAg alloy. (

**a**) shows a dentric structure Sn base, secondary phase flat with microparticles precipitated in the dentric surface of the base of Pb. Spherical particles are observed.

**Figure 3.**Weibull distribution. Adapted from the theories proposed by Ruiz et al. [10].

No. | Solder Alloy | Path | Temperature | Pret | Vibration |
---|---|---|---|---|---|

3 | −1 | −1 | 1 | −1 | −1 |

4 | −1 | 1 | 1 | 1 | −1 |

5 | −1 | 1 | −1 | −1 | −1 |

8 | 1 | −1 | 1 | 1 | −1 |

11 | −1 | −1 | −1 | −1 | 1 |

12 | −1 | 1 | −1 | 1 | 1 |

13 | 1 | 1 | 1 | −1 | −1 |

15 | −1 | 1 | 1 | −1 | 1 |

17 | −1 | −1 | −1 | 1 | −1 |

18 | −1 | −1 | 1 | 1 | 1 |

19 | −1 | −1 | −1 | −1 | 1 |

26 | 1 | −1 | −1 | 1 | 1 |

28 | 1 | −1 | −1 | −1 | −1 |

31 | 1 | 1 | 1 | 1 | 1 |

33 | 1 | 1 | −1 | −1 | 1 |

39 | 1 | −1 | 1 | −1 | 1 |

45 | 1 | 1 | −1 | 1 | −1 |

**Table 2.**Factorial Regression: Failure Time vs. Soldering Alloy, Path, Temperature, Thermal Shock, Vibration.

GL | SC Adjust. | MC Adjust. | ${\mathit{F}}_{\mathit{value}}$ | ${\mathit{P}}_{\mathit{value}}$ | |
---|---|---|---|---|---|

Source | 5 | 726,392 | 145,278 | 27.39 | 0 |

Model | 4 | 699,736 | 174,934 | 32.98 | 0 |

Lineal | 1 | 531,227 | 531,227 | 100.15 | 0 |

Soldering alloy | 1 | 21,415 | 21,415 | 4.04 | 0.07 |

Temperature | 1 | 137,972 | 137,972 | 26.01 | 0 |

Thermal Shock | 1 | 10,158 | 10,158 | 1.92 | 0.194 |

Interactions with 2 terms | 1 | 24,321 | 24,321 | 4.59 | 0.055 |

Soldering alloy*vibration | 1 | 24,321 | 24,321 | 4.59 | 0.055 |

Error | 11 | 58,346 | 5304 | ||

Lack of adjustment | 10 | 53,246 | 5325 | 1.04 | 0.649 |

Pure error | 1 | 5101 | 5101 | ||

Total | 16 | 784,738 |

S | R${}^{2}$ | R${}^{2}$-(Adjust) | R${}^{2}$(Pred) |
---|---|---|---|

72.8301 | 92.56% | 89.19% | 82.52% |

Term | Effect | Coef | SE Coef. | ${\mathit{T}}_{\mathit{value}}$ | ${\mathit{P}}_{\mathit{value}}$ | VIF | |
---|---|---|---|---|---|---|---|

Constant | 378.8 | 17.8 | 21.24 | 0 | |||

Solderingalloy | 361 | 180.5 | 18 | 10.01 | 0 | 1.04 | |

Path | −72.5 | −36.2 | 18 | −2.01 | 0.07 | 1.04 | |

Temperature | −184 | −92 | 18 | −5.1 | 0 | 1.04 | |

ThermalShock | −51.5 | −25.7 | 18.6 | −1.38 | 0.194 | 1.1 | |

Solderalloy-vibration | −76.4 | −38.2 | 17.8 | −2.14 | 0.055 | 1.02 |

Soldering Alloy | Parameters |
---|---|

SnPb | Beta: 2.2923 |

SnPb | Eta: 319.4363 |

SnPb | Failure rate: 0.5364 |

SnPb | Mean Life: 282.9822 |

SnAgCu | Beta: 7.7790 |

SnAgCu | Eta: 665.2968 |

SnAgCu | Failure rate: 5.4508 ×${10}^{5}$ |

SnAgCu | Mean life: 625.6784 |

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## Share and Cite

**MDPI and ACS Style**

Zamora-Antuñano, M.A.; Mendoza-Herbert, O.; Culebro-Pérez, M.; Rodríguez-Morales, A.; Rodríguez-Reséndiz, J.; Gonzalez-Duran, J.E.E.; Mendez-Lozano, N.; Gonzalez-Gutierrez, C.A.
Reliable Method to Detect Alloy Soldering Fractures under Accelerated Life Test. *Appl. Sci.* **2019**, *9*, 3208.
https://doi.org/10.3390/app9163208

**AMA Style**

Zamora-Antuñano MA, Mendoza-Herbert O, Culebro-Pérez M, Rodríguez-Morales A, Rodríguez-Reséndiz J, Gonzalez-Duran JEE, Mendez-Lozano N, Gonzalez-Gutierrez CA.
Reliable Method to Detect Alloy Soldering Fractures under Accelerated Life Test. *Applied Sciences*. 2019; 9(16):3208.
https://doi.org/10.3390/app9163208

**Chicago/Turabian Style**

Zamora-Antuñano, M.A., O. Mendoza-Herbert, M. Culebro-Pérez, A. Rodríguez-Morales, Juvenal Rodríguez-Reséndiz, J.E.E. Gonzalez-Duran, N. Mendez-Lozano, and C.A. Gonzalez-Gutierrez.
2019. "Reliable Method to Detect Alloy Soldering Fractures under Accelerated Life Test" *Applied Sciences* 9, no. 16: 3208.
https://doi.org/10.3390/app9163208