Quality and Reliability Engineering International SPECIAL ISSUE ARTICLE Statistical Procedure for Panel Block Assembly in Shipbuilding Deborah Otero1 Ricardo Cao2 Vicente Blasco3 Álvaro Brage3 Javier Tarrío-Saavedra2 Salvador Naya2 1 Unidade Mixta de Investigación Navantia-Universidade da Coruña, Ferrol, Spain 2 Grupo MODES, Departamento de Matemáticas, CITIC, Universidade da Coruña, A Coruña, Spain 3 Dimensional Control and Alignment, Navantia, Ferrol, Spain Correspondence: Javier Tarrío–Saavedra ([email protected]) Received: 22 October 2023 Revised: 6 November 2024 Accepted: 7 November 2024 Funding: This research was supported by GAIN (Xunta de Galicia) and Navantia company (SEPI), in the framework of the UDC - Navantia joint Research Unit, with the project “Shipyard 4.0. The Shipyard of the Future” and Centro Mixto de Investigación (CEMI) Navantia-UDC, with reference IN853C 2022/01. This research has been also supported by the Ministerio de Ciencia e Innovación grant PID2020-113578RB-100 and PID2023-147127OB-I00, the Ministry for Digital Transformation and Civil Service under Grant TSI-100925-2023-1, the Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2020-14 and ED431C 2024/014), and by the CITIC, also funded by the Xunta de Galicia through the collaboration agreement between the Consellería de Cultura, Educación, Formación Profesional e Universidades and the Galician universities for the reinforcement of the research centers of the Galician University System, CIGUS, with reference ED431G 2023/01. Funding for open access charge: Universidade da Coruña/CISUG. Keywords: block assembly | panel block | probability | sensitivity analysis | shipbuilding | statistical modeling | statistical simulation ABSTRACT A statistical procedure to estimate the probability of successful sliding of transverse elements through the longitudinals in shipbuilding panel block assembly is proposed. It consists of developing a custom statistical solution to control the quality of shipbuilding block assembly process, which helps to meet the requirements of production time, cost, and resources consumption. This proposal addresses a critical shipbuilding challenge: the panel block assembly process, which involves inserting transverse pieces through panels containing longitudinal components. This statistical procedure estimates the probability of successful block assembly before the process starts, taking into account inputs such as panel dimensions, panel structure, and transverse stiffener. A comprehensive simulation study has been performed to evaluate the statistical procedure performance. In addition, an actual database obtained from Navantia shipyards has been used to obtain information about the mean values and dispersion of the block assembly parameters. Finally, a sensitivity analysis is applied in order to obtain information about the most critical inputs for process improvement. This statistical tool proposes an alternative to evaluate the proficiency of shipyards to perform panel block assembly process during the vessel construction. The identification of those critical variables in the panel assembly process and the quantification of their influence in the studied process are goals that have been also achieved. 1 Introduction Shipbuilding has experimented important changes over the last decades due to the increasing market competition [1, 2] and the upcoming of the so called Industry 4.0, involved to industry digitalization [3–5], stressing those dealing with robotics and IoT [6], augmented reality [7], simulation [8], artificial intelligence, big data and analytics [9, 10]. In this framework, shipyards have to improve continuously their products, processes and production facilities. Specifically, this study has developed under the “Dimensional Control Project”, in the framework of Joint Research Unit Navantia - University of A Coruña [11–13], where statistical tools are applied in order to automate and improve the shipbuilding production process, in which metrology plays a This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes. © 2024 The Author(s). Quality and Reliability Engineering International published by John Wiley & Sons Ltd. Quality and Reliability Engineering International, 2025; 41:689–703 https://doi.org/10.1002/qre.3691 689 of 703 Shipbuilding is one of the most complex production systems in industry because of the huge diversity and number of elements involved in the production process [2, 16–20]. In fact, vessels consist of numerous parts, blocks and subsystems. Moreover, nowadays, shipyards work at the request of the clients. Given the great variety of needs that customers have, the design of each boat is different from the previous one. This way of doing makes the degree of shipbuilding automation much lower than in other industries such as automotive. Indeed, unifying all the processes and production line techniques that are applied in the different intermediate products is not seen currently possible. Assuming the large number of sources of variability involved in not automated processes, it is absolutely necessary to implement procedures to ensure the quality of actions and products [21]. Therefore, performing quality control during assembly in shipbuilding is extremely recommended, since improving the accuracy through the production process is the most effective way to improve results [22, 23]. In the shipbuilding industry, accuracy improvement is performed by applying statistical techniques to control, monitor and continuously improve production design and standardized working methods [9, 24–30]. The aim is to reduce the process variation and maximize the productivity [31]. The improvement of the accuracy in vessel production allows to simplify the processes, eliminating accumulated errors corresponding to the early fabrication and assembly stages, minimizing the need of skilled staff, and thus promoting mechanization and ship quality increasing [22, 23]. One of the most complex and critical steps in vessel production is the fitting of transverse elements during the panel block assembly process [2, 32]. This process requires a high dimensional accuracy and precision, only possible through an exhaustive control of those more critical dimensions and an adequate process design. Indeed, the proposal of a statistical methodology that identifies the most influential variables in the process accuracy and precision is absolutely necessary in order to define a proper design for the panel block assembly process. Accordingly, the aim of this paper is to provide a statistical methodology for the analysis and improvement of this process, that estimates the probability of correct panel block assembly from the original block dimensions and, moreover, allows to identify those most influencing variables and their effects over block assembly probability. In order to illustrate the present proposal, a real case study of panel block assembly in the Navantia shipyard (Ferrol, NW Spain) has been performed and shown. The main activity of the shipyards analyzed in this study is the design and build of warships and their control systems. Specialized in the custom manufacturing of one-of-a-kind vessels, Navantia factory in Ferrol is considered as an international reference shipyard. This specialization needs the introduction of automated and flexible systems of manufacturing, which can be easily reconfigurable. This shipyard is now in a transformation process to improve production processes and modernizing its manufacturing facilities. 690 of 703 Its aim is to get more automated or robotized processes through the implementation of digital production control systems. Thus, improvement of the quality, and reduction in costs and working time are intended. These are also the aims of the present proposal, applied to this specific case study. It consists on developing a statistical procedure that allows estimating the probability of sliding the transverse elements through the longitudinals at the beginning of the panel block assembly process. This work is organized as follows. In the Section 2, the panel block assembly process developed in the case study shipyard is described in detail. The statistical procedure developed to estimate the probability of correct assembly of longitudinal and transverse elements in the framework of the panel block assembly process is presented in Section 3. In Section 4, a comprehensive simulation study is included to evaluate the proposed statistical methodology. In addition, a real case study is presented where the proposed statistical procedure is applied to real data provided by the shipyard. Finally, Section 5 contains the results of a sensitivity analysis. It has been performed to identify those more influential dimensional variables in the panel block assembly process on the probability of correct assembly. This provides important information for process improvement. 2 Panel Block Assembly Process Analysis There are different panel block assembly methods [23] in accordance with each shipyard. Among all those methods, the panel assembly procedure is the standard and most popular method for panel block assembly [33, 34]. Taking into account the wide variety of methods, it is necessary to describe the current panel block assembly process (see Figure 1) in our case study shipyard. The panel block assembly process begins in the panel assembly line. This line is one of the most important processes in the shipyard. Ship panels, steel plates butt-welded together with longitudinal stiffeners, are the basic building blocks of well over 60% of the interim products of typical commercial ships [35]. The steel plates, coming from main storage of shipyard, are cut in a plasma cutting machine. They have to meet all the required specifications in order to be assembled at the flat panel assembly line. The process begins by joining and welding the steel plates with one-sided welding technology to form a flat panel. Afterward, the positions of the longitudinal stiffeners are marked. Those positions are to be free of primer paint and oxides. Thus, previously, those positions of the flat panel have been grit blasted. The next step is the fitting and welding of the longitudinals. The first longitudinal is fitted manually. Then the following longitudinals are automatically fitted on the flat panel. The longitudinals are fitted parallel to each other in the same direction, with a right distance between them. It should be noted that the flat panel assembly line is probably the most automated line in the shipyard. Once the previous process is finished, transverse elements are fitted to the panel, which results in a panel block. This process is almost impossible to be automated since there are not two equal panel blocks in vessel projects in shipbuilding industry, and even the transverse elements are defined by different geometries. Quality and Reliability Engineering International, 2025 10991638, 2025, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/qre.3691 by The University Of Newcastle, Wiley Online Library on [27/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License critical role. In fact, this project involves measurements acquisition and traceability study, including also the selection of critical variables, choice of measurement instruments, and everything dealing with the plates and block dimensional control [14, 15]. Panel block assembly process. FIGURE 2 Illustrative information about the the block assembly process (right) and detail of the assembly between longitudinal and slot, which are part of panel and transverse items, respectively. The sliding of transverses through the longitudinals is one the most difficult and critical steps in the panel block assembly process. This is due to the scallops of the transverses are very narrow, in addition to the different errors which can occur during the panel assembly procedure. Specifically, the transverses have a gap with a minimal clearance of 1.5 mm (see Figure 2). Therefore, the width of scallops in each transverse is the thickness of longitudinal plus 3 mm (1.5 mm each side). Furthermore, in the panel assembly process can take place different dimensional errors due to five factors: raw materials, cutting, fitting, welding, and straightening after welding [33, 36]. The above mentioned process errors can produce many reworks and a bottleneck in the production. In fact, the pushing of the transverses over the longitudinals depends on the built-in quality. When this task is achieved, the accuracy of the panel block can be regarded as being assured. This work shows the specific case study described in Figure 2b, in which the block assembly is performed between two main pieces, panel, and transverse. This specific case sakes for illustrating the statistical procedure proposed, which can be extended to more complex pieces. In addition, in order to show from the very beginning those dimensional variables that define panel and transverse in the framework of Navantia company, the schemes of panel (composed of four longitudinals) and transverse jointly which the corresponding measurements taken by the shipyard are included in Figure 3. Moreover, Figure 4 shows two details of panel–transverse assembly, including the measurements of which depends the proposed statistical process. These dimensional measurements are taken from the shipyard databases records in order to help to develop a statistical procedure to estimate the clearance panel-transverse and thus the probability of successful assembly. All these dimensional variables, which are assumed critical to block assembly quality, are described in next sections. 3 Description of the Statistical Methodology Any work process composed of repeatable actions, without changes in the facilities and skills of the workers, provides products defined by variable characteristics that can be modeled as random variables. Further, the measurements obtained for any 691 of 703 10991638, 2025, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/qre.3691 by The University Of Newcastle, Wiley Online Library on [27/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License FIGURE 1 In the framework of the present case study, measurements recorded by the shipyard for panel and transverse elements are shown. FIGURE 4 Panel and transverse dimensional variables that are used in the block assembly statistical procedure for estimating the clearance paneltransverse and the probability of successful assembly. work process, when plotted by frequency of occurrence versus magnitude, generally follows the Gaussian distribution [37]. The proposed statistical procedure assumes independent observations and Gaussian distribution for all the process variables, but Gaussianity could be relaxed if more plausible distribution models can be formulated based on empirical data. We start by defining a simple model to estimate the probability to slide the transverse elements through the longitudinals at the beginning of the process. We assume that the flat panel is flat, the scallops are perfectly perpendicular and have sufficient height. In addition, the number of longitudinals and the scallops is considered to be constant. Let π be the number of longitudinals or scallops. In the following, a description of the assumptions about the variables of the model is presented. In order to help to illustrate the study case, an overview of these variables, including the corresponding symbol and a short description, is presented in Table 1. Firstly, the random variables that define the panel are described for more information see Figure 4. Namely, let ππ be the distance from base edge to left edge of the π-th 692 of 703 TABLE 1 Symbol Meaning of variables of the statistical procedure. Description π1 Distance from base edge to the first longitudinal ππ Distance between longitudinals πΏ1 Panel width ππ Inclination of the longitudinals π1,1 Distance from the edge to the first slit on transverse Δπ Scallop width of the transverse ππ Distance between two adjacent scallops πΏ2 Transverse width longitudinal, with π = 1, … , π. It is assumed that the distance from base edge to the first longitudinal, π1 , and the distance between longitudinals, ππ = ππ+1 − ππ , with π = 2, … , π − 1, can be approximated by π1 ∼ π(π + π1 , π1 ) and ππ ∼ π(π + π2 , π2 ), respectively, where π is the nominal distance from base edge to the first longitudinal and π is the nominal distance between Quality and Reliability Engineering International, 2025 10991638, 2025, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/qre.3691 by The University Of Newcastle, Wiley Online Library on [27/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License FIGURE 3 Meaning of the parameters of the statistical procedure, in terms of mean and standard deviation. Parameter description Related dimensional variables π1 Mean of the distance from the first longitudinal line to the ridge π1 π2 Mean of the difference between the actual value and the nominal value of the distance between longitudinals (hypothesis that π2 = 0 is really accepted) ππ π3 Mean of the width of the panel (assumed equal to 0) πΏ1 π4 Mean of the difference between the actual and nominal values of the distance from the beginning to the end of the first notch Δπ π5 Mean of the difference between actual and nominal value of the distance from the end of one notch to the beginning of the next one (π5 = 0 is assumed) ππ π6 Mean of the difference between the actual and nominal values of the distance from the edge to the beginning of the π−th notch (π6 = 0 is assumed) π1,π π7 Transverse piece width mean (π7 = 0 is assumed) πΏ2 π8 Mean of the difference between real and nominal value of the angle formed by the longitudinal elements with the horizontal plane ππ π1 Standard deviation of the distance from the first longitudinal line to the ridge π1 π2 Standard deviation of the difference between the actual value and the nominal value of the distance between longitudinals (π2 = 0 is really accepted) ππ π3 Standard deviation of the width of the panel (π3 = 0 is assumed) πΏ1 π4 Standard deviation of the difference between the actual and nominal values of the distance from the beginning to the end of the first notch Δπ π5 Standard deviation of the difference between actual and nominal value of the distance from the end of one notch to the beginning of the next one (π5 = 0 is assumed) ππ π6 Standard deviation of the difference between the actual and nominal values of the distance from the edge to the beginning of the π−th notch π1,π π7 Transverse piece width standard deviation (π7 = 0 is assumed) πΏ2 π8 Standard deviation of the difference between real and nominal value of the angle formed by the longitudinal elements with the horizontal plane ππ Parameter the left sides of each pair of adjacent longitudinals. In addition, π1 is the mean of the distance from the first longitudinal line to the ridge, whereas π2 is the mean of the difference between the actual value and the nominal value of the distance between longitudinals, being π1 and π2 are the corresponding standard deviations (the value of these parameters can be estimated from retrospective datasets in Navantia, see Table 2). Moreover, let πΏ1 be the panel width approximated by πΏ1 ∼ π(πΏ + π3 , π3 ), where πΏ is the nominal panel width, π3 and π3 the mean and standard deviation of the panel width (see Table 2). Furthermore, let ππ , for π = 1, … , π, be the inclination of the π-th longitudinal, in other words, the angle of the π-th longitudinal with respect to the flat panel. Taking into account that the angle of the π longitudinals with the flat panel is approximately equal to , ππ β π π 2 , for π = 1, … , π, thus it is also assumed that ππ ∼ π( + π8 , π8 ), 2 2 where π8 and π8 are the mean and standard deviation of the difference between real and nominal value of the angle formed by the longitudinal elements with respect to the horizontal plane (Table 2). Regarding the transverse elements, let [ππ,1 , ππ,2 ] be the distances from edge to the beginning and end of the π-th slot, with π = 1, … , π. Then, Δπ = ππ,2 − ππ,1 , with π = 1, … , π, is the scallop width of the transverse. This random variable is normally distributed according to Δπ ∼ π(π + 2πΏ + π4 , π4 ), where πΏ is the nominal minimal clearance in the nominal gap around stiffener cut-out and π is the web thickness of longitudinals. In addition, π4 and π4 are the mean and standard deviation (respectively) of the difference between the actual and nominal values of the distance from the beginning to the end of the notch. On the other hand, the distance between longitudinals, π, is approximately equal to π β ππ+1,1 − ππ,2 + π + 2πΏ. Hence, if ππ = ππ+1,1 − ππ,2 , for π = 1, … , π − 1, is the distance between two adjacent scallops, then ππ β π − 2πΏ − π. In this way, the model assumes that ππ ∼ π(π − 2πΏ − π + π5 , π5 ). The π5 and π5 parameters are the mean and standard deviation of the difference between actual and nominal value of the distance from the end of one notch to the beginning of the next one. Moreover, the distance from the edge to the first slit on transverse, π1,1 β π − πΏ, is approximated by a normal distribution with mean π − πΏ + π6 and standard deviation π6 . Therefore, it is assumed that π1,1 ∼ π(π − πΏ + π6 , π6 ), where π6 and π6 of the difference between the actual and nominal values of the distance from the edge to the beginning of the first notch (Table 2). Finally, let πΏ2 be the width of the transversal stiffener. This variable is approximated by πΏ2 β½ π(πΏ + π7 , π7 ), with πΏ the nominal transverse width, whereas π7 and π7 are the mean and 693 of 703 10991638, 2025, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/qre.3691 by The University Of Newcastle, Wiley Online Library on [27/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License TABLE 2 The panel block assembly process will be successful if longitudinals slide through the slot on the transverse without intersection of the two elements. Therefore, depending on the inclination of longitudinals, three different cases can take place. Let π be the web thickness of longitudinal and π the longitudinal web height. Thus, the above mentioned cases are as follows: The differences between real and nominal values are modeled in all cases. We obtain the sample mean and standard deviation corresponding to each gap or difference between nominal and actual value. They are considered as parameters in our statistical method. This methodology provides an approximation of the probability of correct panel block assembly by using m Monte Carlo simulation trials. For practical purposes we have chosen of m = 1,000,000 in our simulations. The simulation algorithm is summarized as follows: slide (a) If ππ = 90β¦ , the transverses ] through the longitudinals [ when [ππ , ππ + π] ⊂ ππ,1 , ππ,2 . In other words, they have to satisfy that ππ,1 ≤ ππ and ππ + π ≤ ππ,2 . (b) If ππ < 90β¦ , then the following conditions must be met: ππ,1 ≤ ππ − π cos ππ and ππ + π ≤ ππ,2 . (c) If ππ > 90β¦ , the conditions to satisfy are: ππ,1 ≤ ππ and ππ + π − π cos ππ ≤ ππ,2 . Considering the three above mentioned cases, the transverse elements assembly process will be done correctly when all the following conditions are satisfied. The first condition is: ππ,1 ≤ ππ − π π(ππ ≤ 90β¦ ) cos ππ , π = 1, … , π (1) The second condition is: ππ + π − π π(ππ > 90β¦ ) cos ππ ≤ ππ,2 , π = 1, … , π (2) Accordingly, considering Equations (1) and (2), the probability of correct assembly can be estimated by π(πππππ πππππ ππ π πππππ¦) = π(ππ,1 ≤ ππ − π π(ππ ≤ 90β¦ ) cos ππ , ππ + π − π π(ππ > 90β¦ ) cos ππ ≤ ππ,2 , |πΏ1 − πΏ2 | < π, ∀ π = 1, … , π), (3) where π is the tolerable deviation threshold between the panel width and the transverse width. The probability of successful block assembly is calculated from the clearance between the panel and the transverse variable, which can be defined by min(π2,π − (ππ + π − π π(ππ > 90β¦ ) cos ππ )) π −max (π1,π − (ππ − ππ(ππ ≤ 90β¦ ) cos ππ )). π This variable is the critical to quality variable to define the successful block assembly, thus it is the one used in the sensitivity analysis. 4 Simulation Results In this section, a simulation study is performed to evaluate the statistical methodology described in the previous section. The free statistical software R has been used to implement this procedure [38]. The probability of assembly is estimated by simulation. The random variables (ππ , ππ,1 , ππ,2 ), π = 1, … , π, πΏ1 and πΏ2 are simulated from the distributions specified in Section 3. 694 of 703 1. Generate π1 ∼ π(π + π1 , π1 ), ππ = ππ−1 + ππ−1 , with ππ−1 ∼ π(π + π2 , π2 ), π = 2, … , π. π 2. Generate ππ ∼ π( + π8 , π8 ), π = 1, … , π. 2 3. Generate π1,1 ∼ π(π − πΏ + π6 , π6 ), ππ,2 = ππ,1 + Δπ , with Δπ ∼ π(π + 2πΏ + π4 , π4 ), π = 1, … , π; ππ,1 = ππ−1,2 + ππ−1 , with ππ−1 ∼ π(π − 2πΏ − π + π5 , π5 ), π = 2, … , π. 4. Generate πΏ1 ∼ π(πΏ + π3 , π32 ), πΏ2 ∼ π(πΏ + π7 , π7 ) 5. Check if the 2π + 1 conditions in (3) hold. 6. Repeat Steps 1-5 π times and compute the proportion of times in which the conditions for a correct assembly hold. The unknown means and standard deviations are estimated using two historical data sets provided by the shipyard. At this point, the data that support the findings of this study are available from request to Navantia shipyards of Ferrol. Restrictions apply to the availability of these data, which were used under license for this study. Data are available from the authors with the previous permission of Navantia. Specifically, panel data and transverse data are collected from two data sets provided by the shipyard. Figure 3 illustrates the measurements recorded in the shipyard for these two elements. The sample estimates obtained from the data supplied by the shipyard are collected in Table 3, where π is the sample size from which the mean and standard deviation estimates are obtained. The mean of several parameters in the model can be assumed equal to zero by applying the one sample t-test (p-value > 0.05) for the mean. This is the case of the deviation of distance between longitudinals (π2 ), the deviation of distance between two adjacent scallops (π5 ), the deviation of distance from the edge to the first slit on transverse (π6 ), and the deviation of transverse width (π7 ). Moreover, the following parameters are considered fixed values in the simulation: the web thickness of longitudinal (π = 11.2), the web height of longitudinal (π = 200), the gap around stiffener cutout (πΏ = 1.5), the distance from base edge to the first longitudinal (π = 729), the distance between longitudinals (π = 738), the panel width (πΏ = 5000) which is considered equal to width of transverse and the number of longitudinals (π = 4). With these values the probability to slide the transverses through the longitudinals correctly is quite low (π(πππππ πππππ ππ π πππππ¦) = 0.011558). This means that the shipyard is not currently able to perform successfully this type of panel block assembly process. The proposed statistical procedure can provide information about what are the most influential variables in the probability of correct assembly. Consequently, we can identify which combination of parameter Quality and Reliability Engineering International, 2025 10991638, 2025, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/qre.3691 by The University Of Newcastle, Wiley Online Library on [27/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License standard deviation (respectively) of the transverse piece width (Table 2). π Mean value Standard deviation Deviation of distance from base edge to the first longitudinal 11 π1 = 1.4545 π1 = 1.7529 Deviation of distance between longitudinals 18 π2 = −0.2778a π2 = 0.8264 π3 = 0 π3 = 0 Item Panel b Deviation of panel width 34 π8 = −0.5724 π8 = 0.9520 Deviation of distance from the edge to the first slit on transverse 20 π6 = −0.7000 a π6 = 2.2676 Deviation of scallop width of the transverse 85 π4 = −0.3376 π4 = 1.0742 66 π5 = −0.1545 a π5 = 1.3009 9 π7 = −1.5556 a π7 = 3.9721 Deviation of inclination of the longitudinals Transverse Deviation of distance between two adjacent scallops Deviation of transverse width a b It is accepted that the mean is equal zero. Given the lack of data, the parameters of this item are considered zero. values produces a high increase in the probability of correct panel block assembly process. In other words, the identification of these variables shows what magnitude needs to modified in order to continuously improve the process. This can be conducted by performing a sensitivity analysis. 5 Sensitivity Analysis Finally, in order to improve the analyzed panel block assembly process and to facilitate decision making in the shipyard, a sensitivity analysis has been performed. The aim of this study is to identify the variables which affect in a greater extent the probability of correct sliding between transverses and longitudinals. In this way, the model can provide valuable information about which are the critical variables and which are their optimal values in order to increase the probability of correct panel block assembly. These values will help to the shipyard to execute the correct actions in order to improve the process. The estimations of the parameters are obtained using the data sets provided by the shipyard. To perform the sensitivity analysis, the deviations between theoretical and real values are also statistically modeled as normal distributed variables, using the sample statistics as parameter estimates. Reproducing the scenarios of perfect accuracy and precision is necessary, taking into account that the quality and capability of a process can be characterized attending to its variability and location (assuming that all process improvement should be oriented to reduce the dispersion and correct the position). Thus, the potential capability of the panel assembly process can be analyzed properly. Consequently, some of these parameters, namely mean (π) and standard deviation (π), depending on each simulated scenario, have been fixed to zero with the aim to reproduce the ideal conditions of either perfect accuracy or perfect precision. As shown in Table 4, the value of the parameters is fixed to zero, target value of the studied variables. The different simulation scenarios are developed by fixing to zero one (π or π) or two parameters (π and π) of one critical variable. It is important to note that the values of the remaining parameters are the sample estimates obtained from the real dataset. The probabilities of sliding between transverses and longitudinals are calculated for each scenario (see Table 4). The parameter which offers the best chance of increasing the probability is the mean corresponding to the deviation for inclination of the longitudinals (π4 ), that is, if the angle of the longitudinals with respect to the panel plane were 90β¦ in the mean, then the probability to slide the transverse elements through the longitudinals correctly would increase most. Further, in the scenario defined by the absence of systematic errors in the variables of the model, the probability would be equal to 0.353347. Thus, the recommendation is that the shipyard improves the process methodology, focusing the efforts in all the actions related to the longitudinal angles. In fact, the shipyard has recently begun to implement such improvement procedure, taking into account the above mentioned results. The method shown above has been developed by the authors themselves to evaluate the sensitivity of various parameters of the proposed model on the response variable, the probability of successful block assembly between panel and transverse. This is, therefore, one of the contributions of the work: a very simple sensitivity analysis model, made ad hoc for the specific case that concerns us, the block assembly model in the specific framework of shipbuilding. However, nowadays there is a wide range of procedures to evaluate the importance of each of the parameters (as well as their interactions) that affect one or several response variables, related to each other by means of an expression or transfer function. All these procedures are included in the so-called sensitivity analysis [39], currently one of the most important areas of statistics and characterized by active research and growth [40, 41], due to the current importance of the evaluation of models and algorithms in the industrial field, among others. This research has also focused on computational statistics; in fact, in recent years important open-access computational tools have been developed that allow users to employ sensitivity analysis techniques in an intensive, fast, safe, reliable, and efficient way. In this regard, within the framework of R software, the 695 of 703 10991638, 2025, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/qre.3691 by The University Of Newcastle, Wiley Online Library on [27/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License TABLE 3 Parameters estimated from the two data sets provided by the shipyard, including a short description and the sample size from which mean and standard deviation are obtained. Changed parameter π=π π=π π = π and π=π Deviation of distance from base edge to the first longitudinal 0.011558 0.011558 0.011558 Deviation of distance between longitudinals 0.011558 0.013486 0.013486 Deviation of panel width 0.011558 0.011558 0.011558 Deviation of inclination of the longitudinals 0.277368 0.011698 0.28774 Deviation of distance from the edge to the first slit on transverse 0.011558 0.011558 0.011558 Deviation of scallop width of the transverse 0.024466 0.011248 0.038046 Deviation of distance between two adjacent scallops 0.011558 0.05562 0.05562 Deviation of transverse width 0.011558 0.011558 0.011558 Item Panel Transverse sensitivity package is the most complete and documented [42], in addition to the sensobol package [43] which is, although less complete, of simple, fast and intuitive to use, among many other computational alternatives. These R packages have been used to enrich the simulation study of the present work, taking into account the accessibility of these computational tools, in addition to the complete documentation of each of their functions. Specifically, on the one hand, the application of the Morris screening-type method [44] has been proposed and, on the other hand, the implementation of a variance-based procedure, as is the case of the Sobol indices. In this case, they are estimated from the first order and total order estimators proposed by Azzini et al. [45], obtained by means of Monte Carlo procedures. In order to simplify the application of the aforementioned procedures, we have proposed as response variable the clearance of the block assembly between panel and transverse, from which the block assembly probability was calculated in the previous calculations. The clearance must be positive for success assembly to take place. First, the values of a series of model parameters have been fixed, taking into account real sample values and the experience of the shipyard workers. Specifically, the values shown in Table 3 are taken. We also assume as constants the web thickness of longitudinal (π = 11.2), the web height of longitudinal (π = 200), the gap around stiffener cut-out (πΏ = 1.5), the distance from base edge to the first longitudinal (π = 729), the distance between longitudinals (π = 738), the panel width (πΏ = 5000), and the number of longitudinals (π = 4). As for the parameters affecting sliding between panel and transverse, 16 have been taken into account. Table 5 shows the model parameters, already mentioned in Table 1, including the three nomenclatures used: the one indicated in the methodology section of this article, the equivalent used by the computational tools (sensitivity package) to perform the Morris design, and the one corresponding to the outputs of the R sensobol package for the estimation of the Sobol indices. On the other hand, it is important to note that, in this work, it has been assumed 696 of 703 that the parameters of interest follow a normal distribution, estimating the means and standard deviations of each parameter from sample data (see Table 3). Indeed, the dimensional measurements of manufactured parts in industry (as in Naval industry) very often follow a normal distribution, taking into account they are the result of many small, independent random effects related to the 6 M’s (manpower, mother nature, machines, materials, measurements, and methods). Thus, assuming the Central Limit Theorem, these effects can give rise to a normally distributed variable. Therefore, Table 5 includes the parameters of the normal distribution, mean and variance, which follow each of the influential variables in the model studied (also called parameters), according to the values indicated in Table 3. Alternatively, this work also shows the results obtained assuming a uniform distribution for each of the parameters, a less restrictive assumption when no further information is available on the variables apart from the limits within which their values are distributed. Table 5 also shows the lower and upper limits for each parameter, constructed by subtracting and adding the standard deviation, respectively, to the corresponding mean, simulating tolerance levels for these values, a common practice in this type of industry. The Morris design belongs to the group of screening procedures, whose objective is to identify those factors most relevant to a given response. The Morris method, by calculating the π∗ and π [42] estimators, provides information about the most influential factors on the response (high π∗ and π) and whether these factors have a linear or nonlinear effect (and/or with the presence of interactions). Specifically, π∗ is the sensitivity measure defined by π∗ = πΈ|ππ |, where ππ is the effect of factor π on the response variable and πΈ the expected value. On the other hand, π is the estimator of the standard deviation of the effect of factor π on the response. If the factors, in our case parameters of the block assembly model, have a non-linear effect on the response (and/or present interactions), they will be characterized by a relatively high pair (π∗ , π). Otherwise, although π∗ is high, π is low, this is an indication of the presence of only linear effects. For more information about the expression and description of the Morris model, see Da Veiga et al. [39]. Quality and Reliability Engineering International, 2025 10991638, 2025, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/qre.3691 by The University Of Newcastle, Wiley Online Library on [27/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License TABLE 4 Probability to slide the transverses through the longitudinals setting to zero the mean or/and the variance of the deviations actualnominal in the model. First, the nomenclature used to name each parameter whose influence on the magnitude of the panel-transverse clearance to be studied Gaussian assumption, π΅(π, π) Parameters nomenclature Uniform assumption, πΌ(π, π) Morris Sobol π π π=π−π π=π+π π1 π1 π₯1 π + π1 π1 π + π 1 − π1 π + π 1 + π1 π1 π2 π₯2 π + π2 π2 π + π 2 − π2 π + π 2 + π2 π2 π3 π₯3 π + π2 π2 π + π 2 − π2 π + π 2 + π2 π3 π4 π₯4 π + π2 π2 π + π 2 − π2 π + π 2 + π2 π1 π5 π‘βππ‘π1 πβ2 + π8 π8 πβ2 + π8 − π8 πβ2 + π8 + π8 π2 π6 π‘βππ‘π2 πβ2 + π8 π8 πβ2 + π8 − π8 πβ2 + π8 + π8 π3 π7 π‘βππ‘π3 πβ2 + π8 π8 πβ2 + π8 − π8 πβ2 + π8 + π8 π4 π8 π‘βππ‘π4 πβ2 + π8 π8 πβ2 + π8 − π8 πβ2 + π8 + π8 π1,1 π9 π¦1 π − πΏ + π6 π6 π − πΏ + π 6 − π6 π − πΏ + π 6 + π6 Δ1 π10 π·πππ‘π1 π + 2πΏ + π4 π4 π + 2πΏ + π4 − π4 π + 2πΏ + π4 + π4 Δ2 π11 π·πππ‘π2 π + 2πΏ + π4 π4 π + 2πΏ + π4 − π4 π + 2πΏ + π4 + π4 Δ3 π12 π·πππ‘π3 π + 2πΏ + π4 π4 π + 2πΏ + π4 − π4 π + 2πΏ + π4 + π4 Δ4 π13 π·πππ‘π4 π + 2πΏ + π4 π4 π + 2πΏ + π4 − π4 π + 2πΏ + π4 + π4 π1 π14 ππ‘π1 π − 2πΏ − π + π5 π5 π − 2πΏ − π + π5 − π5 π − 2πΏ − π + π5 + π5 π2 π15 ππ‘π2 π − 2πΏ − π + π5 π5 π − 2πΏ − π + π5 − π5 π − 2πΏ − π + π5 + π5 π3 π16 ππ‘π3 π − 2πΏ − π + π5 π5 π − 2πΏ − π + π5 − π5 π − 2πΏ − π + π5 + π5 Article Note: In addition, assuming normal distribution, the mean and standard deviation of each parameter, calculated from the sample values shown in Table 3, are shown. Finally, assuming uniform distribution for the parameters, the lower and upper limits for a uniform distribution are also indicated. FIGURE 5 The scatterplot of the effects of each of the parameters on the clearance between panel and transverse pieces in the block assembly process is shown. The vertical axis shows the estimates of the standard deviation of the effect of each parameter on the response variable, while the horizontal axis shows the mean of the absolute value of the effect of each parameter. Figure 5 shows the graphical output of the application of the Morris design and procedure for the estimation of the most influential parameters on the clearance size during the block assembly process in the shipbuilding industry. Tentatively, following some of the guidelines shown in De Veiga et al. [39], the parameters π (number of replications of the model) equal to 10, and levels (or number of different values for each parameter in the design) equal to 5 have been defined as inputs of the Morris model. As a result, the most influential parameters due to their high π and π∗ values are, above all, those related to the angles of the panel longitudinals (X5 also called π1 , X6 also called π2 ), the scallops width of the transverse (X10, X11 and X12), in addition to the distance between two adjacent scallops (X14). The fact that they all align, to a greater or lesser extent, indicates that the effect of each of them 697 of 703 10991638, 2025, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/qre.3691 by The University Of Newcastle, Wiley Online Library on [27/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License TABLE 5 is indicated. Sobol indices are variance-based methods, that is, they give an estimate of the sensitivity of the response variable due to the variation of an input variable or parameter, by quantifying the variance produced in the output caused by the variation in the parameter. If the response variable is defined as π as a function of π parameters, π = π(π1 , π2 … ππ ), the first order effect of the parameter ππ on the response π can be denoted as ππ΄π ππ [πΈπ₯∼π (π|ππ )], where π∼π denotes all factors except the factor ππ . That is, the main or first-order effect can be defined as the contribution of ππ alone to the variance of the response variable π, averaged from the variances of the other parameters. If the main effects are scaled by dividing by the total variance, Sobol’s ππ indices are obtained. These indices do not include the effect of interactions, second order effects denoted by πππ . Therefore, total indices, ππ , are also defined, which take into account total variability existing in π and due to the factor ππ together with all its interactions with the other parameters [46]. For more information on the definition and expression of these indices, see Da Veiga et al. [39] and Puy et al. [43]. In our particular case, in addition to calculating the main effects of each parameter on the response, it is important to estimate the effect of the interactions, therefore, both ππ and πππ indices will be calculated, in addition to ππ . For this purpose, as indicated in Puy et al. [43], it is necessary, on the one hand, to have a sample design that orders the various parameter values in a multidimensional space and, on the other hand, an estimator to obtain the ππ , πππ , and ππ effects. In this work, we have used the sampling designs available in the sensobol package, which arrange all the parameter values through the construction of a series of matrices (π) (π) named A, B, Aπ΅ and Bπ΄ . As for the estimator used, following the scheme indicated in Puy et al. [43], the estimator proposed by Azzini et al. is used, which allows both the estimation of firstorder and total second-order effects [43, 45] (in our case, including only second-order interactions). Regarding the sampling plan, a sample of size π = 213 was taken, from which the first and second order effects were estimated by bootstrap resampling composed of 103 resamples [43], which also allows the calculation of confidence intervals (in this case at 95%). Next, before estimating the first-order, second-order and total indices, a descriptive study of the effects of each parameter on the response, the existing clearance between panel and transverse when block assembly, is performed (Figure 6). Figure 6 shows the scatterplots with the heat map effects and mean effect (in red) of each parameter on the value of the clearance. It is observed that the clearances tend to be negative, with a median of −5.8, indicating the difficulty to perform a successful sliding (when the clearance is greater than 0). On the other hand, if the evolution of the mean of the slack (y) is observed as a function of the parameters π1 , π2 , π3 , and π4 (all inclination angles of each one of the longitudinals of the panel) are identified as the most influential variables in the response. In fact, a parabolic trend is observed in the mean of π¦ (in red) for all of them. Some increasing trend on π¦ as a function of parameters is also observed for the scallop width of the transverses parameters (Δ1 , Δ2 , Δ3 , 698 of 703 and Δ4 ), in addition to the distance parameter between two adjoining scallops (π1 , π2 , and π3 ). Similarly, it is important to note that positive clearances (and thus successful sliding) are obtained for central values of the parameters ππ , Δπ , and ππ , that is, for values around the mean values, which correspond to the means of the tolerance intervals. Considering that the most influential parameters are the longitudinal angles, for the sake of simplicity (showing all possible interactions in the same plot would be impossible), a descriptive study of the influence of the interactions of each pair ππ - ππ on the clearance (y) is shown, through the scatterplots shown in Figure 7. It is observed that the clearance tends to be larger the more central are the values of the angles ππ and ππ , besides certain indications of the existence of interaction effects between the parameters are identified. In fact, the clearance decreases when one of the two parameters is high or low, moreover, at small values of ππ - ππ , or large of both, the clearance decreases. Similar patterns can be found when studying the joint variation of other parameters such as ππ and Δπ . Therefore, the estimation of second-order effects is supported. Next, the first and second order Sobol indices, including ππ , ππ,π , and ππ , are calculated. The results of the calculation of ππ and ππ for each parameter are shown in Figure 8. Considering the explained variability, the main effects explain 61% of the model, being, therefore, the most influential, although the interactions are of great importance, as can be seen by the difference between the ππ indices (which include the effects of the iteration of parameter i with the others) and the ππ . All the first-order effects were significant, except π₯1 (distance from the panel edge to the first longitudinal) and π¦1 (distance from the edge to the first recess). Among all the parameters, by far the most influential are the panel longitudinal angles (π‘βππ‘π1, π‘βππ‘π2, π‘βππ‘π3, and π‘βππ‘π4), followed, in order of importance, by the notch widths (π·πππ‘π1, π·πππ‘π2, π·πππ‘π3, and π·πππ‘π4) and the distances between each pair of notches (ππ‘π1, ππ‘π2, and ππ‘π3). The first-order effects of the distances between longitudinals (π₯2, π₯3, π₯4) are very small compared to the effects of the aforementioned parameters. In addition to the first-order effects, the total effects of each of the parameters on the response, ππ , are estimated, which also include the second-order effects, πππ . It is observed that the total effects tend to be at least twice the first-order effects. This is indicative of the relevance of the effects of interactions between pairs of parameters. Figure 8 shows that the significant total effects (compared to the blue boundary) are those related to the parameters π‘βππ‘π1, π‘βππ‘π2, π‘βππ‘π3 and π‘βππ‘π4. Therefore, those interactions of these parameters with the others will be more significant and relevant. In fact, if one looks at the 15 highest second-order effects in mean value (Figure 9), almost all (except one) correspond to interactions in which at least one of the parameters π‘βππ‘π is included. Therefore, the longitudinal angles are the critical parameters in the sliding process. Finally, in order to observe the influence of assuming one parametric distribution or another to model the effects of the parameters, we have alternatively assumed that these effects follow uniform, rather than normal, distributions. Tentatively, the upper and lower bounds of the uniform distributions have been assumed to be the results of adding and subtracting, respectively, the values of the standard deviations from the mean (Table 5). Quality and Reliability Engineering International, 2025 10991638, 2025, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/qre.3691 by The University Of Newcastle, Wiley Online Library on [27/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License may be nonlinear or subject to interactions. Taking the latter into account, in order to estimate the effect of these interactions, we propose the application of variance-based sensitivity methods, such as the calculation of Sobol indices, for instance. FIGURE 7 Scatterplot matrix of ππ - ππ parameters pairs for the clearance block assembly model. 699 of 703 10991638, 2025, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/qre.3691 by The University Of Newcastle, Wiley Online Library on [27/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License FIGURE 6 Scatterplots for each of the effects of the parameters on the response. The red line indicates the mean of the response variable. The value of the response is indicated through a heat map. First order effects, ππ , and total effects, ππ , of each block assembly parameter, assuming Gaussian distributions. FIGURE 9 Confidence intervals (95%) corresponding to the 15 higher second-order effects, πππ , of the parameters on the response, y, assuming Gaussian distributions. 700 of 703 Quality and Reliability Engineering International, 2025 10991638, 2025, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/qre.3691 by The University Of Newcastle, Wiley Online Library on [27/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License FIGURE 8 First order effects, ππ , and total effects, ππ , of each block assembly parameter, assuming uniform distributions. Figure 10 shows the corresponding first order and total order effects, assuming uniform distributions. It can be seen that the most relevant parameters coincide with those obtained assuming normal distribution, both in terms of first order and total order effects, although the total effects of the ππ‘π parameters tend to be larger, with the total effect of ππ‘π2 being significant. the probability of successful panel block assembly is estimated by Monte Carlo simulation. 6 The proposed model allows the users to identify the most critical variables on the probability of correct panel block assembly process. This is a valuable tool to identify the most important assignable causes of fail and the sub-processes that would have to be improved to achieve a higher probability of success. In the present case study, the most influencing variable on the probability of success is the angle of the longitudinals with respect to the panel plane, that has to be fixed at 90β¦ . Thus, the shipyard would have to begin the improvement process by controlling all the sub-processes related to the longitudinals inclination. Conclusions The main contribution of this work is the proposal of a new statistical procedure to estimate the probability of correct panel block assembly (correct sliding of the transverses through the longitudinals) in shipbuilding as a function of the critical variables of the process. This statistical tool proposes an alternative to evaluate the proficiency of shipyards to perform panel block assembly process during the vessel construction. Moreover, the identification of those critical variables and the quantification of their influence in the studied process are goals that have been also achieved. It is also important to note than this statistical proposal has been calibrated, taking into account the sample estimates obtained from a real case study performed in the Navantia shipyards. Specifically, a statistical procedure based on the panel block assembly geometry has been proposed, assuming normal distribution for the group of variables that best defines the problem. The variables included in the model are the differences between the theoretical and actual values of the distance from base edge to the first longitudinal, the distance between longitudinals, the panel width, the inclination of the longitudinals, the distance from the edge to the first slit on transverse, the scallop width of the transverse, the distance between two adjacent scallops, and the transverse width. The latter have been identified by the geometric characteristics of the process and the experience of the trained personnel of the shipyard. The geometric conditions at which the correct sliding between transverses and longitudinals is produced have been properly formalized. Taking into account the distribution, mean and variability of the variables in the process, The proficiency of the case study shipyard for performing a panel block assembly process has been evaluated by the proposed model. The parameters of the variables in the process have been estimated using a representative sample provided by Navantia. In order to complete the information about the most relevant algorithm parameters and parameter interactions, a sensitivity analysis of the panel block assembly model parameters has been carried out, assuming assembly clearance as a response variable. For this purpose, screening methods such as the one proposed by Morris and variance-based procedures such as Sobol’s indices have been applied. The latter indices were estimated using the estimators proposed by Azzini. As a result, the most relevant parameters have been identified as the angles of the longitudinals with the panel, ππ (also called π‘βππ‘π or π5 − π8) either in terms of main or first-order effects or taking into account the interactions. In fact, particularly significant are the interactions of the angles of the longitudinals with themselves, as well as with the parameters ππ (distance between scallops) and Δπ (width of scallops in the transverse), in that order. In this regard, it should be noted that the variations of the response due to interactions (second-order effects) correspond to 39% (the remaining 61% corresponding to firstorder effects). Therefore, in order to increase the clearance and, 701 of 703 10991638, 2025, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/qre.3691 by The University Of Newcastle, Wiley Online Library on [27/12/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License FIGURE 10 9. S. Li, D. K. Kim, and S. Benson, “A Probabilistic Approach to Assess the Computational Uncertainty of Ultimate Strength of Hull Girders,” Reliability Engineering & System Safety 213 (2021): 107688. 10. Y. Ao, Y. Li, J. Gong, and S. Li, “An Artificial Intelligence-Aided Design (AIAD) of Ship Hull Structures,” Journal of Ocean Engineering and Science 8, no. 1 (2021): 15–32. https://doi.org/10.1016/j.joes.2021.11.003 Acknowledgments The authors thank Carlos Blanco Seijo, from I+D+i of Navantia, for his help and comments. In addition, we would like to thank the guidance and work of the reviewers and editor. This research was supported by GAIN (Xunta de Galicia) and Navantia company (SEPI), in the framework of the UDC - Navantia joint Research Unit, with the project “Shipyard 4.0. The Shipyard of the Future” and Centro Mixto de Investigación (CEMI) Navantia-UDC, with reference IN853C 2022/01. This research has been also supported by the Ministerio de Ciencia e Innovación grant PID2020-113578RB-100 and PID2023-147127OB-I00, the Ministry for Digital Transformation and Civil Service under Grant TSI100925-2023-1, the Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2020-14 and ED431C 2024/014), and by the CITIC, also funded by the Xunta de Galicia through the collaboration agreement between the Consellería de Cultura, Educación, Formación Profesional e Universidades and the Galician universities for the reinforcement of the research centers of the Galician University System, CIGUS, with reference ED431G 2023/01. Funding for open access charge: Universidade da Coruña/CISUG. Data Availability Statement The data that support the findings of this study could be available on request from the corresponding author, J. T. 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