# Lean-and-Green Strength Performance Optimization of a Tube-to-Tubesheet Joint for a Shell-and-Tube Heat Exchanger Using Taguchi Methods and Random Forests

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Designing the Experiments

_{9}(3

^{4}) OA [43] accommodates as many as four controlling factors by requiring nine specific experimental recipes to be executed. The four factors are accommodated in a saturated scheme. Saturated experimental plans may also be deemed ‘lean-and-green’, because they promote the maximization of the investigated influences. Each factor participates in the experimental plan at three operating settings through the preset configuration of the OA sampler. The promoted ‘lean-and-green’ engineering aspect is evident at this point, since the total work volume is reduced by a ratio of 1/9; a full-factorial arrangement of the four 3-level factors would otherwise demand a total of 81 (=3

^{4}) trials. In Table 2, we list the scheduled factorial combinations according to the L

_{9}(3

^{4}) OA arrangement. The nine-run OA set-up was makeshift replicated twice. This is another minimal (lean-and-green) replication practice. Finally, the tolerance limits for both the clearance and the groove depth were decided to be restricted within ±0.02 mm.

#### 2.2. Test Tubesheet and Tube Specimens

#### 2.3. CNC Machining of the Test Tubesheet Specimens

_{9}(3

^{4}) OA in the saturated factorial arrangement.

- 1.
- DIJET Drill Bit Inserts (No. TEZ1900, Osaka, Japan): a carbide tool material with PVD coating (JC8050). Two indexable drill-bit inserts, with nominal diameter of 19 mm (Figure 5a), were utilized.They were attached to a drill-body tool-holder (DIJET Drill Body, No. TEZD1900S25-MS). Each drill-bit insert was paired to complete each replicate set of nine workpieces as a preventive measure to curtail interloping variability due to local cutting process flaws.
- 2.
- Sandvik Coromant Boring Inserts (ANSI code: TCGX 1.8 (1.5) 1L-WK 5015, Sandvik Coromant, Sandviken, Sweden): an uncoated carbide tool material. Two indexable boring inserts were utilized with corner radius and thickness dimensions of 0.3969 mm and 2.3812 mm, respectively. They were attached to a boring tool-holder (Sandvik Coromant Boring Bar, ANSI code: CXS-10-17 050TC09) and were mounted to a fine boring head adapter with a nominal accuracy of 0.002 mm (Figure 5b). Each boring insert was paired to process each replicate set of nine workpieces, again as a simple preventive measure in minimizing variability due to cutting process flaws.
- 3.
- UOP T-slot Milling Cutters: solid High-Speed Steel (HSS) tool material (Roncadelle, Brescia, Italy). Two solid HSS T-slot milling cutters (Figure 5c), with cutting diameter and depth dimensions of 16.5 mm and 3 mm, respectively, were also outfitted with eight flutes. They were utilized to etch internal annular grooves on the tubesheet hole surfaces. Each T-slot milling cutter was paired to each separate set of nine workpieces. Upon completion of the machining process, the tubesheet specimens were crafted as shown in Figure 5d.

#### 2.4. The Tube Expansion Process

#### 2.4.1. Tube Expanding Machine and Tube Expander Tool

- A Matex tsx digital controller.
- A F/308-2 telescopic shaft which transmitted the rotational motion between the electric motor and the tube expander.
- An electric rolling motor (Matex R V4) which was composed of a brushless electric motor, and it was coupled to a mechanical gearbox with four speed options, i.e., 200, 300, 540, and 800 rpm.
- A PE900 foot switch control.

Experiment No. | A | B | C | D | E | F | G |
---|---|---|---|---|---|---|---|

Tubesheet Hole ID (mm) | Tube OD (mm) | Clearance (A Minus B) (mm) | Tube ID (mm) | Tube ID at Metal-To-Metal contact (D Plus C) (mm) | Tube Wall Thickness Reduction (%) | Expanded Tube ID [F% of (B-D) Plus E] (mm) | |

1.1 | 19.10 | 18.99 | 0.11 | 14.97 | 15.08 | 4 | 15.24 |

1.2 | 19.10 | 19.00 | 0.10 | 14.96 | 15.06 | 4 | 15.22 |

2.1 | 19.08 | 19.01 | 0.07 | 14.98 | 15.05 | 8 | 15.37 |

2.2 | 19.10 | 19.02 | 0.08 | 14.96 | 15.04 | 8 | 15.36 |

3.1 | 19.10 | 18.99 | 0.11 | 14.97 | 15.08 | 12 | 15.56 |

3.2 | 19.09 | 19.03 | 0.06 | 14.97 | 15.03 | 12 | 15.52 |

4.1 | 19.24 | 19.01 | 0.23 | 14.97 | 15.20 | 12 | 15.68 |

4.2 | 19.24 | 19.00 | 0.24 | 14.98 | 15.22 | 12 | 15.70 |

5.1 | 19.24 | 19.02 | 0.22 | 14.96 | 15.18 | 4 | 15.34 |

5.2 | 19.25 | 19.01 | 0.24 | 14.97 | 15.21 | 4 | 15.37 |

6.1 | 19.24 | 19.02 | 0.22 | 14.98 | 15.20 | 8 | 15.52 |

6.2 | 19.25 | 19.00 | 0.25 | 14.96 | 15.21 | 8 | 15.53 |

7.1 | 19.39 | 19.00 | 0.39 | 14.96 | 15.35 | 8 | 15.67 |

7.2 | 19.40 | 19.01 | 0.39 | 14.97 | 15.36 | 8 | 15.68 |

8.1 | 19.41 | 19.02 | 0.39 | 14.96 | 15.35 | 12 | 15.84 |

8.2 | 19.40 | 19.00 | 0.40 | 14.97 | 15.37 | 12 | 15.85 |

9.1 | 19.40 | 18.99 | 0.41 | 14.97 | 15.38 | 4 | 15.54 |

9.2 | 19.40 | 19.00 | 0.40 | 14.96 | 15.36 | 4 | 15.52 |

#### 2.4.2. Determination of the Proper Expanded Tube Inner Diameter

#### 2.5. Joint Strength Measurements

#### 2.6. Theoretical Aspects and Computational Aids

_{9}(3

^{4}) OA with its coded 3-level settings is shown in Figure 9 for a duplicated output

**R**with its nine-entry replicate vectors

**R1**and

**R2**, respectively. The coded controlling factors in the input nine-run configuration are denoted as A, B, C, and D, respectively.

_{9}(3

^{4}) OA trial planner to schedule the duplicated and saturated multifactorial runs. The ‘STATS/DOE/ Taguchi’ module offered the integrated statistical solution for the dual screening and optimization task by separately arriving at a prediction for the joint strength location (mean of means) and dispersion (mean of SNR) values. Thus, the non-linear response tables and graphs for both the mean and SNR response were generated. The classic ANOVA and regression analysis treatments on the unprocessed joint strength replicates were also employed to: (1) weigh the variance of the individual controlling factors against the residual error, and (2) obtain the coefficients of regression, which give a statistical measure of the magnitude of the potentially non-linear effects. The between-replicates agreement is easily assessed by drawing a simple goodness-of-fit least-squares line plot to evaluate the correlated relationship and possible deviation between the two collected joint strength replicate vectors. In the case of substantial observed deviation, additional replicate runs would be scheduled, and the assessment process would be repeated to determine the variability status between the replicated runs. Boxplots are also drawn to portray in a robust manner the variability within each factor setting and to visually contrast the effects among different settings.

## 3. Results

#### 3.1. Joint Strength Statistical Analysis Using Response Graphs and Tables

^{2}) and the coefficient of determination for prediction (pred R

^{2}) were estimated at 99.43% and 98.89%, respectively, which implies an overall satisfactory interpretation of the explained variation. There is no lack of fit and the stepwise selection terms were determined with the same error rate α ‘to enter’ and ‘to remove’. Only the quadratic term which was related to the number of the grooves was excluded from the model. To differentiate the effects of the linear and quadratic terms in explaining the total variation, the coefficients of regression are indispensable. In Table 13, it is tabulated both regression coefficients, for the linear and the quadratic components for all four controlling factors. It is re-affirmed that the joint strength behaves linearly against the number of the grooves, while the rest of the controlling factors also uphold a quadratic component. For the leading effects, it is the linear part of the effect of the tube wall thickness reduction and the number of grooves that is statistically prevailing. It is additionally noted that the variance inflation factor (VIF) estimations (MINITAB 19.0, State College, PA, USA), for all four parameters, were equal to 1.0 which signifies that there is no issue of multicollinearity between the factorial relationships in the prediction model. This was partly accomplished by standardizing the factorial levels to end point model values of −1 to 1.

^{2}, whereas the Mallows’s Cp statistic (MINITAB 19.0) is minimized to a value of 5.0, which signifies that there is no appreciable bias in the finalized model selection (C

_{p}= 5.0 < 2p = 8).

#### 3.2. Proposed Optimal Solution for the Screening/Optimization of the Joint Strength

- Tube wall thickness reduction at level 3 (12%).
- Number of grooves at level 3 (Three).
- Groove depth at level 2 (0.40 ± 0.02 mm).
- Clearance at level 1 (0.10 ± 0.02 mm).

_{9}(3

^{4}) OA sampler (Table 2). It is also noted that the groove depth is finally adjusted in accordance with the TEMA standards [7,51,52], which specify that the deep annular grooves are to be machined at approximately 0.40 mm. This is a practical intervention in view of the fact that the magnitude of the influence of the groove depth is, arguably, mildly active even if it appears to be statistically significant.

#### 3.3. Confirmation Run for the Optimal Parameter Settings

## 4. Discussion

_{try}) was determined upon minimization of the ‘out-of-bag’ error (OOB). From Figure 17, the optimal m

_{try}number is 4 variables. Consequently, the partial dependence plots for tracking the behavior pattern of the joint strength, in terms of the four screened factors, are shown in Figure 18. It is now unequivocal that primarily the tube wall thickness reduction and, next, the number of grooves in the tubesheet hole, might stimulate enough variability to be classified as active influences. Thus, they might pass the screening filter phase and proceed next to undergo the optimization drill. In agreement with the explained variation estimation (Table 17), the Random Forest regression manages to attribute 85.13 % of the variability to the four profiled factors with an assorted increasing node purity (mean of squared residuals) of 17,843,680. From the derived Random Forest importance measures, the fluctuation of the mean squared error is essentially identified to the tube wall thickness reduction (33.21%) and the number of grooves in the tubesheet hole (25.06%).

## 5. Conclusions

- Tube wall thickness reduction at level 3 (12%).
- Number of grooves at level 3 (Three).
- Groove depth at level 2 (0.40 mm).
- Clearance at level 1 (0.10 mm).

- Further testing would be informative in investigating the joint leakage by exposing the joint in either pneumatic or hydraulic pressure tests; joint leak tightness cannot be measured directly by push-out testing.
- Further testing is needed to be conducted to study the influence of surface finish of the tubesheet holes on joint strength and joint leak tightness.
- The effect of a five-roller tube expander and a tube expander which incorporates three expansion rollers with three flare rollers on joint strength and joint leak tightness would be beneficial.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**(

**a**) Drill inserts and drill-body tool-holder; (

**b**) drill inserts, boring tool-holder, and finish boring head adapter; (

**c**) T-slot milling cutters; (

**d**) tubesheet specimens after exiting the machining process.

**Figure 7.**(

**a**) Tubesheet hole ID measurement; (

**b**) tube OD measurement; (

**c**) tube ID measurement; (

**d**) tube rolling (expansion).

**Figure 8.**(

**a**) Tube end sealing; (

**b**) push-out testing machine; (

**c**) round S355 steel bar; (

**d**) preparation for push-out testing; (

**e**) before tube displacement; (

**f**) after tube displacement; (

**g**) tested tube-to-tubesheet specimens after tube push-out testing completed.

**Figure 10.**The two separate data reduction steps to generate the mean (M) and SNR responses, respectively.

**Figure 14.**Boxplots for the joint strength (JS in N) due to: (

**A**) clearance (

**A**in mm), (

**B**) number of grooves (

**B**), (

**C**) groove depth (

**C**in mm), and (

**D**) tube wall thickness reduction (

**D**in %).

**Figure 16.**Error convergence according to the tree number selection in the Random Forest routine execution.

**Figure 17.**Minimization of the out-of-bag error (OOB) due to number of variables randomly sampled as candidates at each split (m

_{try}) in the Random Forest solver.

**Figure 18.**Factorial profiling using the Random Forest solver to evaluate the partial dependence of: (1) Clearance (

**A**), (2) Number of Grooves (

**B**), (3) Groove Depth (

**C**), and (4) Tube Wall Thickness Reduction (

**D**).

Controlling Factor (Units) | Level 1 | Level 2 | Level 3 | |
---|---|---|---|---|

1 | Clearance (mm) | 0.10 | 0.25 | 0.40 |

2 | Number of Grooves | One | Two | Three |

3 | Groove Depth (mm) | 0.20 | 0.40 | 0.60 |

4 | Tube Wall Thickness Reduction (%) | 4 | 8 | 12 |

Run | Clearance | Number of Grooves | Groove Depth | Tube Wall Thickness Reduction |
---|---|---|---|---|

1 | 0.10 ± 0.02 | One | 0.20 ± 0.02 | 4 |

2 | 0.10 ± 0.02 | Two | 0.40 ± 0.02 | 8 |

3 | 0.10 ± 0.02 | Three | 0.60 ± 0.02 | 12 |

4 | 0.25 ± 0.02 | One | 0.40 ± 0.02 | 12 |

5 | 0.25 ± 0.02 | Two | 0.60 ± 0.02 | 4 |

6 | 0.25 ± 0.02 | Three | 0.20 ± 0.02 | 8 |

7 | 0.40 ± 0.02 | One | 0.60 ± 0.02 | 8 |

8 | 0.40 ± 0.02 | Two | 0.20 ± 0.02 | 12 |

9 | 0.40 ± 0.02 | Three | 0.40 ± 0.02 | 4 |

Type P265GH (1.0425)/EN 10028-2 | ||||||

Chemical Composition % | ||||||

C | Mn | Si | P | S | Cu | Ni |

Max 0.2 | 0.8–1.4 | Max 0.4 | Max 0.025 | Max 0.01 | Max 0.3 | Max 0.3 |

Cr | Mo | Al | V | Nb | Ti | N |

Max 0.3 | Max 0.08 | Min 0.02 | Max 0.02 | Max 0.03 | Max 0.03 | Max 0.012 |

Mechanical Properties | ||||||

Yield strength (ReH) [MPa] | Min 255 | |||||

Tensile strength (Rm) [MPa] | 410–530 | |||||

Elongation (A%) | Min 22 |

Type P215NL (1.0451)/EN 10216-4 | ||||||

Chemical Composition % | ||||||

C | Mn | Si | P | S | Cu | Ni |

0.09 | 0.48 | 0.18 | 0.011 | 0.002 | 0.01 | 0.02 |

Cr | Mo | Al | V | Nb | Ti | |

0.03 | 0.01 | 0.028 | 0.001 | 0.001 | 0.003 | |

Mechanical Properties | ||||||

Yield strength (ReH) [MPa] | Min 225 | |||||

Tensile strength (Rm) [MPa] | Min 360 | |||||

Elongation (A%) | Min 25 |

Tube Wall Thickness Reduction (%) | Torque (Nm) |
---|---|

4 | 8 |

8 | 12 |

12 | 15 |

Run# | Joint Strength (N) Trial #1 | Joint Strength (N) Trial #2 | Joint Strength Mean (N) | SNR-Joint Strength (dB) |
---|---|---|---|---|

1 | 17,880.00 | 16,597.50 | 17,238.75 | 84.71 |

2 | 37,552.50 | 38,400.00 | 37,976.25 | 91.60 |

3 | 45,371.25 | 44,913.75 | 45,142.50 | 93.09 |

4 | 31,263.75 | 29,811.25 | 30,537.50 | 89.70 |

5 | 11,935.00 | 13,500.00 | 12,717.50 | 82.04 |

6 | 39,768.75 | 39,330.00 | 39,549.38 | 91.94 |

7 | 17,523.75 | 18,288.75 | 17,906.25 | 85.05 |

8 | 38,662.50 | 37,706.25 | 38,184.38 | 91.64 |

9 | 24,318.75 | 26,525.00 | 25,421.88 | 88.08 |

Level | Clearance | Number of Grooves | Groove Depth | Tube Wall Thickness Reduction |
---|---|---|---|---|

1 | 33,452.50 | 21,894.17 | 31,657.50 | 18,459.37 |

2 | 27,601.46 | 29,626.04 | 31,311.87 | 31,810.62 |

3 | 27,170.83 | 36,704.58 | 25,255.42 | 37,954.79 |

Difference | 6281.67 | 14,810.42 | 6402.08 | 19,495.42 |

Rank | 4 | 2 | 3 | 1 |

Level | Clearance | Number of Grooves | Groove Depth | Tube Wall Thickness Reduction |
---|---|---|---|---|

1 | 89.80 | 86.49 | 89.43 | 84.94 |

2 | 87.89 | 88.42 | 89.79 | 89.53 |

3 | 88.26 | 91.04 | 86.73 | 91.47 |

Delta | 1.91 | 4.55 | 3.06 | 6.53 |

Rank | 4 | 2 | 3 | 1 |

Factor | DF | adj SS | adj MS | F-Value | p-Value | Contribution (%) | Rank |
---|---|---|---|---|---|---|---|

Clearance | 2 | 73,879,463 | 36,939,731 | * | * | 6.86 | 4 |

Number of Grooves | 2 | 329,236,085 | 164,618,042 | * | * | 30.57 | 2 |

Groove Depth | 2 | 77,786,815 | 38,893,408 | * | * | 7.22 | 3 |

Tube Wall Thk. Reduction | 2 | 596,077,932 | 298,038,966 | * | * | 55.35 | 1 |

Error | 0 | * | * | * | |||

Total | 8 | 1,076,980,294 | 100.00 | ||||

Model Summary | |||||||

S R-sq R-sq (adj) R-sq (pred) | |||||||

* 100.00% * * |

Factor | DF | adj SS | adj MS | F-Value | p-Value | Contribution (%) | Rank |
---|---|---|---|---|---|---|---|

Clearance | 2 | 6.146 | 3.073 | * | * | 5.05 | 4 |

Number of Grooves | 2 | 31.321 | 15.661 | * | * | 25.74 | 2 |

Groove Depth | 2 | 16.777 | 8.389 | * | * | 13.79 | 3 |

Tube Wall Thk. Reduction | 2 | 67.423 | 33.712 | * | * | 55.42 | 1 |

Error | 0 | * | * | * | |||

Total | 8 | 121.668 | 100.00 | ||||

Model Summary | |||||||

S R-sq R-sq (adj) R-sq (pred) | |||||||

* 100.00% * * |

Source | DF | adj SS | adj MS | F-Value | p-Value |
---|---|---|---|---|---|

Regression | 7 | 2,153,533,744 | 307,647,678 | 423.04 | 0.000 |

A | 1 | 118,378,008 | 118,378,008 | 162.78 | 0.000 |

B | 1 | 658,045,326 | 658,045,326 | 904.86 | 0.000 |

C | 1 | 122,960,013 | 122,960,013 | 169.08 | 0.000 |

D | 1 | 1,140,213,813 | 1,140,213,813 | 1567.87 | 0.000 |

A∗A | 1 | 29,380,917 | 29,380,917 | 40.40 | 0.000 |

C∗C | 1 | 32,613,617 | 32,613,617 | 44.85 | 0.000 |

D∗D | 1 | 51,942,050 | 51,942,050 | 71.42 | 0.000 |

Error | 10 | 7,272,359 | 727,236 | ||

Lack-of-Fit | 1 | 426,844 | 426,844 | 0.56 | 0.473 |

Pure Error | 9 | 6,845,515 | 760,613 | ||

Total | 17 | 2,160,806,104 | |||

Model | Summary | ||||

S | R^{2} | R^{2} (adj) | R^{2} (pred) | ||

852.78 | 99.66% | 99.43% | 98.89% |

**A**= Clearance,

**B**= Number of Grooves,

**C**= Groove Depth,

**D**= Tube Wall Thickness Reduction.

Term | COEF | SE COEF | T-Value | p-Value | VIF |
---|---|---|---|---|---|

Constant | 31,907 | 532 | 60.00 | 0.000 | |

A | −3141 | 246 | −12.76 | 0.000 | 1.00 |

B | 7405 | 246 | 30.08 | 0.000 | 1.00 |

C | −3201 | 246 | −13.00 | 0.000 | 1.00 |

D | 9748 | 246 | 39.60 | 0.000 | 1.00 |

A∗A | 2710 | 426 | 6.36 | 0.000 | 1.00 |

C∗C | −2855 | 426 | −6.70 | 0.000 | 1.00 |

D∗D | −3604 | 426 | −8.45 | 0.000 | 1.00 |

Regression | Equation: | ||||

Joint Strength | = | 31907 − 3141 A + 7405 B − 3201 C + 9748 D + 2710 A^{2} − 2855 C^{2} − 3604 D^{2} |

**A**= Clearance,

**B**= Number of Grooves,

**C**= Groove Depth,

**D**= Tube Wall Thickness Reduction.

Total Variables | R^{2} | R^{2} (adj) | PRESS | R^{2} (Pred) | Mallows’s C_{P} | S | A | C |
---|---|---|---|---|---|---|---|---|

3 | 88.9 | 86.5 | 323,492,722.0 | 85.0 | 15.7 | 4136.8 | X | |

3 | 88.7 | 86.3 | 374,906,004.8 | 82.6 | 16.2 | 4176.2 | X | |

4 | 94.4 | 92.7 | 199,192,722.4 | 90.8 | 5.0 | 3053.5 | X | X |

**A**= Clearance,

**B**= Number of Grooves,

**C**= Groove Depth,

**D**= Tube Wall Thickness Reduction.

Prediction Method | Predicted Maximum Joint Strength |
---|---|

Taguchi Method | Mean = 51,199.00 N (s = 729 N) SNR = 96.1 dB |

Stepwise Regression | 51,307 N |

Run# | Max. Joint Strength (N) | Max. Joint Strength Mean (N) |
---|---|---|

1 | 44,013.75 | $\stackrel{-}{x}$ = 43,861.75 ($\stackrel{-}{s}$ = 424.45) 95% C.I. (43,334.73, 44,388.77) Coefficient of Variation = 0.0098 |

2 | 43,218.75 | |

3 | 44,392.50 | |

4 | 43,813.75 | |

5 | 43,870.00 |

**Table 17.**Random Forest trial statistics to fit the saturated L

_{9}(3

^{4}) OA joint strength dataset.

N | Mean | Std. Deviation | Std. Error Mean | 95% Confidence Interval | ||
---|---|---|---|---|---|---|

Lower | Upper | |||||

MSR | 10 | 17,843,680 | 1,115,982 | 352,904 | 17,045,354 | 18,642,006 |

VE | 10 | 85.13 | 0.93 | 0.29 | 84.47 | 85.80 |

MSE A | 10 | 8.03 | 0.75 | 0.24 | 7.50 | 8.57 |

MSE B | 10 | 25.06 | 0.61 | 0.19 | 24.62 | 25.50 |

MSE C | 10 | 3.74 | 0.99 | 0.31 | 3.03 | 4.45 |

MSE D | 10 | 33.21 | 0.95 | 0.30 | 32.53 | 33.88 |

**MSR**= Mean of Squared Residuals,

**VE**= Variation Explained (%),

**MSE**= Mean Squared Error:

**A**= Clearance,

**B**= Number of Grooves,

**C**= Groove Depth,

**D**= Tube Wall Thickness Reduction.

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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Boulougouras, P.; Besseris, G.
Lean-and-Green Strength Performance Optimization of a Tube-to-Tubesheet Joint for a Shell-and-Tube Heat Exchanger Using Taguchi Methods and Random Forests. *Processes* **2023**, *11*, 1211.
https://doi.org/10.3390/pr11041211

**AMA Style**

Boulougouras P, Besseris G.
Lean-and-Green Strength Performance Optimization of a Tube-to-Tubesheet Joint for a Shell-and-Tube Heat Exchanger Using Taguchi Methods and Random Forests. *Processes*. 2023; 11(4):1211.
https://doi.org/10.3390/pr11041211

**Chicago/Turabian Style**

Boulougouras, Panagiotis, and George Besseris.
2023. "Lean-and-Green Strength Performance Optimization of a Tube-to-Tubesheet Joint for a Shell-and-Tube Heat Exchanger Using Taguchi Methods and Random Forests" *Processes* 11, no. 4: 1211.
https://doi.org/10.3390/pr11041211