esa-sceva/satcom-chunk-collection huggingface dataset:
# Electrical Resistance Response to Strain in 3D-Printed Conductive Thermoplastic Polyurethane (TPU)
## 2 Materials and Methods  
### Sensor Evaluation Methods  
NinjaTek Eel test specimens were printed on a Prusa i3 MK2S FFF 3D-Printer (Prusa Research, Prague, Czech Republic). Print parameters used to fabricate the test specimens can be seen in Table 1. The geometry of the specimens can be seen in Table 2. The specimens were printed with the length and width in the x-y plane. The fabrication parameters were chosen based on trial and error as there exist no acceptable printing guidelines for printing NinjaTek Eel.  
A custom test rig, as seen in Figure 2, was developed to evaluate the electrical resistance response to strain. The setup consisted of two NEMA 17 stepper motors with lead screws driven by an Arduino Uno and an Arduino Motor Shield (Arduino, Turin, Italy). To measure the electric resistance, the Arduino Uno was set up to measure the current over a known resistance and the specimen.  
To validate the electrical resistance measurement in the test rig, resistors with known resistances were measured with a multimeter and placed in the test rig. The resistors with verified resistances of 4.16, 5.56, and 21.8 k\(\Omega\) were measured to 4.11, 5.49, and 21.8 k\(\Omega\), respectively, indicating that the test rig is capable of accurately measuring the resistance.  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Printer & Prusa i3 MK2S \\ Slicer & PrusaSlicer-2.5.1 \\ Nozzle Diameter & 0.6 mm \\ Nozzle temperature & 238 \({}^{\circ}\)C \\ Bed Temperature & 50 \({}^{\circ}\)C \\ Extrusion Multiplier & 1 \\ Max Volumetric Flow & 1 mm\({}^{3}\)/s \\ Part Cooling Fan Speed & 100\% \\ Layer Height & 0.2 mm \\ \hline \end{tabular}
\end{table}
Table 1: Fabrication parameters.  
\begin{table}
\begin{tabular}{c c} \hline
**Dimension** & **Value** \\ \hline Length & 120 mm \\ Width & 1.2 mm \\ Height & 2 mm \\ Cross-Section Area & 2.4 mm\({}^{2}\) \\ \hline \end{tabular}
\end{table}
Table 2: Specim geometry.  
To evaluate the electric resistance response to strain, a variation in tests was conducted to observe the behavior in different situations. The following tests were conducted:  
* Cyclic loading test--1000 cycles of strain were applied to the sensor. The sensor was strained to a strain of 0.5 at a strain rate of 0.306 s\({}^{-1}\) before being unloaded again.
* Initial cycle and strain rate test--The sensors were cyclically strained to a strain of 0.05, 0.1, 0.2, 0.5, and 1 before being unloaded, i.e., within the elastic region of the material [33]. This was carried out for 3 different strain rates; 0.306, 0.037, and 0.015 s\({}^{-1}\).
* Validation test--10 samples of the sensor were strained for 100 cycles up to a strain of 0.5 at a strain rate of 0.307 s\({}^{-1}\).
* Creep--The sensor was strained to 1 and maintained for 15 s before unloading the sensor and letting it rest for 15 s. This was carried out to evaluate any creeps in the sensor. The test was performed at a strain rate of 0.306 s\({}^{-1}\).
# Advances in Three Dimensional Bioprinting for Wound Healing: A Comprehensive Review
## 4 3D Bioprinting Techniques
### Laser-Based Bioprinting
#### 4.1.1 Stereolithography (SLA)  
SLA is prototyped by combining 2D polymer layers cured with UV laser light [102; 103]. Via sequential scanning by laser, the printed sheets are lowered, which allows the polymer to create one layer with a required thickness and to scan the following layer. Photopolymers converted into polymer chains bind to the next layer and form the structure. The resin that holds the printing scaffold during the process is removed when the printing is completed. SLA technology has an approximate resolution of 10 \(\upmu\)m, thus enabling the production of sensitive biomedical products [104]. This technology has advantages of both high-resolution and multi-layer printing quality in producing large print volumes in the range of 200-2000 mm. In addition, the printing product, formed due to the easy control over printing parameters, has a consistent and stable structure [105]. The limited light-curing hydrogel structure is one of the advantages of SLA techniques in the production of hydrogel composites. However, the need for supporting structures during printing and the final curing process is the main downside of SLA printing technology.  
In the field of bioprinting, SLA is highly preferred because of its high resolution. Micro stereolithography technology, which controls tiny spaces with precise beam control, is divided into two subgroups. The first is the scanning uSLA, in which UV is focused on the bioink surface and avoids disadvantageous parameters such as poor focusing and low resolution during scanning [106,107]. Mask projection, another 3D printing method, is achieved under radiation with the help of a patterned mask, leaving each layer of liquid bioink under the influence of the beam. These bioprinting systems allow the 3D printing of structures in skin applications, wound dressings, and applications such as microelectromechanical systems (MEMS) due to their excellent printability properties on very small areas [108, 109, 110].
## 4 Experimental Evaluation and Performance Analysis
### Concerning Users' Demands and Satisfaction  
Users hope to lower prices while shortening the maintenance time. This section only considers user interests. Therefore, using the experimental parameters shown in Table 3, the effects of different maintenance times and price weights on the calculation results were studied.  
Figure 6: The fitness curves of the genetic algorithm after operation. (**a**) Experimental parameters of No. 1. (**b**) Experimental parameters of No. 2. (**c**) Experimental parameters of No. 3. (**d**) Experimental parameters of No. 4. (**e**) Experimental parameters of No. 5.  
The change in users' satisfaction is shown in Figure 7, the changes in the maintenance time and price evaluation values under different parameters are shown in Figure 8, and the change in the fitness value is shown in Figure 9.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & \(\mathbf{\tau}\) & \(\mathbf{w_{t}}\) & \(\mathbf{w_{c}}\) & \(\mathbf{k_{t}}\) & \(\mathbf{k_{p}}\) \\ \hline No. 6 & 0 & 0.5 & 0.5 & 0.9 & 0.1 \\ No. 7 & 0 & 0.5 & 0.5 & 0.7 & 0.3 \\ No. 8 & 0 & 0.5 & 0.5 & 0.5 & 0.5 \\ No. 9 & 0 & 0.5 & 0.5 & 0.3 & 0.7 \\ No. 10 & 0 & 0.5 & 0.5 & 0.1 & 0.9 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Experimental parameters of the users.  
Figure 7: Iterative curves for user evaluations of the maintenance time and maintenance price. (**a**) Experimental parameters of No. 6. (**b**) Experimental parameters of No. 7. (**c**) Experimental parameters of No. 8. (**d**) Experimental parameters of No. 9. (**e**) Experimental parameters of No. 10.  
It can be seen from Figure 7 that, with an increase in the price weight, the satisfaction degree of the price increased. From Figure 8, the evaluation value of the maintenance price also increased, the corresponding evaluation value of the maintenance time decreased, and the evaluation value of the maintenance cost remained relatively stable. Obviously, the proportions in the goal value can be adjusted by assigning different weight coefficients, reflecting the results envisaged by the scheme decision maker when assigning the weight coefficients, such that the results of the simulation experiment are in accordance with the expectations.  
Figure 8: The changes in the evaluation value of the maintenance time, total maintenance cost, and price under different parameters. (**a**) Experimental parameters of No. 6. (**b**) Experimental parameters of No. 7. (**c**) Experimental parameters of No. 8. (**d**) Experimental parameters of No. 9. (**e**) Experimental parameters of No. 10.
## 8 Anonymity and Security Analysis
### Timing Privacy  
By using fake messages at variable interval times and message delays, it becomes super hard for the ADV to correlated messages being transmitted over the network as exhibited in Figure 12.
## 2 System Architecture
### Integration Process Workflow  
The workflow includes the processes for combining spatial data, acquired by the laser scanner in the form of a point cloud (spatial coordinates and normal vectors in each point) and the two-dimensional temperature map provided by the thermal camera, available as a temperature matrix. Before proceeding to the actual integration, it was necessary to have a post-processed point cloud, i.e., the registration of several range maps (by the well-known ICP algorithm) and all the post-processing operations have to be done previously.  
There are three main processes characterizing the workflow (see Figure 2): acquisition, geometrical calibration (subdivided into intrinsic and extrinsic calibration) and data fusion. The emphasis of this work was both on the extrinsic calibration and on the data fusion process, which were carried out by Matlab programming (Supplementary Materials).
# Performance Analysis of Two-Way Satellite-Terrestrial Relay Network with SWIPT
## 3 System Performance Analysis  
In this section, the exact expressions for instantaneous end-to-end throughput, average end-to-end throughput, and the proposed network's energy efficiency with SWIPT for SPNC protocol are obtained, respectively.
## 4 Example of Application: Performance Simulations using the EIPS framework
### Microwave System Configurations  
#### 4.2.1 Configuration A: ATMS-Type and Configuration B: AMSU-A-Type  
Configuration A corresponds to an existing MW instrument, the Advanced Technology Microwave Sounder (ATMS) (\"ATMS-type\") and configuration B corresponds to Advanced Microwave Sounding, Unit-A (\"AMSU-A-type\"). The spectral and radiometric characteristics of configuration A and B has been kept exactly the same as the ATMS and AMSU-A instruments respectively (see Table 2).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**System Parameters** & **Settings** \\ \hline Geometrical configuration & \
\begin{tabular}{c} Sensor zenith angle 53 degree, \\ fixed single field of view is considered \\ \end{tabular} \\ \hline Spectral Range &
\begin{tabular}{c} 23 GHz- 183 GHz \\ (for all the configurations A, B and C) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 1: End-to-End simulation settings for three MW instrument configurations set up.
## 3 Results and Discussion
The equival  
Figure 4: (**a**) Cyclic voltammogram (CV) curves and (**b**) specific capacitances of the Co\({}_{3}\)O\({}_{4}\) electrode at various scan rates. impedance spectrum, which involves \(R_{\rm s}\), \(R_{\rm ct}\), \(C_{\rm dl}\), \(W\), and pseudocapacitance (\(C_{\rm ps}\)), is shown in the inset of Figure 6.  
Long-term cycling stability is an important parameter required for practical application. Hence, the GCD tests were repeated for 6000 cycles at a current density of 20 A/g. As shown in Figure 7, 96.6% of the specific capacitance value is still retained. In addition, the coulombic efficiency is deduced from Equation (5) [37; 39]:  
\[\eta=\frac{t_{d}}{t_{c}}, \tag{5}\]  
where \(t_{d}\) (s) and \(t_{c}\) (s) are, respectively, the discharge and charge times; a high efficiency exceeding 95% is achieved. This reveals that long-lasting cycling assessment does no obvious damage to the nanostructure and a feasible redox process is generated from the obtained material and verifies the remarkable electrochemical stability. A comparison between our work and Co\({}_{3}\)O\({}_{4}\)-based electrode materials in current reports was made, as summarized in Table 1. Unfortunately, the high capacitive performances obtained through tremendous efforts usually accompany poor rate capability, which severely limits their wide application in high-power energy storage devices. The Co\({}_{3}\)O\({}_{4}\) in this paper can meet the need of not only high specific capacitance but also excellent rate capability. In addition, the performance of the Co\({}_{3}\)O\({}_{4}\) is  
\[\mathrm{Co_{3}O_{4}+OH^{-}+H_{2}O\leftrightarrow 3 CoOOH+e^{-}}, \tag{3}\]0 **(a)** Discharge curves and **(b)** specific capacitances of the Co\({}_{3}\)O\({}_{4}\) electrode at different current densities. \[\mathrm{Co_{3}O_{4}+OH^{-}+H_{2}O\leftrightarrow 3 CoOOH+e^{-}}, \tag{3}\]1 Electrochemical impedance spectrum (EIS) plot of the Co\({}_{3}\)O\({}_{4}\) electrode over a frequency range from 100 mHz to 100 kHz. The insets show the equivalent circuit and an enlarged view of the high frequency region. even better than some composites of cobalt oxides [34; 42; 43]. The superior electrochemical behaviors can first be explained by the stable morphology. Secondly, the large surface and inner space favors an efficient contact between active material and electrolyte, ensuring a high utilization rate of active material. Thirdly, the interconnected nanoparticles with an increased surface-to-bulk ratio offer more sites for ions to enter and, more importantly, allow facile ion diffusion at a high current density [44]. Finally, the hollow spheres are interconnected with one another, contributing to an even longer ionic diffusion channel [37].
# Prediction of Arrival Time of Vessels Considering Future Weather Conditions
## 4 Verification of the Prediction Accuracy of the Proposed Method
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Vessel Name**} & \multicolumn{2}{c}{**Target Voyage**} & \multicolumn{2}{c}{**Arrival Time**} & \multicolumn{2}{c}{**Prediction Accuracy**} \\ \cline{2-7}  & **Depature** & **Arrival** & **Actual** & **Proposed Method** & **Previous Research** & **Proposed Method** & **Previous Research** \\ \hline \multirow{7}{*}{TS TOKYO} & KOBE & NAGOYA & 2020/4/19 & 2020/4/19 & 2020/4/19 & 88\% & 53\% \\  & & 8:57 & 10:56 & 16:35 & (2 h) & (7.7 h) \\ \cline{2-7}  & NAGOYA & YOKOHAMA & 2020/4/20 & 2020/4/20 & 2020/4/20 & 98\% & 59\% \\  & & 8:38 & 8:16 & 14:42 & (-0.4 h) & (6.1 h) \\ \cline{2-7}  & TOKYO & KEELUNG & 2020/4/25 & 2020/4/25 & 2020/4/25 & 95\% & 84\% \\  & & 10:28 & 14:19 & 21:55 & (3.9 h) & (11.5 h) \\ \cline{2-7}  & KEELUNG & TAICHUNG & 2020/4/26 & 2020/4/26 & 2020/4/26 & 99\% & 89\% \\  & & 2:03 & 2:06 & 1:12 & (0.1 h) & (-0.8 h) \\ \hline \multirow{7}{*}{TS OSAKA} & KOBE & NAGOYA & 2020/4/24 & 2020/4/24 & 2020/4/24 & 82\% & 45\% \\  & & 2:41 & 5:30 & 11:10 & (2.8 h) & (8.5 h) \\ \cline{2-7}  & NAGOYA & YOKOHAMA & 2020/4/25 & 2020/4/25 & 2020/4/25 & 79\% & 40\% \\  & & 1:13 & 3:59 & 9:02 & (2.8 h) & (7.8 h) \\ \cline{2-7}  & TOKYO & KEELUNG & 2020/4/28 & 2020/4/29 & 2020/4/29 & 93\% & 79\% \\  & & 23:28 & 4:02 & 13:54 & (4.6 h) & (14.4 h) \\ \cline{2-7}  & KEELUNG & TAICHUNG & 2020/4/29 & 2020/4/29 & 2020/4/29 & 71\% & 58\% \\  & & 22:57 & 19:38 & 18:10 & (-3.3 h) & (-4.8 h) \\ \hline NEW & & 2020/8/21 & 2020/8/21 & 2020/8/26 & 99\% & 59\% \\  & CENTURY 1 & LONG & 6:12 & 7:54 & 13:55 & (2.3 h) & (127.7 h) \\ \hline NEW & & 2020/8/12 & 2020/8/12 & 2020/8/17 & 99\% & 50\% \\  & & 2020/8/12 & 2020/8/12 & 2020/8/17 & 99\% & 50\% \\  & & 6:04 & 8:22 & 13:45 & (1.7 h) & (127.7 h) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of prediction accuracy. However, the arrival time predicted by the proposed method is three hours earlier than the actual arrival time, which may result from a detour the vessel took before entering Taichung port (see the pink circle in Figure 9). As the voyage speed during the detour was 5 knots or lower, Taichung port may have been crowded, delaying vessel entry into the port. We have shown that the proposed method is more accurate than the one of [PERSON] et al. for predicting the time of arrival to the destination port. The congestion status en route or at the destination port can also affect the prediction accuracy. Therefore, the congestion status at the destination port will be considered in a future study to increase the prediction accuracy of the proposed method.
## 7 Polymeric-Based Nanocarriers  
### Polymeric Nanoparticles  
Polymeric nanoparticles (NPs) are made from biodegradable polymers and have strong structural integrity, which helps stabilize volatile drugs and enables their controlled release [119]. Additionally, they are simple to scale up and economical, and maintain high stability during storage [116,120]. Among various polymers, poly(lactic-co-glycolic acid) (PLGA) is the most frequently used for drug delivery because it is both biocompatible and biodegradable [123]. Numerous studies have documented the successful use of PLGA micro- and nanoparticles for delivering antibiotics to bacterial biofilms [121,124,170].  
Other polymers, such as chitosan, are extensively used in pharmaceutical and medical fields. Chitosan, derived from chitin, is both biocompatible and biodegradable and is known to have inherent antibacterial properties [122]. Leveraging these characteristics, [PERSON] et al. [117] developed chitosan nanoparticles for the combined delivery of an antibacterial agent (oxacillin) and a biofilm matrix-disrupting agent (Deoxyribonuclease I).
# Antimicrobial and Odour Qualities of Alkylpyrazines Occurring in Chocolate and Cocoa Products
## 4 The Quantification of the Impact of Alkylpyrazine Compounds on the Aroma of Cocoa and Chocolate
### Odour Values of Pyrazine Compounds in Cocoa
** & **Coos** & **Dark Chocolate** & **Milk Chocolate** & **Values** & **Coos** & **Dark Chocolate** & **Milk Chocolate** \\ \hline
31 & 24\({}^{\circ}\) [25] & & & & & \\
32 & 2-2000\({}^{\circ}\) [28] & & & & & \\
33 & 33\({}^{\circ}\) [65] & & & & & \\  
Summarizing the information from Table 5, the main contributors to cocoa aroma are: 2-methylpyrazine (OAV = 4.83 [17]), trimethylpyrazine (OAV = 3.2 [16]), tetramethylpyrazine (relatively high concentrations covering high OT), 2-ethyl-3-methylpyrazine (OAV = 1.62 [17]), 2-ethyl-5-methylpyrazine (OAV = 2.8 [17]), 2-ethyl-3,5-dimethylpyrazine (7.6 [16], 14 [7]), 2-ethyl-3,6-dimethylpyrazine (OAV = 1[16], 1.2 [7]), 2,3-diethyl-5-methylpyrazine (OAV = 6.6 [16], 16 [7]), 2-methoxy-3-isopropylpyrazine (very low OT = 0.002 ug/L [3, 12], 0.002 ug/L [28], 0.0039 ug/L [33], 0.004-0.024 ug/L [33], 0.01 ug/L [31], 0.024 ug/L [66], 0.001-0.1 ug/L [69]), 2-methoxy-3-isobutylpyrazine (OAV = 1.2 [16], 12 [7]). The main contributors to dark chocolate aroma are trimethylpyrazine (OAV = 1 [31]), tetramethylpyrazine (very high concentration (mg/kg)--6.135-7.983 [20], 60.31-285.74 [15]), 2-ethyl-3,5-dimethylpyrazine (OAV = 16, 24 [31]), 2,3-diethyl-5-methylpyrazine (OAV = 2 [31]), 2-methoxy-3-isopropylpyrazine (OAV = 1, 8 [31]), 2-methoxy-3-isobutylpyrazine (OAV = 6, 9 [31]) and 2-sec-butyl-3-methoxypyrazine (OAV = 1 [31]). [PERSON] and [PERSON] [30] were the first researchers to identify the main odour-active components in cocoa mass and milk chocolate by using GC-O in conjunction with an AEDA. Two pyrazine compounds were found to have the highest flavour dilution (FD) factors: 2-ethyl-3,5-dimethylpyrazine and 2,3-diethyl-5-methylpyrazine both in cocoa mass and in milk chocolate. The findings showed that the roasted cocoa mass is probably where these milk chocolate scent components come from. Obviously, however, the most prevalent volatiles in the samples are usually not the odourants with a low OT and high OAVs, as is typical in GC-O analyses. The high concentration here seems to be crucial and makes up for the lack of strong odour characteristics. In [PERSON] et al. 's investigation [29], trimethylpyrazine and tetramethylpyrazine were the two pyrazines which were present in the highest concentrations across all of the dark chocolate samples and played a key role in chocolate odour.
###### Abstract  
With the booming development of satellite applications, the giant constellations of low Earth orbit (LEO) satellites have introduced challenges for the data relay service. The multi-beam satellite not only offers concurrent access to a large number of objects, but can also meet the high data requirements toward specific coverage of the LEO constellation. However, the multi-beam satellite often faces the mismatch problem of spot allocation and data requirements, which can cause an overload traffic jam or a waste of resources. An optimization algorithm on spot beam allocation is necessary to automatically place the spot centers with appropriate beam widths in line with the density of the traffic demands and to realize the uniformity of the beam occupation. Compared with the conventional K-means algorithm, two adjustable parameters \(\alpha\) and \(\beta\) are introduced: one for tuning the ratio of two components making up the distance matrix, and the other for setting the obligatory minimum number of objects per beam. In this paper, the whole process of the proposed method is demonstrated, including the establishment of the low-orbit satellite constellation model, the extraction of the distribution features, and the implementation and evaluation of the modified K-means algorithm. The results prove the validity of the proposed algorithm. A larger value of \(\beta\) with a relative smaller value of \(\alpha\) tends to obtain the uniformity of beam occupation; the minimum standard deviation of objects per beam is achieved when \(\alpha\) is 0.2 and \(\beta\) is 0.8. This demonstrates that the uniformity of objects per beam can be realized by adjusting the parameters of the distance determination matrix and the obligatory minimal number of objects in each beam. The impact of parameter range on the results is also analyzed.  
data relay service; multi-beam satellite; beam spot allocation; modified K-means +
Footnote †: journal: Mathematics  
0000-0001-9178-22021
# Performance Analysis of IoT-Based Health and Environment WSN Deployment
## 3 Health and Environment Sensor Network Deployment
### GIS-Based WSN Deployment
#### 3.1.2 Lifetime  
Energy power consumption of battery-powered sensor nodes of WSN especially for transitions of information is one of the constraints of the network that affect the lifetime of the network and thereby the applicability for environmental and health purposes. Lifetime is one of the big challenges of adopting WSN for environmental and health services [5]. Lifetime addresses how to reduce the energy consumption of the sensor nodes by increasing the time until one of the sensor nodes runs out of energy [16; 67]. Therefore, It is the time until the energy supply of the first sensor node is depleted, which is the maximum number of sensing cycles. The coverage and lifetime are affect to each other so that obtaining a good coverage objective is related to network lifetime or energy saving [66]. As energy is a vital resource in designing WSNs, lifetime is considered the other main challenge in much research [16; 17; 80]. Lifetime can be stated as [16]:  
\[\text{lifetime}=\frac{\min\left\{\text{T}_{\text{failure},\ i}\right\}_{i=1,\ 2,\ 3,\ldots,n}}{\text{T}_{\text{max}}} \tag{4}\]\[\mathrm{T_{max}}=\frac{\mathrm{E\ (initial\ energy)}}{\mathrm{E_{min}*}\in _{amp}} \tag{5}\]  
Only the transmitting (\(E_{T}\)) and receiving energy (\(E_{R}\)) are considered for WSN lifetime, which is calculated as follows for one unit message at a distance of \(d\)[81]:  
\[\mathrm{E}=\ E_{T}\ +\ r\ \mathrm{E_{R}} \tag{6}\]  
\[\mathrm{E_{T}}=(E_{elec}+\ \in_{amp}\ \ d^{2}) \tag{7}\]  
\[\mathrm{E_{R}}=\ r\ E_{elec} \tag{8}\]  
In the equations, \(r\), \(E_{elec}\), and \(\mathrm{\epsilon_{amp}}\) represent the number of receiving, the transmitter or receiver circuitry, and the transmit amplifier, respectively. The number of receiving is used to calculate the total energy consumptions from the viewpoint of receiving messages by Equation (12) based on the [49], because the sensors consume energy power to receive each unit message. The number of reviving messages is calculated using the number of inbound links of each sensor node. Since coverage and lifetime are important issues in WSN deployment, the objective function can be formulated as follows:  
\[\mathrm{max}f(x)=\ \alpha(\mathrm{coverage})+\beta(\mathrm{lifetime})=\alpha\frac{ \sum_{i=1}^{n}C_{i}-C_{o}}{C_{R}}+\beta\ \frac{\min\left\{\mathrm{T_{failure},\ i}\right\}_{i=1,\ 2,\ 3,\ldots,n}}{\mathrm{T_{ max}}} \tag{9}\]