esa-sceva/satcom-chunk-collection huggingface dataset:
# Efficient Multi-Identity Full Homomorphic Encryption Scheme on Lattice
## 2 Preliminaries
### Preimage Matrix  
Lemma 2: ([25]) Consider an odd prime \(q\) and a positive integer \(n,m,m^{\prime}\). For any \(m\geq n\log q\), there exists a fixed efficiently computable preimage matrix \(\mathbf{M}\in\mathbb{Z}_{q}^{n\times m}\) and an efficiently computable deterministic \"short preimage\" function \(\mathbf{M}^{-1}(\cdot):\mathbb{Z}_{q}\overset{\rightarrow}{\times m^{\prime}} \mathbb{Z}_{q}^{m\times m^{\prime}}\) that satisfies the following conditions. For any \(m^{\prime}\), when matrix \(\mathbf{A}\in\mathbb{Z}_{q}^{n\times m^{\prime}}\) is input, the function \(\mathbf{M}^{-1}(\mathbf{A})\) outputs a bit-matrix \(\mathbf{M}^{-1}(\mathbf{A})\in\{0,1\}^{m\times m^{\prime}}\) such that \(\mathbf{M}\mathbf{M}^{-1}(\mathbf{A})=\mathbf{A}\).  
We can regard \(\mathbf{M}\) as a special matrix. For those familiar with GSW13 [7] encryption, multiplication \(\mathbf{M}\) is the BitDecomp\({}^{-1}\) operation, and the function \(\mathbf{M}^{-1}(\cdot)\) is called BitDecomp. Note that \(\mathbf{M}^{-1}(\cdot)\) itself is not a matrix, but rather an efficiently computable function.  
Let \(\mathbf{x},\mathbf{y}\) be vectors of some dimension \(n\) over \(\mathbb{Z}_{q}\). Let \(k=\lceil\log q\rceil\) and \(w=nk\). Let \(\text{BitDecomp}(\mathbf{x})\) be the \(w\)-dimension vector \(\mathbf{x}^{\prime}=\left(\mathbf{x}_{1,0},\ldots,\mathbf{x}_{1,k-1},\ldots,\mathbf{x}_{n,0}, \ldots,\mathbf{x}_{n,k-1}\right)\), where \(\mathbf{x}_{i,j}\) is the \(j\)-th bit in \(\mathbf{x}_{i}\)'s binary representation. bits ordered least significant to most significant. Let \(\text{BitDecomp}^{-1}(\mathbf{x}^{\prime})=\left(\sum 2^{j}\cdot\mathbf{x}_{1,j}, \ldots,\sum 2^{j}\cdot\mathbf{x}_{n,j}\right)=\)x be the inverse of BitDecomp, but well-defined even when the input is not a 0/1 vector. Let \(\text{Flatten}(\mathbf{x}^{\prime})=\text{BitDecomp}\left(\text{BitDecomp}^{-1}( \mathbf{x}^{\prime})\right)\), a \(w\)-dimension vector with 0/1 coefficients. \(\text{BitDecomp}(\mathbf{A})\), \(\text{BitDecomp}^{-1}(\mathbf{A})\), or \(\text{Flatten}(\mathbf{A})\) be the matrix formed by applying the operation to each column of \(\mathbf{A}\) separately. Finally, let \(\text{Powersof}2(\mathbf{y})=\left(\mathbf{y}_{1},2\mathbf{y}_{1},\ldots,2^{k-1}\mathbf{y}_{1},\ldots,\mathbf{y}_{n},2\mathbf{y}_{n},\ldots,2^{k-1}\mathbf{y}_{n}\right)\). Has the following properties:  
(1) \(\langle\text{BitDecomp}(\mathbf{x})\rangle,\text{Powersof}2(\mathbf{y})=\langle\mathbf{x },\mathbf{y}\rangle\).  
(2) \(\langle\mathbf{x}^{\prime},\text{Powersof}2(\mathbf{y})\rangle=\langle\text{BitDecomp}^ {-1}(\mathbf{x}^{\prime}),\mathbf{y}\rangle=\langle\text{Flatten}(\mathbf{x}^{\prime}), \text{Powersof}2(\mathbf{y})\rangle\).
# A Comprehensive Survey on Knowledge-Defined Networking
## 2 Overview of Knowledge-Defined Networking (KDN)
### KDN vs. SDN vs. Conventional Network
#### 2.3.1 Decoupling of Logical Planes  
In traditional networks, the data plane and control plane are tightly coupled, and devices such as routers perform both data processing and control functions. Thus, traditional networks are difficult to manage and automate.  
In SDN, the main purpose is to decouple the data and control planes logically, which allows network administrators to manage and program networks using software rather than hardware. The logically decoupled controllers communicate with forwarding elements using protocols such as OpenFlow, ForCES, etc. However, in SDN, network management is embedded in the control plane, and there is no knowledge plane to generate knowledge. Thus, SDN does not emphasize knowledge generation in arriving at control decisions.  
Note that KDN architecture is an extension of the originally proposed SDN architecture by decoupling the management plane from control logic and introducing a new logically decoupled knowledge plane. KDN emphasizes knowledge representation, reasoning, and decision-making to manage, configure, and control networks. It uses domain-specific knowledge representation (knowledge ontologies) to automate the management of network devices and create an intelligent network that can learn and adapt to changing conditions.  
Thus, the key differences in KDN with respect to SDN lie in the logical decoupling of the management plane from control logic and the introduction of a new logically decoupled knowledge plane.
# Two Decades of Groundwater Variability in Peru Using Satellite Gravimetry Data
## 3 Results
### Comparative Analysis: Precipitation vs Groundwater Storage (2003-2023)
#### 3.2.2 Central Zone  
- _Precipitation_: Stable (\(\sim\)930 mm/year) with nearly zero slope.  
- _Interpretation_: Over the 20-year period, estimated precipitation increased by only 13.5 mm, reflecting a minimal upward trend of approximately +0.67 mm per year.  
\(\circ\) Nevertheless, the very low R2 value suggests that the trend line poorly represents annual variability, as precipitation exhibits notable interannual fluctuations.  
\(\circ\) Overall, the trend remains nearly stable or slightly increasing, with values consistently around 930 mm.  
\(\circ\) Compared to the northern and southern regions, this area shows greater interannual stability, without abrupt changes in precipitation.  
- _GWS_: Moderate decline from \(\sim\)75% to \(\sim\)45%.  
- _Relation_: The stability of rainfall does not prevent GWS depletion, reinforcing that intensive and unsustainable groundwater use is the main cause.  
Figure 6: Annual evolution of regional average precipitation in Peru (2003–2023). Zones: north (blue), central (red), and south (green). The solid lines indicate the annual precipitation values (in mm) for each region. The dotted lines represent the fitted linear trends for each zone (north, central, and south). The y-axis shows the amount of precipitation in millimeters (mm), and the x-axis shows the years of analysis.
## 3 Results and Discussion
### Descriptive Analysis
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multicolumn{1}{c}{**Compound**} & \multicolumn{1}{c}{**RT (min) \({}^{\text{\textdagger}}\)**} & \multicolumn{1}{c}{**RI\({}_{\text{Exp}}\)**\({}^{\text{\textdagger}}\)**} & \multicolumn{1}{c}{**RI\({}_{\text{Lk}}\)**\({}^{\text{\textdagger}}\)**} & \multicolumn{1}{c}{**ANOVA \({}^{\text{\textdagger}}\)**} & \multicolumn{5}{c}{**Irrigation Treatment**} \\ \cline{4-9} \cline{8-9}  & & & & & \multicolumn{1}{c}{**T\({}_{\text{0}}\)**} & \multicolumn{1}{c}{**T\({}_{\text{1}}\)**} & \multicolumn{1}{c}{**T\({}_{\text{2}}\)**} & \multicolumn{1}{c}{**T\({}_{\text{3}}\)**} \\ \hline Ethanol & 2.263 & 419 & 427 & *** & 12.85 a \({}^{\text{\textdagger}}\) & 7.10 b & 7.16 b & 7.87 b \\ Acetic acid & 3.383 & 680 & 660 & n.s. & 3.14 & 3.65 & 3.83 & 1.96 \\
3-Pentanone & 4.381 & 737 & 703 & n.s. & 1.35 & 1.35 & 0.77 & 1.05 \\ Propanoic acid & 4.677 & 750 & 745 & n.s. & 0.11 & 0.33 & 0.83 & 1.05 \\ Hexanal & 6.688 & 831 & xxx & n.s. & 4.45 & 3.43 & 3.65 & 3.33 \\ _trans_-2-Hexenal & 8.903 & 904 & 854 & *** & 91.67 a & 70.69 b & 56.08 c & 96.28 a \\ _trans_-2-Hexen-l & 9.157 & 910 & 887 & n.s. & 47.22 & 47.46 & 38.06 & 43.98 \\
4-8-Dimethyl-1,7-nonadiene & 12.998 & 1000 & - & n.s. & 1.67 & 1.72 & 1.70 & 2.54 \\ Benzaldehyde & 13.893 & 1017 & 961 & ** & 2.05 b & 8.14 a & 1.47 b & 1.30 b \\
3-Hexen-1-ol, acetate & 14.579 & 1031 & 1009 & n.s. & 9.47 & 3.47 & 11.77 & 15.53 \\ Hexyl acetate & 14.806 & 1035 & 997 & ** & 3.54 a & 0.35 c & 2.33 b & 4.77 a \\ Hexanoic acid & 15.571 & 1050 & 1010 & n.s. & 1.03 & 0.43 & 0.63 & 0.38 \\ _trans_-8-Ocimene & 16.005 & 1058 & 1050 & *** & 0.56 b & 2.19 a & 0.61 b & 0.64 b \\ Benzyl alcohol & 18.621 & 1109 & 1046 & * & 2.66 a & 0.15 b & 2.15 a & 0.99 b \\
1-Octanol & 18.967 & 1115 & 1068 & n.s. & 0.47 & 0.28 & 0.26 & 0.06 \\ Acetophenone & 19.628 & 1127 & 1065 & ** & 0.27 b & 4.85 a & 0.43 b & 0.25 b \\ Benzoic acid & 27.670 & 1269 & 1210 & ** & 3.89 a & 1.04 b & 3.67 a & 2.50 b \\ Nonanoic acid & 31.899 & 1354 & 1303 & n.s. & 1.24 & 1.98 & 1.98 & 1.05 \\ Total & & *** & 188 a & 159 b & 137 b & 186 a \\ \hline \hline \end{tabular} \({}^{\text{\textdagger}}\) n.s. = not significant at \(p>0.05\), \({}^{\text{\textdagger}}\)** and *** significant at \(p<0.05\), \(p<0.01\) and \(p<0.005\); \({}^{\text{\textdagger}}\) Values followed by the same letter, within the same row, were not significantly different (\(p>0.05\)), according to [PERSON]’s least significant difference test. \({}^{\text{\textdagger}}\) RT = retention time; RE\({}_{\text{\textdagger}}\) = experimental retention index; RE\({}_{\text{\textdagger}}\) = literature retention index.  
\end{table} 
Table 5: Volatile composition (mg 100 g\({}^{-1}\) olive oil) of ‘Arbequina’ olive oil samples obtained from a super-high-density olive tree orchard. Data are the mean of two seasons, 2018 and 2019.
# An Integrated Fuzzy C-Means Method for Missing Data Imputation Using Taxi GPS Data
## 2 Literature Review
### EMI Method  
[PERSON] et al. [30] pointed out that the critical step in the expectation maximization imputation (EMI) was to develop the maximum likelihood estimation (MLE) [40; 41]. Then, missing data were predicted by a known probability distribution of the MLE, and the iteration was terminated when the estimated data stopped changing. Therefore, this method is only applicable to data missing at random. Evidently, the main drawback of the EMI is the estimation of parameters through the MLE, and how to provide a reasonable assumption of the estimated parameters through the MLE is another interesting topic.
## 4 Problem Formulation and Scheduling Algorithm
### Scheduling Algorithm
#### 4.10.2 Mode 2  
In Mode 2, since only the thermal appliances are running, the optimization problem is formulated just as a linear program (LP) rather than MILP  
\[\min J_{\mathcal{P}}, \tag{16}\]subject to  
\[\mathbf{u}_{\min,i}\leq\mathbf{u}_{k,i}\leq\mathbf{u}_{\max,i}\quad k \in\mathcal{N},i\in\mathcal{P}, \tag{17a}\] \[\mathbf{y}_{k,\min,i}\leq\mathbf{y}_{kj}+\mathbf{v}_{k,i}\quad k\in \mathcal{N},i\in\mathcal{P},\] (17b) \[\mathbf{y}_{k,\max,i}\geq\mathbf{y}_{k,i}-\mathbf{v}_{k,i}\quad k \in\mathcal{N},i\in\mathcal{P},\] (17c) \[\sum_{i\in\mathcal{P}}\mathbf{u}_{k,i}\leq C_{k}-\mathbf{w}_{k} \quad k\in\mathcal{N},i\in\mathcal{P}. \tag{17d}\]  
The above constraint considers the total power consumption by only the thermal appliances, since no non-thermal appliance is running.  
In both the modes, at each time step, a control decision policy \(\{\mathbf{u}_{k}^{*}\}_{k=1}^{N}\) is obtained for next \(N\) time steps by solving the formulated optimization. MILP and only the first control input \(\{\mathbf{u}_{1}^{*}\}\) is applied to the system and rest of the control inputs \(\{\mathbf{u}_{k}^{*}\}_{k=2}^{N}\) are discarded. The optimization problem is formulated and solved again in the similar manner at the next time step as per the receding horizon strategy.  
For the present study, it is assumed that perfect electricity prices forecast and weather forecast are available as this is not the focus of the paper.
## 3 Results
### Hand Gesture Recognition Performance  
#### 3.2.1 Gesture Recognition Accuracy  
To assess the accuracy of the hand gesture recognition system, a controlled test was performed using all eight predefined gestures: pointing, peace, thumbs up, pinky, open hand, fist, okay, and love. Each gesture was presented perpendicularly and approximately one foot away from the laptop's webcam--identified as the optimal distance and orientation for consistent detection. The gesture was raised and removed from the frame 25 times per test. The pointing, pinky, open hand, fist, okay, and love gestures were correctly identified in all 25 attempts, achieving a 100% recognition rate. However, the peace and thumbs up gestures occasionally exhibited inconsistencies in recognition. The peace gesture was sometimes initially misclassified as an open hand before correcting itself shortly after. Similarly, the thumbs up gesture was misidentified once as a fist, likely due to the visual similarity between the two gestures when the thumb is bent. Despite these minor issues, the system demonstrated high overall accuracy, as proven in Table 2, particularly when gestures were presented in the ideal position relative to the camera.  
While MediaPipe Hands provided tracking capabilities, its accuracy could be inconsistent due to the system's sensitivity to hand positioning. For optimal recognition, the user's hand needed to be perfectly perpendicular and close to the camera as seen in Figure 8a. If the hand was at an angle or too far away, the system sometimes failed to recognize gestures properly, leading to delays as users had to adjust their hand positioning multiple times.  
Several factors impacted the system's reliability:  
* **Gesture Misclassification:** The system occasionally misinterpreted one gesture as another (Figure 8b), especially when switching between gestures, leading to unintended drone movements. Also, if a gesture was presented at an unfavorable angle or partially obscured, it sometimes failed to register as any labeled gesture (Figure 8c), resulting in no response from the drone.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Hand Gesture** & **Accuracy** \\ \hline Pointing & 100 \\ Peace & 88 \\ Thumbs Up & 96 \\ Pinky & 100 \\ Open Hand & 100 \\ Fist & 100 \\ Okay & 100 \\ Love & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Accuracy of gesture recognition for each predefined hand gesture used in the system.  
Despite these limitations, keeping the hand close to the camera and maintaining a stable positioning significantly improved detection reliability. Future improvements could include additional filtering techniques to reduce misclassification and enhance reliability in changing scenarios.
# Novel Internet of Things Platform for In-Building Power Quality Submetering
## 3 Power Quality Functionality Implementation
### Energy  
Following the same working methodology as in the case of RMS, the designed prototype has been calibrated to measure active and apparent energy. The MCU has been programmed to access to the ADE7758 IC [41], which has several registers to calculate the energy consumed. The energy is calculated by integrating the instantaneous power (active or apparent) of the phase to be measured. The energy integration factor is programmable; therefore, when this integration ends, an interruption request is triggered (In line energy accumulation (LENERGY) flag in RSTATUS) in the IC and the register allocating the accumulated energy is accessed (see flowchart in Figure 8). The energy resolution of this register is programmed, i.e., in other words, the resolution of the energy meter in Wh/LSB (Watts-Hour per Less Significant Bit) is programmed for each increase in the energy meter, and in this particular case, represents a value of 0.00906997 mWh/LSB in the accumulation register. The MCU extracts the measurement updating the active and apparent energy consumed since the start of the measurement, adding the last energy calculated by integration. The active energy accumulated can be found in the watt-hour accumulation register (WATTHR) and the apparent energy in the VA-hour accumulation register (VAHR).
# Tailored Quantum Alternating Operator Ansatzes for Circuit Fault Diagnostics
## 4 QAOA Approaches to CFD
### Approach 1: Transverse Field with a QUBO  
This approach is closely related to a Hamiltonian description of this problem, which is similar to, for example, the approach described in [2] for using a transverse field and an Ising Hamiltonian with explicit fault mappings to represent this problem. As such, our approach is in the spirit of QAOA1 for Ising spin problems.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Entry** & **IO Pair** & **Valid Configurations** \\ \hline
1 & (0,0;0) & (0,0,0),1), (1,1,0;1,1,0), \\  & & (1,0,0;1,0),1), (1,0,1,0,0,1), \\
2 & (1,0;0) & (1,0,0;0,1), (1,1,0;0,1,0), \\  & & (0,0,0;1,0),1), (0,1,0;1,1,1) \\
3 & (0,1;0) & (0,1,0;0,1), (1,1,0;1,0), \\  & & (0,0,0,0,1), (1,0,0;1,1), \\
4 & (1,1;0) & (1,1,0,0,0), (0,0,0;1,1), \\  & & (1,0,0;0,1), (0,1,0;1,0), \\
5 & (0,0;1) & (0,0,1;0,0), (1,1,1;1,1), \\  & & (1,0,1;1,0), (0,1,1,0), (0,1,1,0), \\
6 & (1,0;1) & (0,0,1;1,0), (0,1,1,1,0), \\  & & (0,0,1;1,0), (0,1,1,1,1,0) \\
7 & (0,1;1) & (0,0,1;0,1), (1,0,1;1,1,0) \\  & & (1,1,1;0,0), (0,0,1;1,1,0), \\
8 & (1,1;1) & (1,0,1;0,1), (0,1,1;1,0), \\ \hline \hline \end{tabular}
\end{table}
Table 1: Each kind of input/output pair for a faulty NAND is described. Each entry has different valid configurations, and configurations in the same entry form a subspace such that the action of the driver terms we construct connects the configurations of this subspace.  
The mixing operators are the Pauli X operators:  
\[U_{d}(\beta_{t})=\prod_{i=1}^{n-n_{o}}e^{-i\beta_{t}\sigma_{i}^{x}}.\]  
Since the output values of the circuit have to match the given empirical values, they are not allowed to change during the problem. As such, these qubits can be integrated out of the problem. The phase-separating operators are associated with an Ising Hamiltonian:  
\[U_{c}(\alpha_{t})=e^{i\alpha_{t}H_{f}},\]  
where the Hamiltonian counts the number of faults and enforces the logic of the gates:  
\[H_{f}=\left(\sum_{i=n-n_{o}+1}^{2\,n-n_{o}}(1-\sigma_{i}^{z})/2\right)+\kappa \left(\sum_{g\in\mathcal{G}}H_{g}\right),\]  
where \(H_{g}=\sum_{V_{g}^{x}\in V_{g}}\left(1-\sum_{v\in V_{g}^{y}}\left|\,v\,\middle| \,\right)\) associates a cost to the state being in an invalid set for that particular gate. If a configuration \(x\) fails to be a valid configuration in the fault around a gate \(g\), then \(H_{g}\) will associate a cost to the state \(x\).  
To ensure consistency with the model, we can set \(\kappa=n_{o}+1\), the number of outputs, so that it is never advantageous to break a gate over placing the faults at the very end of the circuit. The number of output bits is an upper bound on the number of faults of the minimal fault diagnosis. For individual instances, we can set \(\kappa\) to any value greater than the number of faulty output bits, which is less than or equal to \(n_{o}\).  
As in QAOA1, our initial state is the uniform superposition over \(2\,n-n_{o}\) qubits: \(\left|\,\psi\,\right\rangle=\left|\,+\right\rangle^{\otimes 2n-n_{o}}=\frac{1}{ \sqrt{2^{n-n_{o}}}}\sum_{x\in\{0,1\}^{2\,n-n_{o}}}\left|\,x\,\right\rangle\).
_Applied_  
_sciences_  
_Article_  
**Combination of High-Resolution Optical Coherence Tomography and Raman Spectroscopy for Improved Staging and Grading in Bladder Cancer**  
**[PERSON] 1,\({}^{\dagger}\), [PERSON] 1,\({}^{\dagger}\), [PERSON] 1, [PERSON] 1, [PERSON] 1, [PERSON] 1, [PERSON] 1, [PERSON] 1, [PERSON] 2, [PERSON] 2, [PERSON] 3, [PERSON] 3, [PERSON] 3, [PERSON] 1,\({}^{\star}\) and [PERSON] 1**  
1 Center for Medical Physics and Biomedical Engineering, Medical University of Vienna,  
Waehringenguertel 18-20, 1090 Vienna, Austria; [PERSON]D.B.); [PERSON]SS] (R.S.); [PERSON]S] (E.R.); [PERSON]] (M.T.E.); [PERSON]] (F.P.); [PERSON]] (J.P.); [PERSON](W.D.); [PERSON]] (R.A.L.); [PERSON]U.)  
2 Department of Urology, Medical University of Vienna, Waehringerguertel 18-20, 1090 Vienna, Austria; [PERSON](N.G.); [PERSON](S.F.S.)  
3 Leibniz Institute of Photonic Technology, Albert-Einstein-Str. 9, 07745 Jena, Germany; [EMAIL_ADDRESS] (C.S.); [PERSON]RESS] (I.W.S.); [EMAIL_ADDRESS] (J.P.)  
* Correspondence: [PERSON]]  
+ Both authors contributed equally to this work  
Received: 15 October 2018; Accepted: 20 November 2018; Published: 23 November 2018  
**Featured Application: Optical coherence tomography (OCT) and Raman spectroscopy (RS) evaluated with Principal Component Analysis (PCA) and k-nearest neighbor classification (kNN).**  
**Abstract:** We present a combination of optical coherence tomography (OCT) and Raman spectroscopy (RS) for improved diagnosis and discrimination of different stages and grades of bladder cancer ex vivo by linking the complementary information provided by these two techniques. Bladder samples were obtained from biopsies dissected via transurethral resection of the bladder tumor (TURBT). As OCT provides structural information rapidly, it was used as a red-flag technology to scan the bladder wall for suspicious lesions with the ability to discriminate malignant tissue from healthy urothel. Upon identification of degenerated tissue via OCT, RS was implemented to determine the molecular characteristics via point measurements at suspicious sites. Combining the complementary information of both modalities allows not only for staging, but also for differentiation of low-grade and high-grade cancer based on a multivariate statistical analysis. OCT was able to clearly differentiate between healthy and malignant tissue by tomogram inspection and achieved an accuracy of 71% in the staging of the tumor, from pTa to pT2, through texture analysis followed by k-nearest neighbor classification. RS yielded an accuracy of 93% in discriminating low-grade from high-grade lesions via principal component analysis followed by k-nearest neighbor classification. In this study, we show the potential of a multi-modal approach with OCT for fast pre-screening and staging of cancerous lesions followed by RS for enhanced discrimination of low-grade and high-grade bladder cancer in a non-destructive, label-free and non-invasive way.  
**Keywords:** optical coherence tomography (OCT); Raman spectroscopy (RS); principal component analysis (PCA); k-nearest neighbor classification (kNN); bladder cancer
## 5 Implementation
### Phase 3--Selected Methodology Application
#### 5.3.1 Data Preparation and Modeling/Analyze/Evaluation
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Size**} & **Number of** & \multirow{2}{*}{**Cpk**} & **Ppk** & \multirow{2}{*}{**\(p\)-Value**} \\  & **Parts Machined** & & & \\ \hline
3 & 27 & 5.73 & 5.78 & \textless{}0.005 \\
4 & 30 & 2.91 & 2.94 & \textless{}0.005 \\
3 & 10 & 19.52 & 20.07 & 0.444 \\
6 & 34 & 14.18 & 14.29 & 0.066 \\
4 & 32 & 14.62 & 14.74 & 0.117 \\
5 & 2 & 19.56 & 24.51 & 0.227 \\
4 & 7 & 21.31 & 22.21 & 0.355 \\
5 & 3 & 19.98 & 22.55 & 0.487 \\
3 & 11 & 22.59 & 23.16 & 0.482 \\
5 & 9 & 32.63 & 33.67 & 0.074 \\
5 & 21 & 16.47 & 16.68 & 0.059 \\
3 & 8 & 18.98 & 19.66 & 0.122 \\
3 & 35 & 0.06 & 0.06 & \textless{}0.005 \\
2 & 34 & 26.10 & 26.3 & \textless{}0.005 \\
5 & 8 & 19.51 & 20.21 & 0.076 \\
4 & 19 & 23.75 & 24.08 & 0.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Normality and capability analysis based on size. Figure 15: Plot of capability index for all DIMs based on sizes. However, it was not possible to filter data for all DIMs based on sizes and LengthA changes because,  
* The DIM-tool association was identified for only specified DIMs and tools. * Each tool had more than 1 DIM associated. * Some tools had no LengthA changes, so there was nothing to filter. * Some tools had too many LengthA changes. * Traceability of any drift in the CMM data were difficult to identify because it was difficult to correlate the CMM data with the LengthA changes (assuming they are tool adjustment changes). * Tool adjustments could be automatically made by the machine (NOT operator) in certain cases, such as for DIM A where the operator has little control over tool adjustments to keep DIM A within specification. The Cpk and Ppk values were higher than the index '1.67' after the data were filtered to sizes and LengthA changes. Outliers were identified in the dataset, which were removed during the data preparation step to improve the accuracy of the results. The capability study reflected the low scrap rate from profile damage, which has a defect rate of 0.6%, i.e., 5 parts out of 882 machined parts were scrapped due to process parameter #1 caused by CNC tools over a period of 9 months. Thus, the statistical analysis showed that the variables had minimal effect on the dimensional accuracy of the part and the process was considered stable.