# Statistical Approach to the Analysis of the Corrosive Behaviour of NiTi Alloys under the Influence of Different Seawater Environments

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Proposed Problem and Related Methodology

#### 2.3. Probabilistic Corrosion Rate Estimation Model

#### 2.4. FIB Corrosion Depth Measurement Data Analysis

## 3. Results

**H0.**

**Ha.**

**H1.**

**H2.**

#### 3.1. Results of Statistical Analysis for the NiTi-1 alloy

**H**

_{0}.**H**

_{a}.#### 3.2. Results of Statistical Analysis for the NiTi-2 Alloy

#### 3.3. Comparative Statistical Analysis of NiTi-1 and NiTi-2 Alloys’ Corrosion Behaviour in Different Seawater Environments

**H**

_{0}.**H**

_{a}.**H**

_{0}.**Ha.**

## 4. Discussion

- NiTi-1 alloy behaved similarly in conditions in which the dominant influence on the corrosion rate is air or tide, while corrosion processes were significantly more pronounced in conditions of exposure to the sea;
- NiTi-2 alloy did not show similarities from the point of view of corrosion processes in any of the three observed environments;
- NiTi-2 alloy behaved completely differently from the NiTi-1 alloy in all three environments.

- For air influence, three-parameter Log-Logistic and Burr distribution;
- For tide influence, Burr and three-parameter Log-Logistic distribution;
- For sea influence, Generalised Extreme Value and General Pareto distribution.

- The corrosion processes of the observed alloys were statistically significantly different if the samples came under the influence of air, and they also differed significantly if the corrosion processes developed under the influence of the tide;
- The largest differences in corrosion rate values occurred under the influence of the tide;
- In all three environments, the corrosion rate values of the NiTi-1 alloy were generally lower than the corrosion rate of the NiTi-2 alloy. This corrosion behaviour of the NiTi-1 alloy can be explained by its homogeneous microstructure (see Figure 2). However, more extensive studies and additional methodologies are needed to draw a definite conclusion about the corrosive behaviour quality of these two NiTi alloys. In this way, an insight into the deeper layers of the alloy would be obtained, as well as into their detailed chemical structure, which would increase both the empirical database and the statistical significance of the obtained results.

## 5. Conclusions

- NiTi-1 alloy corrodes significantly faster in conditions of exposure to the sea;
- NiTi-1 alloy shows similar corrosive behaviour under the influence of air and tide;
- The corrosive characteristics of the NiTi-2 alloy differ significantly when samples come out affected by different marine environments;
- In all marine environments, the NiTi-2 alloy behaved completely differently from the NiTi-1 alloy.

- NiTi-1, air influence, three-parameter Log-Logistic distribution;
- NiTi-2, air influence, Burr distribution;
- NiTi-1, tide influence, Burr distribution;
- NiTi-2, tide influence, three-parameter Log-Logistic distribution;
- NiTi-1, sea influence, Generalised Extreme Value distribution;
- NiTi-2, sea influence, General Pareto distribution.

- Statistically significant differences were observed when samples were exposed to air or tide;
- The largest differences in the depth of corrosive changes in NiTinol alloys occurred in samples exposed to the effects of the tides;
- The NiTi-1 alloy showed a tendency of reduced corrosive processes in relation to the values of corrosion depth in the NiTi-2 alloy in all three observed seawater environments.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Review of the most prominent models of corrosion loss [35].

**Figure 4.**Presentation of corresponding FIB measuring locations: (

**a**) NiTi-1, (

**b**) NiTi-2; Micro-view of an FIB cut: (

**c**) NiTi-1, (

**d**) NiTi-2; Corrosion depth values after 1 year in the sea measured by FIB: (

**e**) NiTi-1, (

**f**) NiTi-2; Presentation the places where the EDS analyses were performed: (

**g**) NiTi-1, (

**h**) NiTi-2.

**Figure 11.**Empirical PDF and the three best fitted three-parameter distributions of the NiTi-1 alloy corrosion rate in the air environment.

**Figure 12.**Empirical PDF and the three best fitted three-parameter distributions of NiTi-1 alloy corrosion rate in a tide environment.

**Figure 13.**Empirical CDF and the three best fitted three-parameter distributions of the NiTi-1 alloy corrosion rate in the sea environment.

**Figure 14.**P-P plot comparing the fitted theoretical CDFs against the empirical CDF of corrosion rate in a sea environment related to the NiTi-1 alloy.

**Figure 15.**Empirical PDF and the three best fitted three-parameter distributions of the NiTi-2 alloy corrosion rate in the air environment.

**Figure 16.**Empirical PDF and the three best fitted three-parameter distributions of the NiTi-2 alloy corrosion rate in a tidal environment.

**Figure 17.**Empirical PDF and the three best fitted three-parameter distributions of NiTi-2 alloy corrosion rate in the sea environment.

**Figure 19.**PDF of the NiTi-1 and NiTi-2 alloys corrosion rate differences under air, tide and sea influences.

**Figure 20.**CDF of the NiTi-1 and NiTi-2 alloys’ corrosion rate difference under air, tide, and sea influences.

Sample | % Ni | % Ti | % Fe | |||
---|---|---|---|---|---|---|

ICP | XRF | ICP | XRF | ICP | XRF | |

NiTi-1 | 55.4 | 55.2–55.5 | 44.6 | 44.4–44.8 | / | |

NiTi-2 | 62.6 | 62.5–62.6 | 35.9 | 35.9 | 1.4 | 1.4 |

NiTi-1 Chemical composition | |||||||||
---|---|---|---|---|---|---|---|---|---|

Spectrum | In stats. | C | O | Na | Cl | Ti | Fe | Ni | Total |

Spectrum 1 | Yes | 30.87 | 24.69 | 44.44 | 100.00 | ||||

Spectrum 2 | Yes | 32.89 | 67.11 | 100.00 | |||||

Spectrum 3 | Yes | 45.49 | 54.51 | 100.00 | |||||

Spectrum 4 | Yes | 8.97 | 24.98 | 2.79 | 2.87 | 25.54 | 9.00 | 25.85 | 100.00 |

NiTi-2 Chemical composition | |||||
---|---|---|---|---|---|

Spectrum | In stats. | O | Ti | Ni | Total |

Spectrum 1 | Yes | 4.55 | 37.08 | 58.37 | 100.00 |

Spectrum 2 | Yes | 4.81 | 37.26 | 57.94 | 100.00 |

Spectrum 3 | Yes | 46.03 | 53.97 | 100.00 | |

Spectrum 4 | Yes | 44.47 | 55.53 | 100.00 |

**Table 4.**The number of measurements performed on each alloy in different seawater environments after 6, 12 and 18 months of exposure.

Alloy/Environment/Time | 6 | 12 | 18 | Total | |
---|---|---|---|---|---|

NiTi-1 | air | 15 | 10 | 30 | 55 |

tide | 20 | 20 | 26 | 66 | |

sea | 15 | 37 | 25 | 77 | |

NiTi-2 | air | 22 | 20 | 40 | 82 |

tide | 25 | 22 | 32 | 79 | |

sea | 24 | 22 | 29 | 75 | |

Total | 121 | 131 | 182 | 434 |

**Table 5.**Mean values and Standard Deviations ($\mu \pm \sigma $) of measured corrosion wear on the NiTi-1 and NiTi-2 alloys exposed to the influence of air, tide and sea, measured after 6, 12 and 18 months.

Alloy/Environment/Time | 6 | 12 | 18 | |
---|---|---|---|---|

NiTi-1 | air | 32.75 ± 4.48 | 39.00 ± 43.42 | 53.11 ± 6.96 |

tide | 31.11 ± 6.08 | 34.41 ± 8.25 | 54.50 ± 7.71 | |

sea | 48.75 ± 8.94 | 316.39 ± 200.88 | 476.17 ± 151.33 | |

NiTi-2 | air | 35.80 ± 4.20 | 36.17 ± 4.41 | 58.58 ± 9.74 |

tide | 47.93 ± 10.52 | 158.02 ± 116.09 | 286.59 ± 190.89 | |

sea | 144.27 ± 73.66 | 239.28 ± 97.55 | 548.02 ± 227.56 |

${\mathit{d}}_{\mathit{a}}^{\left(\mathbf{1}\right)}$ | ${\mathit{d}}_{\mathit{t}}^{\left(\mathbf{1}\right)}$ | ${\mathit{d}}_{\mathit{s}}^{\left(\mathbf{1}\right)}$ | ${\mathit{d}}_{\mathit{a}}^{\left(\mathbf{2}\right)}$ | ${\mathit{d}}_{\mathit{t}}^{\left(\mathbf{2}\right)}$ | ${\mathit{d}}_{\mathit{s}}^{\left(\mathbf{2}\right)}$ | |

W | 0.775 | 0.830 | 0.945 | 0.807 | 0.900 | 0.918 |

p-value | <0.0001 | <0.0001 | 0.0048 | <0.0001 | <0.0001 | 0.0002 |

**Table 7.**The three best-fitted three-parameter distributions for the NiTi-1 alloy in air, tide and sea environments.

Environment | Distribution (Parameters) | KS Ranking | AD Ranking |
---|---|---|---|

Air | Log-Logistic (1.879, 1.0814, 2.0076) | 1 | 3 |

Fréchet (0.85151, 1.3076, 1.8696) | 2 | 2 | |

Burr (0.15485, 18.168, 2.4178) | 3 | 1 | |

Tide | Burr (0.28059, 10.198, 2.4222) | 1 | 1 |

Log-Logistic (2.5145, 1.5899, 1.5086) | 2 | 2 | |

Dagum (28.81, 3.4851, 1.0721) | 3 | 3 | |

Sea | GEV (−0.11404, 9.9232, 17.683) | 1 | 2 |

Dagum (0.33963, 5.5711, 30.551) | 2 | 1 | |

General Pareto (−0.64068, 27.101, 5.878) | 3 | 12 |

Air: 1.Log-Logistic (1.879, 1.0814, 2.0076) | |||||||

Kolmogorov–Smirnov test | Anderson–Darling test | ||||||

Statistic p-value | 0.12767 0.31491 | Statistic | 1.367 | ||||

α | 0.05 | 0.02 | 0.01 | α | 0.05 | 0.02 | 0.01 |

Critical Value | 0.18144 | 0.20289 | 0.21768 | Critical Value | 2.5018 | 3.2892 | 3.9074 |

Air: 2.Fréchet (0.85151, 1.3076, 1.8696) | |||||||

Kolmogorov–Smirnov test | Anderson–Darling test | ||||||

Statistic p-value | 0.12975 0.29694 | Statistic | 1.3179 | ||||

α | 0.05 | 0.02 | 0.01 | α | 0.05 | 0.02 | 0.01 |

Critical Value | 0.18144 | 0.20289 | 0.21768 | Critical Value | 2.5018 | 3.2892 | 3.9074 |

Air: 3.Burr (0.15485, 18.168, 2.4178) | |||||||

Kolmogorov–Smirnov test | Anderson–Darling test | ||||||

Statistic p-value | 0.13164 0.28121 | Statistic | 1.2547 | ||||

α | 0.05 | 0.02 | 0.01 | α | 0.05 | 0.02 | 0.01 |

Critical Value | 0.18144 | 0.20289 | 0.21768 | Critical Value | 2.5018 | 3.2892 | 3.9074 |

**Table 9.**The empirical values and the values of PDF for the three best-fitted distributions for ${c}_{1}$ concerning NiTi-1.

Air | |||||

Lower Bound | Upper Bound | Empirical PDF of${\mathit{c}}_{\mathbf{1}}$ | ${\mathit{f}}_{{\mathit{a}}_{\mathbf{1}}}^{\left(\mathit{l}\right)}$ | ${\mathit{f}}_{{\mathit{a}}_{\mathbf{1}}}^{\left(\mathit{f}\right)}$ | ${\mathit{f}}_{{\mathit{a}}_{\mathbf{1}}}^{\left(\mathit{b}\right)}$ |

2 | 2.5045 | 0.148 | 0.18829 | 0.17834 | 0.15185 |

2.5045 | 3.009 | 0.333 | 0.27567 | 0.28288 | 0.30930 |

3.009 | 3.5135 | 0.241 | 0.18676 | 0.18733 | 0.18950 |

3.5135 | 4.018 | 0.019 | 0.11154 | 0.11138 | 0.10980 |

4.018 | 4.5225 | 0.000 | 0.06776 | 0.06814 | 0.06780 |

4.5225 | 5.027 | 0.037 | 0.04315 | 0.04376 | 0.04420 |

5.027 | 5.5315 | 0.000 | 0.02882 | 0.02944 | 0.03009 |

5.5315 | 6.036 | 0.074 | 0.02009 | 0.02061 | 0.02122 |

6.036 | 6.5405 | 0.093 | 0.01451 | 0.01492 | 0.01541 |

6.5405 | 7.045 | 0.056 | 0.01080 | 0.01112 | 0.01147 |

Tide | |||||

Lower Bound | Upper Bound | Empirical PDF of${\mathit{c}}_{\mathbf{1}}$ | ${\mathit{f}}_{{\mathit{t}}_{\mathbf{1}}}^{\left(\mathit{b}\right)}$ | ${\mathit{f}}_{{\mathit{t}}_{\mathbf{1}}}^{\left(\mathit{l}\right)}$ | ${\mathit{f}}_{{\mathit{t}}_{\mathbf{1}}}^{\left(\mathit{d}\right)}$ |

1 | 1.743333 | 0.017 | 0.00959 | 0.00808 | 0.00776 |

1.743333 | 2.486667 | 0.133 | 0.19950 | 0.21955 | 0.21636 |

2.486667 | 3.23 | 0.433 | 0.35833 | 0.32213 | 0.31896 |

3.23 | 3.973333 | 0.167 | 0.19035 | 0.20092 | 0.19905 |

3.973333 | 4.716667 | 0.033 | 0.09372 | 0.10316 | 0.10625 |

4.716667 | 5.46 | 0.050 | 0.05078 | 0.05412 | 0.05750 |

5.46 | 6.203333 | 0.033 | 0.02989 | 0.03037 | 0.03269 |

6.203333 | 6.946667 | 0.117 | 0.01876 | 0.01822 | 0.01958 |

6.946667 | 7.69 | 0.000 | 0.01238 | 0.01158 | 0.01229 |

7.69 | 8.433333 | 0.017 | 0.00851 | 0.00772 | 0.00804 |

Sea | |||||

Lower Bound | Upper Bound | Empirical PDF of${\mathit{c}}_{\mathbf{1}}$ | ${\mathit{f}}_{{\mathit{s}}_{\mathbf{1}}}^{\left(\mathit{g}\right)}$ | ${\mathit{f}}_{{\mathit{s}}_{\mathbf{1}}}^{\left(\mathit{d}\right)}$ | ${\mathit{f}}_{{\mathit{s}}_{\mathbf{1}}}^{\left(\mathit{g}\mathit{p}\right)}$ |

0 | 4.75275 | 0.000 | 0.02808 | 0.02958 | 0.02285 |

4.75275 | 9.5055 | 0.179 | 0.07661 | 0.08017 | 0.10774 |

9.5055 | 14.25825 | 0.075 | 0.13488 | 0.12560 | 0.16092 |

14.25825 | 19.011 | 0.119 | 0.17146 | 0.16283 | 0.14874 |

19.011 | 23.76375 | 0.164 | 0.17137 | 0.17866 | 0.13570 |

23.76375 | 28.5165 | 0.224 | 0.14352 | 0.15896 | 0.12160 |

28.5165 | 33.26925 | 0.090 | 0.10540 | 0.11273 | 0.10607 |

33.26925 | 38.022 | 0.045 | 0.07004 | 0.06728 | 0.08852 |

38.022 | 42.77475 | 0.015 | 0.04293 | 0.03689 | 0.06758 |

42.77475 | 47.5275 | 0.090 | 0.02455 | 0.01989 | 0.03880 |

**Table 10.**The empirical values and the values of CDF for the three best-fitted distributions for ${c}_{1}$ concerning NiTi-1.

Air | |||||

Lower Bound | Upper Bound | Empirical CDF of${\mathit{c}}_{\mathbf{1}}$ | ${\mathit{F}}_{{\mathit{a}}_{\mathbf{1}}}^{\left(\mathit{l}\right)}$ | ${\mathit{F}}_{{\mathit{a}}_{\mathbf{1}}}^{\left(\mathit{f}\right)}$ | ${\mathit{F}}_{{\mathit{a}}_{\mathbf{1}}}^{\left(\mathit{b}\right)}$ |

2 | 2.5045 | 0.148 | 0.18829 | 0.17834 | 0.15185 |

2.5045 | 3.009 | 0.481 | 0.46397 | 0.46123 | 0.46115 |

3.009 | 3.5135 | 0.722 | 0.65073 | 0.64855 | 0.65065 |

3.5135 | 4.018 | 0.741 | 0.76227 | 0.75993 | 0.76045 |

4.018 | 4.5225 | 0.741 | 0.83003 | 0.82808 | 0.82825 |

4.5225 | 5.027 | 0.778 | 0.87318 | 0.87184 | 0.87245 |

5.027 | 5.5315 | 0.778 | 0.90201 | 0.90128 | 0.90254 |

5.5315 | 6.036 | 0.852 | 0.92209 | 0.92188 | 0.92376 |

6.036 | 6.5405 | 0.944 | 0.93660 | 0.93680 | 0.93917 |

6.5405 | 7.045 | 1.000 | 0.94741 | 0.94792 | 0.95065 |

Tide | |||||

Lower Bound | Upper Bound | Empirical CDF of${\mathit{c}}_{\mathbf{1}}$ | ${\mathit{F}}_{{\mathit{t}}_{\mathbf{1}}}^{\left(\mathit{b}\right)}$ | ${\mathit{F}}_{{\mathit{t}}_{\mathbf{1}}}^{\left(\mathit{l}\right)}$ | ${\mathit{F}}_{{\mathit{t}}_{\mathbf{1}}}^{\left(\mathit{d}\right)}$ |

1 | 1.743333 | 0.017 | 0.00959 | 0.00808 | 0.00776 |

1.743333 | 2.486667 | 0.150 | 0.20910 | 0.22763 | 0.22412 |

2.486667 | 3.23 | 0.583 | 0.56744 | 0.54977 | 0.54309 |

3.23 | 3.973333 | 0.750 | 0.75779 | 0.75070 | 0.74214 |

3.973333 | 4.716667 | 0.783 | 0.85150 | 0.85385 | 0.84838 |

4.716667 | 5.46 | 0.833 | 0.90228 | 0.90797 | 0.90588 |

5.46 | 6.203333 | 0.867 | 0.93218 | 0.93835 | 0.93857 |

6.203333 | 6.946667 | 0.983 | 0.95094 | 0.95657 | 0.95815 |

6.946667 | 7.69 | 0.983 | 0.96332 | 0.96815 | 0.97045 |

7.69 | 8.433333 | 1.000 | 0.97183 | 0.97587 | 0.97848 |

Sea | |||||

Lower Bound | Upper Bound | Empirical CDF of${\mathit{c}}_{\mathbf{1}}$ | ${\mathit{F}}_{{\mathit{s}}_{\mathbf{1}}}^{\left(\mathit{g}\right)}$ | ${\mathit{F}}_{{\mathit{s}}_{\mathbf{1}}}^{\left(\mathit{d}\right)}$ | ${\mathit{F}}_{{\mathit{s}}_{\mathbf{1}}}^{\left(\mathit{g}\mathit{p}\right)}$ |

0 | 4.75275 | 0.000 | 0.03439 | 0.02958 | 0.02285 |

4.75275 | 9.5055 | 0.179 | 0.11100 | 0.10975 | 0.13059 |

9.5055 | 14.25825 | 0.254 | 0.24588 | 0.23534 | 0.29151 |

14.25825 | 19.011 | 0.373 | 0.41733 | 0.39816 | 0.44024 |

19.011 | 23.76375 | 0.537 | 0.58871 | 0.57682 | 0.57593 |

23.76375 | 28.5165 | 0.761 | 0.73224 | 0.73579 | 0.69754 |

28.5165 | 33.26925 | 0.851 | 0.83765 | 0.84853 | 0.80362 |

33.26925 | 38.022 | 0.896 | 0.90769 | 0.91581 | 0.89213 |

38.022 | 42.77475 | 0.910 | 0.95062 | 0.95270 | 0.95972 |

42.77475 | 47.5275 | 1.000 | 0.97517 | 0.97259 | 0.99852 |

**Table 11.**The three best-fitted three-parameter distributions for the NiTi-2 alloy in air, tide and sea environments.

Environment | Distribution (Parameters) | KS Ranking | AD Ranking |
---|---|---|---|

Air | Burr (0.15416, 21.51, 2.715) | 1 | 1 |

Log-Logistic (2.2589, 1.1902, 2.1909) | 2 | 3 | |

Fréchet (0.68413, 1.4445, 2.0152) | 3 | 2 | |

Tide | Log-Logistic (2.9765, 9.4705, −0.31248) | 1 | 1 |

Dagum (0.80238, 3.1011, 10.229) | 2 | 2 | |

Gamma (2.0829, 4.4208, 1.43) | 3 | 3 | |

Sea | General Pareto (−0.33758, 17.894, 10.585) | 1 | 20 |

Dagum (3.16, 3.1334, 13.409) | 2 | 8 | |

Fatigue Life (0.48433, 19.344, 2.3488) | 3 | 2 |

Air: 1. Burr (0.15416, 21.51, 2.715) | |||||||

Kolmogorov–Smirnov test | Anderson–Darling test | ||||||

Statistic p-value | 0.11397 0.23764 | Statistic | 1.5013 | ||||

α | 0.05 | 0.02 | 0.01 | α | 0.05 | 0.02 | 0.01 |

Critical Value | 0.15052 | 0.16832 | 0.1806 | Critical Value | 2.5018 | 3.2892 | 3.9074 |

Air: 2. Log-Logistic (2.2589, 1.1902, 2.1909) | |||||||

Kolmogorov–Smirnov test | Anderson–Darling test | ||||||

Statistic p-value | 0.1292 10.13081 | Statistic | 1.9414 | ||||

α | 0.05 | 0.02 | 0.01 | α | 0.05 | 0.02 | 0.01 |

Critical Value | 0.15052 | 0.16832 | 0.1806 | Critical Value | 2.5018 | 3.2892 | 3.9074 |

Air: 3. Frechet (0.68413, 1.4445, 2.0152) | |||||||

Kolmogorov–Smirnov test | Anderson–Darling test | ||||||

Statistic p-value | 0.13424 0.10566 | Statistic | 1.8828 | ||||

α | 0.05 | 0.02 | 0.01 | α | 0.05 | 0.02 | 0.01 |

Critical Value | 0.15052 | 0.16832 | 0.1806 | Critical Value | 2.5018 | 3.2892 | 3.9074 |

**Table 13.**The empirical values and the values of PDF for the three best-fitted distributions for ${c}_{1}$ concerning NiTi-2.

Air | |||||

Lower Bound | Upper Bound | Empirical PDF of${\mathit{c}}_{\mathbf{1}}$ | ${\mathit{f}}_{{\mathit{a}}_{\mathbf{2}}}^{\left(\mathit{b}\right)}$ | ${\mathit{f}}_{{\mathit{a}}_{\mathbf{2}}}^{\left(\mathit{l}\right)}$ | ${\mathit{f}}_{{\mathit{a}}_{\mathbf{2}}}^{\left(\mathit{f}\right)}$ |

2 | 2.435 | 0.025 | 0.01385 | 0.02715 | 0.02134 |

2.435 | 2.87 | 0.190 | 0.18738 | 0.19253 | 0.19026 |

2.87 | 3.305 | 0.329 | 0.27879 | 0.24306 | 0.24657 |

3.305 | 3.74 | 0.165 | 0.17412 | 0.18184 | 0.18053 |

3.74 | 4.175 | 0.013 | 0.10563 | 0.11573 | 0.11574 |

4.175 | 4.61 | 0.013 | 0.06723 | 0.07201 | 0.07337 |

4.61 | 5.045 | 0.038 | 0.04466 | 0.04590 | 0.04758 |

5.045 | 5.48 | 0.051 | 0.03073 | 0.03034 | 0.03182 |

5.48 | 5.915 | 0.089 | 0.02179 | 0.02079 | 0.02195 |

5.915 | 6.35 | 0.089 | 0.01585 | 0.01473 | 0.01557 |

Tide | |||||

Lower Bound | Upper Bound | Empirical PDF of${\mathit{c}}_{\mathbf{1}}$ | ${\mathit{f}}_{{\mathit{t}}_{\mathbf{2}}}^{\left(\mathit{l}\right)}$ | ${\mathit{f}}_{{\mathit{t}}_{\mathbf{2}}}^{\left(\mathit{d}\right)}$ | ${\mathit{f}}_{{\mathit{t}}_{\mathbf{2}}}^{\left(\mathit{g}\right)}$ |

0 | 2.3685 | 0.028 | 0.02283 | 0.02602 | 0.01590 |

2.3685 | 4.737 | 0.097 | 0.11048 | 0.11122 | 0.13891 |

4.737 | 7.1055 | 0.222 | 0.19252 | 0.18541 | 0.18772 |

7.1055 | 9.474 | 0.264 | 0.19857 | 0.19567 | 0.17524 |

9.474 | 11.8425 | 0.056 | 0.15321 | 0.15575 | 0.14199 |

11.8425 | 14.211 | 0.028 | 0.10362 | 0.10700 | 0.10670 |

14.211 | 16.5795 | 0.083 | 0.06723 | 0.06945 | 0.07647 |

16.5795 | 18.948 | 0.069 | 0.04373 | 0.04480 | 0.05310 |

18.948 | 21.3165 | 0.083 | 0.02900 | 0.02935 | 0.03601 |

21.3165 | 23.685 | 0.069 | 0.01973 | 0.01969 | 0.02399 |

Sea | |||||

Lower Bound | Upper Bound | Empirical PDF of${\mathit{c}}_{\mathbf{1}}$ | ${\mathit{f}}_{{\mathit{s}}_{\mathbf{2}}}^{\left(\mathit{g}\mathit{p}\right)}$ | ${\mathit{f}}_{{\mathit{s}}_{\mathbf{2}}}^{\left(\mathit{d}\right)}$ | ${\mathit{f}}_{{\mathit{s}}_{\mathbf{2}}}^{\left(\mathit{f}\mathit{l}\right)}$ |

0 | 4.8685 | 0.000 | 0 | 0.00004 | 0.00011 |

4.8685 | 9.737 | 0.014 | 0.00026 | 0.01563 | 0.01936 |

9.737 | 14.6055 | 0.194 | 0.20807 | 0.15039 | 0.15149 |

14.6055 | 19.474 | 0.250 | 0.21117 | 0.25947 | 0.22978 |

19.474 | 24.3425 | 0.139 | 0.16989 | 0.20983 | 0.20386 |

24.3425 | 29.211 | 0.097 | 0.33230 | 0.13252 | 0.14745 |

29.211 | 34.0795 | 0.139 | 0.10092 | 0.07957 | 0.09698 |

34.0795 | 38.948 | 0.042 | 0.07300 | 0.04848 | 0.06067 |

38.948 | 43.8165 | 0.083 | 0.04955 | 0.03054 | 0.03690 |

43.8165 | 48.685 | 0.042 | 0.03057 | 0.01994 | 0.02206 |

**Table 14.**The empirical values and the values of CDF for the three best-fitted distributions for ${c}_{1}$ concerning NiTi-2.

Air | |||||

Lower Bound | Upper Bound | Empirical CDF of${\mathit{c}}_{\mathbf{1}}$ | ${\mathit{F}}_{{\mathit{a}}_{\mathbf{2}}}^{\left(\mathit{b}\right)}$ | ${\mathit{F}}_{{\mathit{a}}_{\mathbf{2}}}^{\left(\mathit{l}\right)}$ | ${\mathit{F}}_{{\mathit{a}}_{\mathbf{2}}}^{\left(\mathit{f}\right)}$ |

2 | 2.435 | 0.025 | 0.01407 | 0.02715 | 0.02143 |

2.435 | 2.87 | 0.215 | 0.20144 | 0.21968 | 0.21159 |

2.87 | 3.305 | 0.544 | 0.48023 | 0.46274 | 0.45816 |

3.305 | 3.74 | 0.709 | 0.65435 | 0.64458 | 0.63869 |

3.74 | 4.175 | 0.722 | 0.75999 | 0.76030 | 0.75444 |

4.175 | 4.61 | 0.734 | 0.82722 | 0.83232 | 0.82781 |

4.61 | 5.045 | 0.772 | 0.87187 | 0.87822 | 0.87539 |

5.045 | 5.48 | 0.823 | 0.90261 | 0.90855 | 0.90721 |

5.48 | 5.915 | 0.911 | 0.92440 | 0.92935 | 0.92916 |

5.915 | 6.35 | 1.000 | 0.94025 | 0.94408 | 0.94473 |

Tide | |||||

Lower Bound | Upper Bound | Empirical CDF of${\mathit{c}}_{\mathbf{1}}$ | ${\mathit{F}}_{{\mathit{t}}_{\mathbf{2}}}^{\left(\mathit{l}\right)}$ | ${\mathit{F}}_{{\mathit{t}}_{\mathbf{2}}}^{\left(\mathit{d}\right)}$ | ${\mathit{F}}_{{\mathit{t}}_{\mathbf{2}}}^{\left(\mathit{g}\right)}$ |

0 | 2.3685 | 0.028 | 0.02283 | 0.02602 | 0.01590 |

2.3685 | 4.737 | 0.125 | 0.13332 | 0.13725 | 0.15482 |

4.737 | 7.1055 | 0.347 | 0.32584 | 0.32266 | 0.34254 |

7.1055 | 9.474 | 0.611 | 0.52441 | 0.51832 | 0.57780 |

9.474 | 11.8425 | 0.667 | 0.67761 | 0.67407 | 0.65977 |

11.8425 | 14.211 | 0.694 | 0.78121 | 0.78105 | 0.76645 |

14.211 | 16.5795 | 0.778 | 0.84844 | 0.85050 | 0.84292 |

16.5795 | 18.948 | 0.847 | 0.89216 | 0.89529 | 0.89601 |

18.948 | 21.3165 | 0.931 | 0.92116 | 0.92464 | 0.93202 |

21.3165 | 23.685 | 1.000 | 0.94089 | 0.94434 | 0.95601 |

Sea | |||||

Lower Bound | Upper Bound | Empirical CDF of${\mathit{c}}_{\mathbf{1}}$ | ${\mathit{F}}_{{\mathit{s}}_{\mathbf{2}}}^{\left(\mathit{g}\mathit{p}\right)}$ | ${\mathit{F}}_{{\mathit{s}}_{\mathbf{2}}}^{\left(\mathit{d}\right)}$ | ${\mathit{F}}_{{\mathit{s}}_{\mathbf{2}}}^{\left(\mathit{f}\mathit{l}\right)}$ |

0 | 4.8685 | 0.000 | 0 | 0.00004 | 0.00011 |

4.8685 | 9.737 | 0.014 | 0.00026 | 0.01567 | 0.01947 |

9.737 | 14.6055 | 0.208 | 0.20833 | 0.16606 | 0.17096 |

14.6055 | 19.474 | 0.458 | 0.41949 | 0.42550 | 0.40071 |

19.474 | 24.3425 | 0.597 | 0.58938 | 0.63533 | 0.60457 |

24.3425 | 29.211 | 0.694 | 0.72263 | 0.76786 | 0.75204 |

29.211 | 34.0795 | 0.833 | 0.82355 | 0.84743 | 0.84902 |

34.0795 | 38.948 | 0.875 | 0.89656 | 0.89591 | 0.90970 |

38.948 | 43.8165 | 0.958 | 0.94611 | 0.92644 | 0.94660 |

43.8165 | 48.685 | 1.000 | 0.97667 | 0.94639 | 0.96566 |

${\mathit{W}}_{\mathit{i}\mathit{j}}$ | p-Value | Significant Differences | |||||||
---|---|---|---|---|---|---|---|---|---|

Air | Tide | Sea | Air | Tide | Sea | Air | Tide | Sea | |

air | 0.414 | −13.284 | 0.954 | <0.0001 | No | Yes | |||

tide | −0.414 | −13.645 | 0.954 | <0.0001 | No | Yes | |||

sea | 13.284 | 13.645 | <0.0001 | <0.0001 | Yes | Yes |

${\mathit{W}}_{\mathit{i}\mathit{j}}$ | p-Value | Significant Differences | |||||||
---|---|---|---|---|---|---|---|---|---|

Air | Tide | Sea | Air | Tide | Sea | Air | Tide | Sea | |

air | −11.898 | −14.990 | 1 | <0.0001 | <0.0001 | Yes | Yes | ||

tide | 11.898 | −10.876 | <0.0001 | 1 | <0.0001 | Yes | Yes | ||

sea | 14.990 | 10.876 | <0.0001 | <0.0001 | 1 | Yes | Yes |

Air Environment | Tide Environment | Sea Environment | |
---|---|---|---|

D | 0.251 | 0.725 | 0.180 |

p-value | 0.029 | <0.0001 | 0.189 |

$\alpha $ | 0.05 | 0.05 | 0.05 |

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## Share and Cite

**MDPI and ACS Style**

Kovač, N.; Ivošević, Š.; Vastag, G.; Vukelić, G.; Rudolf, R. Statistical Approach to the Analysis of the Corrosive Behaviour of NiTi Alloys under the Influence of Different Seawater Environments. *Appl. Sci.* **2021**, *11*, 8825.
https://doi.org/10.3390/app11198825

**AMA Style**

Kovač N, Ivošević Š, Vastag G, Vukelić G, Rudolf R. Statistical Approach to the Analysis of the Corrosive Behaviour of NiTi Alloys under the Influence of Different Seawater Environments. *Applied Sciences*. 2021; 11(19):8825.
https://doi.org/10.3390/app11198825

**Chicago/Turabian Style**

Kovač, Nataša, Špiro Ivošević, Gyöngyi Vastag, Goran Vukelić, and Rebeka Rudolf. 2021. "Statistical Approach to the Analysis of the Corrosive Behaviour of NiTi Alloys under the Influence of Different Seawater Environments" *Applied Sciences* 11, no. 19: 8825.
https://doi.org/10.3390/app11198825