07_PCAcode_PekkaR

In [1]:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy import linalg

%matplotlib inline

#Data paths
path = 'd00.dat'
path1 = 'd00_te.dat'

#Load from a file to create a control limit
file = pd.DataFrame(np.loadtxt(path)).T

import numpy as np import pandas as pd import matplotlib.pyplot as plt from scipy import linalg %matplotlib inline #Data paths path = 'd00.dat' path1 = 'd00_te.dat' #Load from a file to create a control limit file = pd.DataFrame(np.loadtxt(path)).T

PCA Calculations¶

In [2]:

#Calculation of the averages
averages = file.mean()

#Calculation of the standard deviations
desv_pad = file.std()

#Calculation of the averages averages = file.mean() #Calculation of the standard deviations desv_pad = file.std()

In [3]:

#Normalizing the data to balance variances
file_norm = file.copy()

for i in file_norm:
    file_norm[i] = (file_norm[i]-averages[i])/desv_pad[i]
    
file_norm.head()

#Normalizing the data to balance variances file_norm = file.copy() for i in file_norm: file_norm[i] = (file_norm[i]-averages[i])/desv_pad[i] file_norm.head()

Out[3]:

	0	1	2	3	4	5	6	7	8	9	...	42	43	44	45	46	47	48	49	50	51
0	-0.044401	-0.653661	0.885207	-0.861360	1.400405	-0.410481	-0.227496	0.960375	0.03002	0.197452	...	-0.908680	-0.004696	0.795260	-0.068298	-0.248827	1.211723	1.575293	-0.023624	-0.003330	0.090802
1	0.001481	0.975980	0.071957	-0.799933	0.810940	1.797914	0.000494	-0.675350	0.56609	-0.170456	...	-0.186296	-0.050358	-0.013818	-0.670200	0.116256	-1.347466	-0.752507	-0.009022	0.396246	1.085388
2	0.024947	0.623204	-0.208583	1.512065	0.379625	-0.424057	-0.037504	-1.267921	1.10216	0.001520	...	0.061513	-0.070888	-0.666817	-1.479989	-0.054811	1.754909	-0.204315	0.053153	0.809141	1.485239
3	0.011638	-0.300884	0.642493	0.024754	0.360455	1.435882	0.171487	0.950909	-0.50605	-0.109709	...	-0.695939	-0.057791	0.146479	0.173430	0.055062	-0.105333	-1.108344	0.068226	0.360094	0.908648
4	-0.352618	-1.068876	0.488038	-0.048436	0.638414	0.820428	0.038492	0.657463	-1.04212	0.923857	...	-1.745617	-0.246810	-0.456743	0.613375	0.612074	-1.327750	0.647061	0.058334	-0.277325	-0.774757

5 rows × 52 columns

In [4]:

#Calculation of the covariance matrix
cov_matx = file_norm.cov()
cov_matx.head()

#Calculation of the covariance matrix cov_matx = file_norm.cov() cov_matx.head()

Out[4]:

	0	1	2	3	4	5	6	7	8	9	...	42	43	44	45	46	47	48	49	50	51
0	1.000000	-0.053143	0.087308	-0.125095	-0.034186	0.096849	0.037762	-0.000808	0.033830	-0.095712	...	-0.157492	0.996026	0.011927	-0.168890	-0.073512	-0.016769	-0.067947	0.019396	-0.008225	0.030122
1	-0.053143	1.000000	-0.080170	0.002743	-0.029287	0.089881	0.040008	0.033844	0.306023	0.029428	...	0.039268	-0.050384	0.031489	-0.017904	0.023872	-0.033287	-0.005640	-0.004802	0.263422	0.015172
2	0.087308	-0.080170	1.000000	-0.064671	0.008701	0.017448	0.172244	0.023339	-0.038357	-0.035725	...	0.122340	0.085266	0.035843	0.076345	-0.021281	-0.009332	-0.045860	-0.108795	0.004047	0.031235
3	-0.125095	0.002743	-0.064671	1.000000	-0.019997	0.000929	0.144486	-0.059398	0.061911	0.055488	...	-0.052638	-0.123406	-0.268673	0.136402	0.028164	-0.042984	0.057462	0.090396	0.062539	0.008467
4	-0.034186	-0.029287	0.008701	-0.019997	1.000000	-0.070870	0.005314	0.041767	-0.003187	0.004439	...	-0.009292	-0.032946	-0.014366	0.193271	0.000694	0.031186	-0.024664	-0.023938	0.002518	0.032227

5 rows × 52 columns

In [5]:

#Eigenvalues and eigenvectors, disordered of the covariance matrix
auto_val, auto_vet = linalg.eig(cov_matx)

#Total variability
total_var = auto_val.sum()
auto_val, auto_vet

#Eigenvalues and eigenvectors, disordered of the covariance matrix auto_val, auto_vet = linalg.eig(cov_matx) #Total variability total_var = auto_val.sum() auto_val, auto_vet

Out[5]:

(array([6.60744438e+00+0.j, 3.93323628e+00+0.j, 2.80935503e+00+0.j,
        2.33132861e+00+0.j, 2.19472439e+00+0.j, 2.08346458e+00+0.j,
        1.93404945e+00+0.j, 1.73451928e+00+0.j, 1.62614994e+00+0.j,
        1.50266333e+00+0.j, 1.40347239e+00+0.j, 1.28702998e+00+0.j,
        1.25481303e+00+0.j, 1.22652047e+00+0.j, 1.19460639e+00+0.j,
        1.12156103e+00+0.j, 1.07244796e+00+0.j, 1.05304280e+00+0.j,
        9.94682043e-01+0.j, 9.61477795e-01+0.j, 9.36017944e-01+0.j,
        8.96243624e-01+0.j, 8.74467422e-01+0.j, 2.13160863e-01+0.j,
        8.29732991e-01+0.j, 8.10779540e-01+0.j, 2.84436618e-01+0.j,
        3.36627879e-01+0.j, 7.64501204e-01+0.j, 7.71762702e-01+0.j,
        3.90905573e-01+0.j, 7.20527305e-01+0.j, 6.97765167e-01+0.j,
        4.43360347e-01+0.j, 4.51107062e-01+0.j, 4.91617086e-01+0.j,
        5.22560458e-01+0.j, 6.60936436e-01+0.j, 6.31249365e-01+0.j,
        5.81702307e-01+0.j, 5.79897774e-01+0.j, 6.10960969e-01+0.j,
        7.97975962e-02+0.j, 4.62961552e-02+0.j, 2.13918453e-02+0.j,
        1.09907140e-02+0.j, 7.97018198e-03+0.j, 3.71081523e-03+0.j,
        2.86249749e-03+0.j, 7.03350976e-05+0.j, 3.77068323e-08+0.j,
        4.75793488e-08+0.j]),
 array([[ 2.01469182e-02, -1.30043381e-01,  3.22721696e-01, ...,
          7.43922099e-03,  3.62311837e-05, -9.07903178e-08],
        [-4.33036173e-02,  8.07259136e-02,  2.01432039e-01, ...,
          5.52292021e-04, -9.71032512e-06,  1.06184980e-05],
        [-7.85306092e-02, -3.99376298e-02, -3.53581219e-03, ...,
         -6.78473277e-05, -7.80133521e-06,  1.24579984e-06],
        ...,
        [ 2.10728355e-01,  3.55727565e-01,  6.51414896e-02, ...,
          2.65868970e-02, -1.08076942e-04,  7.35250293e-06],
        [-7.59863195e-02,  1.14740230e-01,  3.10401488e-01, ...,
         -4.93321785e-04, -6.39916187e-06,  1.33031172e-05],
        [-6.52529490e-04,  4.66005889e-03,  8.52874689e-02, ...,
         -7.06336799e-01,  5.89148035e-04, -1.04942026e-03]]))

In [6]:

#Organizing the eigenvalues
##argsort() retrieves an array with eigenvalue indices so that they are,
##arranged in ascending order, order is reversed with [::-1]
idx = auto_val.argsort()[::-1]

##Reorganizing the vector of eigenvalues and eigenvectors
auto_val = auto_val[idx]
auto_vet = auto_vet[:,idx]
auto_val, auto_vet

#Organizing the eigenvalues ##argsort() retrieves an array with eigenvalue indices so that they are, ##arranged in ascending order, order is reversed with [::-1] idx = auto_val.argsort()[::-1] ##Reorganizing the vector of eigenvalues and eigenvectors auto_val = auto_val[idx] auto_vet = auto_vet[:,idx] auto_val, auto_vet

Out[6]:

(array([6.60744438e+00+0.j, 3.93323628e+00+0.j, 2.80935503e+00+0.j,
        2.33132861e+00+0.j, 2.19472439e+00+0.j, 2.08346458e+00+0.j,
        1.93404945e+00+0.j, 1.73451928e+00+0.j, 1.62614994e+00+0.j,
        1.50266333e+00+0.j, 1.40347239e+00+0.j, 1.28702998e+00+0.j,
        1.25481303e+00+0.j, 1.22652047e+00+0.j, 1.19460639e+00+0.j,
        1.12156103e+00+0.j, 1.07244796e+00+0.j, 1.05304280e+00+0.j,
        9.94682043e-01+0.j, 9.61477795e-01+0.j, 9.36017944e-01+0.j,
        8.96243624e-01+0.j, 8.74467422e-01+0.j, 8.29732991e-01+0.j,
        8.10779540e-01+0.j, 7.71762702e-01+0.j, 7.64501204e-01+0.j,
        7.20527305e-01+0.j, 6.97765167e-01+0.j, 6.60936436e-01+0.j,
        6.31249365e-01+0.j, 6.10960969e-01+0.j, 5.81702307e-01+0.j,
        5.79897774e-01+0.j, 5.22560458e-01+0.j, 4.91617086e-01+0.j,
        4.51107062e-01+0.j, 4.43360347e-01+0.j, 3.90905573e-01+0.j,
        3.36627879e-01+0.j, 2.84436618e-01+0.j, 2.13160863e-01+0.j,
        7.97975962e-02+0.j, 4.62961552e-02+0.j, 2.13918453e-02+0.j,
        1.09907140e-02+0.j, 7.97018198e-03+0.j, 3.71081523e-03+0.j,
        2.86249749e-03+0.j, 7.03350976e-05+0.j, 4.75793488e-08+0.j,
        3.77068323e-08+0.j]),
 array([[ 2.01469182e-02, -1.30043381e-01,  3.22721696e-01, ...,
          7.43922099e-03, -9.07903178e-08,  3.62311837e-05],
        [-4.33036173e-02,  8.07259136e-02,  2.01432039e-01, ...,
          5.52292021e-04,  1.06184980e-05, -9.71032512e-06],
        [-7.85306092e-02, -3.99376298e-02, -3.53581219e-03, ...,
         -6.78473277e-05,  1.24579984e-06, -7.80133521e-06],
        ...,
        [ 2.10728355e-01,  3.55727565e-01,  6.51414896e-02, ...,
          2.65868970e-02,  7.35250293e-06, -1.08076942e-04],
        [-7.59863195e-02,  1.14740230e-01,  3.10401488e-01, ...,
         -4.93321785e-04,  1.33031172e-05, -6.39916187e-06],
        [-6.52529490e-04,  4.66005889e-03,  8.52874689e-02, ...,
         -7.06336799e-01, -1.04942026e-03,  5.89148035e-04]]))

In [7]:

#Determination of the number of the eigenvectors (main components)

##Variability that the PCA wants to explain
var_exp = 0.55

##Variability explained by the PCA model
pca_var = 0

##Counter of the number of the eigenvalues, whose sum results 
##in the variability are explained by the PCA model

k = 0

for v in (auto_val/total_var):
    if pca_var < var_exp:
        pca_var += v
        k += 1
   
print(pca_var , k)

#Determination of the number of the eigenvectors (main components) ##Variability that the PCA wants to explain var_exp = 0.55 ##Variability explained by the PCA model pca_var = 0 ##Counter of the number of the eigenvalues, whose sum results ##in the variability are explained by the PCA model k = 0 for v in (auto_val/total_var): if pca_var < var_exp: pca_var += v k += 1 print(pca_var , k)

(0.5662968774464168+0j) 12

In [8]:

#Determination of the matrix from the chosen eigenvectors
auto_vet_matx = auto_vet[:,:k]
pd.DataFrame(auto_vet_matx).head()

#Determination of the matrix from the chosen eigenvectors auto_vet_matx = auto_vet[:,:k] pd.DataFrame(auto_vet_matx).head()

Out[8]:

	0	1	2	3	4	5	6	7	8	9	10	11
0	0.020147	-0.130043	0.322722	0.341378	-0.173761	-0.109300	-0.232458	-0.175618	0.075228	-0.073972	-0.019257	0.113088
1	-0.043304	0.080726	0.201432	-0.282919	0.207416	-0.012425	-0.147961	-0.016737	0.159367	-0.040801	-0.100897	-0.005794
2	-0.078531	-0.039938	-0.003536	0.068262	-0.069503	0.040955	-0.008116	-0.170822	0.147699	-0.014439	-0.031828	-0.107166
3	-0.039561	0.134866	-0.048981	-0.009387	-0.004504	0.022555	-0.069127	0.117917	-0.350712	0.058633	-0.377825	0.142473
4	-0.017772	0.010568	-0.029999	-0.011481	-0.046363	0.056850	0.062207	-0.002660	-0.164355	-0.197179	0.104951	-0.263393

In [9]:

#Determination of the matrix from scores of the main components
pca_matx = pd.DataFrame(np.dot(file_norm , auto_vet_matx))
pca_matx.head()

#Determination of the matrix from scores of the main components pca_matx = pd.DataFrame(np.dot(file_norm , auto_vet_matx)) pca_matx.head()

Out[9]:

	0	1	2	3	4	5	6	7	8	9	10	11
0	0.389324	-0.376349	-1.156285	-0.573847	-0.772950	-1.335586	-1.318887	-0.648729	0.036428	-0.458188	1.214514	-1.286229
1	0.296007	0.204152	2.585195	0.084934	0.607965	2.363568	0.319504	0.176160	-1.171449	0.692436	0.801259	-1.130705
2	1.407427	-0.532290	1.492117	-2.258270	-2.021969	-0.731180	0.388124	0.034379	-2.076691	1.719053	0.069406	0.579185
3	0.529524	0.065838	1.696614	-0.169174	-0.894811	0.746732	1.095781	0.013380	-0.027765	1.325123	-0.215860	-0.435222
4	-0.259884	0.965696	-0.855565	1.577553	1.051710	0.792403	-0.271149	-0.085631	-0.679807	0.583123	-0.766042	-1.034184

T2 Calculations¶

In [10]:

#Loading the second database of the normal operation
file2 = pd.DataFrame(np.loadtxt(path1))
file2.head()

#Loading the second database of the normal operation file2 = pd.DataFrame(np.loadtxt(path1)) file2.head()

Out[10]:

	0	1	2	3	4	5	6	7	8	9	...	42	43	44	45	46	47	48	49	50	51
0	0.24889	3702.3	4502.7	9.4170	26.996	42.183	2705.2	75.173	120.40	0.33611	...	54.059	24.804	63.269	21.950	40.188	39.461	47.000	47.594	41.384	18.905
1	0.24904	3666.2	4526.0	9.2682	26.710	42.332	2705.5	74.411	120.41	0.33676	...	53.781	24.790	62.171	22.239	40.108	43.710	46.128	47.508	41.658	18.976
2	0.25034	3673.3	4501.3	9.4212	26.842	42.360	2705.3	75.125	120.41	0.33739	...	54.075	24.669	61.585	22.191	40.030	39.480	44.121	47.612	41.721	16.562
3	0.25109	3657.8	4497.8	9.3792	26.528	41.982	2707.3	73.992	120.38	0.33664	...	54.117	24.595	61.561	21.959	40.121	32.848	45.858	47.459	40.836	20.094
4	0.24563	3698.0	4537.4	9.3746	26.736	42.354	2705.3	75.283	120.42	0.32521	...	53.906	24.451	61.388	22.271	39.538	36.682	45.753	47.458	41.727	18.330

5 rows × 52 columns

In [11]:

#Normalizing the data to balance variances
file2_norm = file2.copy()

for i in file2_norm:
    file2_norm[i] = (file2_norm[i]-averages[i])/desv_pad[i]
    
file2_norm.head()

#Normalizing the data to balance variances file2_norm = file2.copy() for i in file2_norm: file2_norm[i] = (file2_norm[i]-averages[i])/desv_pad[i] file2_norm.head()

Out[11]:

	0	1	2	3	4	5	6	7	8	9	...	42	43	44	45	46	47	48	49	50	51
0	-0.078726	1.210124	-0.277930	0.950076	0.422756	-0.704632	-0.037504	0.356444	0.03002	-0.126821	...	0.124633	0.029285	1.642302	-0.730632	0.073837	0.385605	0.206723	0.062573	0.550368	0.463100
1	-0.073472	0.083112	0.456517	-0.994669	-0.947869	-0.030347	0.019493	-1.086174	0.56609	-0.071206	...	-0.525279	0.024330	0.715955	-0.032039	0.018205	1.781855	-0.163551	0.022066	1.071719	0.510813
2	-0.027940	0.304768	-0.322060	1.004968	-0.315273	0.096364	-0.018505	0.265570	0.56609	-0.017304	...	0.162038	-0.018500	0.221566	-0.148068	-0.036035	0.391849	-1.015775	0.071052	1.191592	-1.111439
3	-0.001671	-0.179129	-0.432384	0.456048	-1.820085	-1.614237	0.361478	-1.879425	-1.04212	-0.081474	...	0.260227	-0.044694	0.201318	-0.708877	0.027246	-1.787470	-0.278200	-0.001015	-0.492334	1.262129
4	-0.192906	1.075882	0.815860	0.395928	-0.823266	0.069211	-0.018505	0.564696	1.10216	-1.059425	...	-0.233052	-0.095665	0.055363	0.045314	-0.378171	-0.527592	-0.322785	-0.001486	1.203008	0.076689

5 rows × 52 columns

In [12]:

#Main component matrix
pca_matx2 = pd.DataFrame(np.dot(file2_norm , auto_vet_matx))
pca_matx2.head()

#Main component matrix pca_matx2 = pd.DataFrame(np.dot(file2_norm , auto_vet_matx)) pca_matx2.head()

Out[12]:

	0	1	2	3	4	5	6	7	8	9	10	11
0	0.248419	-0.111171	0.112608	-0.744816	-0.589237	0.015378	-0.547747	-0.231284	-0.209839	-0.281063	0.521029	-0.374197
1	0.219771	-0.314852	0.489009	-1.432270	-1.547129	-1.543413	0.458725	-0.980608	0.129236	-0.215872	0.639770	0.300001
2	0.370839	0.202034	1.408385	-0.327969	1.160541	-1.085822	1.529507	-0.407484	-1.187968	0.744050	0.296890	0.810662
3	0.847076	0.365621	0.425124	0.613854	-0.460821	2.032385	-0.465346	0.869648	-0.305852	1.412494	0.459374	1.607641
4	-0.505365	0.726729	2.209690	-0.954871	1.222154	0.336813	-0.077150	0.672718	0.935958	1.202801	0.119179	-0.763029

In [13]:

#Statistical calculation of T^2

def el2(valor):
    return valor**2

T2_matx = pca_matx2.apply(el2)

for i in T2_matx:
    T2_matx[i] = T2_matx[i]/auto_val[i]
    
T2_matx

#Statistical calculation of T^2 def el2(valor): return valor**2 T2_matx = pca_matx2.apply(el2) for i in T2_matx: T2_matx[i] = T2_matx[i]/auto_val[i] T2_matx

Out[13]:

	0	1	2	3	4	5	6	7	8	9	10	11
0	(0.00933979836550647+0j)	(0.003142174794540556+0j)	(0.004513676977208643+0j)	(0.2379545565439716+0j)	(0.15819749418430254+0j)	(0.0001135065831443769+0j)	(0.15512881459096117+0j)	(0.03083975730448195+0j)	(0.027077803914681828+0j)	(0.052570955495377894+0j)	(0.1934283919544311+0j)	(0.10879598406097603+0j)
1	(0.007309827823018061+0j)	(0.025203635310830145+0j)	(0.08511904831403724+0j)	(0.8799259035024474+0j)	(1.0906195438663984+0j)	(1.143347497003345+0j)	(0.10880227260968663+0j)	(0.5543857308424333+0j)	(0.010270865467822994+0j)	(0.03101201799939934+0j)	(0.29163759943573336+0j)	(0.06992903412451713+0j)
2	(0.02081307770139083+0j)	(0.01037761006915072+0j)	(0.7060515620857167+0j)	(0.04613845679711649+0j)	(0.613678270100067+0j)	(0.5658886714112256+0j)	(1.209582018961139+0j)	(0.0957284738458299+0j)	(0.8678580133456546+0j)	(0.36841964525001863+0j)	(0.0628040533145891+0j)	(0.5106114798754994+0j)
3	(0.10859546863552992+0j)	(0.03398692802473205+0j)	(0.06433167433095374+0j)	(0.16163171144401114+0j)	(0.09675748626335771+0j)	(1.9825582845514749+0j)	(0.11196570080645901+0j)	(0.4360218463912988+0j)	(0.05752566304411154+0j)	(1.3277350054046924+0j)	(0.15035880879538796+0j)	(2.008120006183809+0j)
4	(0.03865242446387418+0j)	(0.13427480338634795+0j)	(1.7380249176716982+0j)	(0.3910981344232168+0j)	(0.6805689650517625+0j)	(0.05444917833697084+0j)	(0.0030775832339271485+0j)	(0.260907855581065+0j)	(0.5387065964152522+0j)	(0.9627767548857606+0j)	(0.010120368472429316+0j)	(0.45237009323540356+0j)
5	(0.028662279881340482+0j)	(0.07089423864612772+0j)	(0.013962850466701399+0j)	(0.5654834779420694+0j)	(0.017668579048842194+0j)	(0.14446328324342397+0j)	(2.179738828801702+0j)	(0.011214220884659423+0j)	(4.320298978905325+0j)	(1.6452964050998367+0j)	(0.005906746667066029+0j)	(1.6474789157972096+0j)
6	(0.05559420055818776+0j)	(0.29282735525648973+0j)	(0.01610601065815919+0j)	(0.7154567796383899+0j)	(1.1376197167137678+0j)	(6.855523580737727+0j)	(0.3893579006795946+0j)	(0.0377603572161168+0j)	(3.6945378770224075+0j)	(0.055463217018983685+0j)	(1.7577221211662886+0j)	(0.6437185843447258+0j)
7	(0.11772929695488134+0j)	(0.5247654444270198+0j)	(0.2219694810178344+0j)	(0.01725469136376236+0j)	(2.25650814911534+0j)	(0.023865556368922423+0j)	(0.4299777150700757+0j)	(0.17892437200195474+0j)	(1.1262167349158558+0j)	(0.023645172424085+0j)	(0.43835149937499585+0j)	(0.07958428764803639+0j)
8	(0.11222779843994894+0j)	(0.08298839693933713+0j)	(0.007560818290629651+0j)	(0.0025816721006877677+0j)	(0.04787646651477343+0j)	(0.14163508429612884+0j)	(2.8020094187844107+0j)	(0.7951404581870695+0j)	(1.1784126973514957+0j)	(0.9685587149976174+0j)	(0.8241000115423787+0j)	(1.4423263121762266+0j)
9	(0.004151674752623375+0j)	(0.0889827761198925+0j)	(4.779483685174108+0j)	(0.7378166452287063+0j)	(2.6540878839982294+0j)	(0.09115767350342137+0j)	(0.05265751337997856+0j)	(1.019569680134666+0j)	(0.3653176357241717+0j)	(1.1832176327618866+0j)	(0.29648671943549626+0j)	(0.7883675177515524+0j)
10	(0.03757913020836374+0j)	(0.12416537403584152+0j)	(0.006058797450334903+0j)	(0.7397820169456913+0j)	(0.2689260829833453+0j)	(1.176949575073162+0j)	(0.36868744978690204+0j)	(0.17856534827026355+0j)	(0.7370820429305389+0j)	(0.7632013174056345+0j)	(0.952577838124274+0j)	(0.8356892836195804+0j)
11	(0.07903345478704223+0j)	(0.21838363143182984+0j)	(0.009752359402856237+0j)	(0.9797322622455046+0j)	(0.45341650166106473+0j)	(0.272297047331006+0j)	(0.9264347592252513+0j)	(0.2574605193437611+0j)	(0.5140914448940866+0j)	(1.1966200905001003+0j)	(0.33915473237609767+0j)	(0.08644279173572776+0j)
12	(0.00539773523932341+0j)	(0.19045062467798382+0j)	(1.9847285109715274+0j)	(1.0010319278932822+0j)	(0.7377995055320654+0j)	(0.02134189434153517+0j)	(0.6543384416668844+0j)	(1.9334762838606334+0j)	(5.425320858428372e-05+0j)	(0.013832395923797605+0j)	(0.0007154523632896491+0j)	(0.3552681270232199+0j)
13	(0.013157184294017495+0j)	(2.463532326895136e-05+0j)	(0.2324845101385961+0j)	(0.08545307358701991+0j)	(0.2997899216965683+0j)	(0.588889010251785+0j)	(9.091990257422774+0j)	(0.7165522465241817+0j)	(2.7244924855199124+0j)	(1.7774350122948008+0j)	(1.1595660110849406+0j)	(2.016919681963174+0j)
14	(0.023775153797179444+0j)	(0.11252822862678429+0j)	(0.5756900706597144+0j)	(0.21680916027885533+0j)	(0.9272447057886836+0j)	(0.298500830511797+0j)	(0.6425933277620209+0j)	(1.2505086561284355+0j)	(0.8609984774608672+0j)	(0.007292569948611241+0j)	(0.018591561526291534+0j)	(3.2033320638129514+0j)
15	(0.006315207255162222+0j)	(0.05559583117935085+0j)	(0.2354023711901752+0j)	(0.47914411699006065+0j)	(0.0008102908500525928+0j)	(0.0013692803611167674+0j)	(0.0003283574422447729+0j)	(1.7632556564809383+0j)	(0.08572809360640753+0j)	(1.1174213677292475+0j)	(0.9311280411288047+0j)	(2.8129535413957036+0j)
16	(0.3078035288146006+0j)	(0.385366280210386+0j)	(0.13846754795183594+0j)	(2.3112320849877275+0j)	(0.63662584167622+0j)	(0.0011556440456313335+0j)	(0.10482170402356851+0j)	(7.277933284192602+0j)	(0.5153662949010327+0j)	(2.4178362256775423+0j)	(0.06598923448548609+0j)	(1.5671878486145931+0j)
17	(0.26750929164356896+0j)	(0.13343007049141944+0j)	(1.5932275720243067e-05+0j)	(0.8241632318377293+0j)	(0.0027216744712775577+0j)	(0.06711004864982677+0j)	(1.7954651977710745+0j)	(8.776068970893467+0j)	(0.11666408919786679+0j)	(0.3395900636202333+0j)	(1.3469278541122627+0j)	(0.6279456832909958+0j)
18	(0.001233850247929226+0j)	(0.007763849794156559+0j)	(1.2781965263885857+0j)	(2.1196324617756255+0j)	(0.05155711905161549+0j)	(0.15230620828468613+0j)	(1.821542117011183+0j)	(0.07974678801473516+0j)	(0.05982415817569005+0j)	(1.022149698099956+0j)	(0.3434824479363612+0j)	(0.7393560986627614+0j)
19	(0.03656392093719149+0j)	(0.000234991239010438+0j)	(2.3943864523822644+0j)	(1.2159829454657456+0j)	(0.00029499385046515307+0j)	(0.2622747331617338+0j)	(0.21645929843654843+0j)	(0.035781486003551626+0j)	(0.0026842422070823663+0j)	(0.11920430861103606+0j)	(0.07476102987520075+0j)	(2.398333983498609+0j)
20	(0.025137912438632958+0j)	(0.12916679585636823+0j)	(0.001863206380130935+0j)	(0.06355753133878524+0j)	(0.2379129753024431+0j)	(2.60599832656719+0j)	(0.31135165908423773+0j)	(0.28608644680707657+0j)	(4.983332994920723+0j)	(1.4263278538195214+0j)	(2.668313273934686+0j)	(0.07362943768919251+0j)
21	(0.08309980757822162+0j)	(0.32164650985788523+0j)	(1.8418711006867603+0j)	(0.04905105254283032+0j)	(0.06022045843661099+0j)	(0.6550712652259386+0j)	(1.5536241479951423+0j)	(0.3197411632156164+0j)	(0.036993925054403826+0j)	(0.2033363721667648+0j)	(1.9200782333975743+0j)	(0.4044833350166278+0j)
22	(0.3223343476074279+0j)	(0.023542145425926562+0j)	(0.4926630361066709+0j)	(0.005484965483026156+0j)	(2.3626523022377133+0j)	(2.192685470425327+0j)	(4.388912933266664+0j)	(0.48641430238976346+0j)	(0.5820619354297201+0j)	(0.17796924480176787+0j)	(2.968942947200642+0j)	(0.31857462300780254+0j)
23	(0.4688186174512749+0j)	(0.2474196466687811+0j)	(4.235766960473181+0j)	(0.8070485161058942+0j)	(0.021028862345714657+0j)	(2.280109158706329+0j)	(1.8096030411922117+0j)	(3.772588857280091e-05+0j)	(0.2943263018232657+0j)	(0.41517691490880465+0j)	(1.999883462042052+0j)	(0.15716888579967792+0j)
24	(1.3986756009811165e-05+0j)	(0.02216004255455788+0j)	(0.025642353429696986+0j)	(1.1939916810661035+0j)	(1.110676510230148+0j)	(1.777423904747777+0j)	(0.04777423010849025+0j)	(0.07957568418941006+0j)	(1.3269728544452968+0j)	(1.7517709034394262+0j)	(0.37661612251149+0j)	(0.0010114151563292647+0j)
25	(0.029728097910036104+0j)	(0.03675626542561087+0j)	(0.8333490364127417+0j)	(4.993991959649486+0j)	(0.07196850752991053+0j)	(1.2417460863134355+0j)	(1.0829633047717315+0j)	(0.5295599727192907+0j)	(1.2120373017995523+0j)	(0.2950989474859779+0j)	(1.1959396249571426+0j)	(0.036902074430999056+0j)
26	(0.07650065198084756+0j)	(0.43326667657815376+0j)	(0.28748436615097683+0j)	(0.0001062359543223437+0j)	(0.015709437929970156+0j)	(1.6346180005578035+0j)	(3.70094698807515+0j)	(0.00298178047953042+0j)	(4.1619568904564926e-05+0j)	(1.8096995874906279+0j)	(0.7966388666047839+0j)	(0.5062090638621988+0j)
27	(0.10996252555168674+0j)	(0.4331779003360636+0j)	(2.6981225416077104+0j)	(0.8273401510626112+0j)	(0.950737791761243+0j)	(0.04370125150160605+0j)	(0.05468934430809346+0j)	(0.06819699996645191+0j)	(1.1551502907939746+0j)	(0.3346736534609096+0j)	(4.344488077076453+0j)	(0.29283051033479063+0j)
28	(0.00036332020800605464+0j)	(0.0009879002705321192+0j)	(2.3136085979501333+0j)	(0.4711167384860809+0j)	(2.598450517378809+0j)	(0.15023286466221186+0j)	(0.21702289989405615+0j)	(0.7416557894927269+0j)	(0.010666439879300865+0j)	(2.9152511229987805+0j)	(0.0016812154765787504+0j)	(0.11624441797256604+0j)
29	(0.006111033496491403+0j)	(1.6586879465571742e-05+0j)	(6.602073232818178+0j)	(0.762193131041005+0j)	(0.01601119904926266+0j)	(0.023297689378973748+0j)	(0.46253215670755427+0j)	(0.09575998294351662+0j)	(0.7533866711169142+0j)	(2.441714484877876+0j)	(0.00983305210652795+0j)	(3.2253878413317243+0j)
...	...	...	...	...	...	...	...	...	...	...	...	...
930	(0.6225264065544687+0j)	(3.2205003432766124+0j)	(0.00698185783366087+0j)	(0.18396952565299768+0j)	(0.6163449191484653+0j)	(0.20553793183222913+0j)	(1.0807230792678355+0j)	(0.1708630088866433+0j)	(0.04099258811285639+0j)	(0.0015158420361831685+0j)	(0.4895869596010753+0j)	(0.007140468165861643+0j)
931	(0.4770361257107589+0j)	(4.349117533086288+0j)	(1.37535136397493+0j)	(4.021927378250594e-06+0j)	(1.8218755537504239+0j)	(0.00012876013833738526+0j)	(2.648355666054771+0j)	(0.22364642075209112+0j)	(0.036494216438784324+0j)	(5.121610834705279e-06+0j)	(1.6451658311984507+0j)	(0.5001584828959832+0j)
932	(0.477171610954048+0j)	(3.1480684695901333+0j)	(4.822723788526226+0j)	(0.8054133442439151+0j)	(3.6556469703831995+0j)	(0.11478662119663341+0j)	(0.24803931751426583+0j)	(2.413175324939287+0j)	(0.000854786711057645+0j)	(0.0025736076204225995+0j)	(0.03811626049371059+0j)	(1.7808109436761517+0j)
933	(0.9415574662613357+0j)	(1.7950804667728435+0j)	(10.6474439298958+0j)	(0.5981686160526367+0j)	(1.0183737710069731+0j)	(2.0193786493691444+0j)	(0.6408694162468886+0j)	(4.776672263039484+0j)	(0.2597275219707448+0j)	(0.2494829829800176+0j)	(0.6314941860071787+0j)	(0.29997732490475687+0j)
934	(0.20207972823522324+0j)	(1.4372441007679821+0j)	(0.003774885355943659+0j)	(0.4214995758303916+0j)	(0.9876170684707226+0j)	(2.6198867966775214+0j)	(0.6045388879684422+0j)	(0.39319293517266674+0j)	(0.027925908017257518+0j)	(0.9700587028143812+0j)	(0.6755208386416797+0j)	(0.006310447275219282+0j)
935	(0.1408717379720138+0j)	(1.3697275459813605+0j)	(0.11422736583703641+0j)	(0.6330644503669453+0j)	(1.1481683303445398+0j)	(0.0009502009398127816+0j)	(0.0013624094563200698+0j)	(0.480907631294589+0j)	(0.01621725732368298+0j)	(0.01695835752359359+0j)	(0.027498453029697306+0j)	(0.4013342275002517+0j)
936	(0.016035271860208828+0j)	(1.5428042700635618+0j)	(0.01909590412458977+0j)	(0.02440101093191267+0j)	(0.1799289830339428+0j)	(0.21085600926959422+0j)	(1.5197894692765002+0j)	(0.00013789069235359928+0j)	(0.4953575615881757+0j)	(1.0018449903748028+0j)	(0.0016018826305618543+0j)	(0.6168124645944701+0j)
937	(0.04856529969907437+0j)	(1.3694485750873289+0j)	(0.27375330120288+0j)	(0.2972268721409792+0j)	(5.585083078530154e-06+0j)	(0.7769761425014667+0j)	(1.6297549652849137+0j)	(0.021947524222842994+0j)	(1.7415571302554336+0j)	(3.017724601596637+0j)	(3.8402537385122955+0j)	(0.17747872263813422+0j)
938	(0.003436016035269262+0j)	(3.1436417165021733+0j)	(1.898180508091935+0j)	(0.07658076119623955+0j)	(2.5689394290560914+0j)	(0.34791412200523075+0j)	(0.11353463265038899+0j)	(0.5576453575174618+0j)	(0.003105129779089095+0j)	(0.18587575337322265+0j)	(0.4600946631734635+0j)	(1.8564300957584774+0j)
939	(0.010945131266147566+0j)	(1.4005611201140022+0j)	(0.9294842333430431+0j)	(1.1014105106772905+0j)	(5.062843675641124+0j)	(0.1473689837619602+0j)	(0.7318685900789472+0j)	(0.006124171487994809+0j)	(0.05427536453852763+0j)	(0.06334015629073435+0j)	(0.6322555899586826+0j)	(0.011116540864217882+0j)
940	(0.23423096846739727+0j)	(1.0158094583499253+0j)	(0.8306647698131906+0j)	(1.0885052976695502+0j)	(3.7571709737044565+0j)	(1.6235481353900698+0j)	(0.06359349110836292+0j)	(0.02076099055353984+0j)	(2.188447967260663+0j)	(0.05918398134535314+0j)	(0.8821617923299777+0j)	(2.2525278631000325+0j)
941	(0.18948813161134886+0j)	(1.1850210114986675+0j)	(0.4026970224512126+0j)	(0.5539409872293777+0j)	(0.014251339212326537+0j)	(0.08569507854746819+0j)	(0.17168427922425689+0j)	(0.7099249893731968+0j)	(0.4192965884965119+0j)	(0.031798910540289306+0j)	(0.006395904902157099+0j)	(1.0383446594484973+0j)
942	(0.2226288640697862+0j)	(0.061207390212027944+0j)	(3.5018124740893315+0j)	(0.02579439354185705+0j)	(1.6910507158038683+0j)	(0.004726550207749239+0j)	(2.407764899559851+0j)	(0.5282384442086158+0j)	(0.01897834452407716+0j)	(0.40325373273080456+0j)	(1.6475848362158048+0j)	(0.6313451671754768+0j)
943	(0.054576249923155115+0j)	(0.13923333950179814+0j)	(1.5159181989010233+0j)	(0.21401648447709617+0j)	(0.4750099485813324+0j)	(0.7482806288908329+0j)	(0.5681700473381219+0j)	(0.9582317563867715+0j)	(0.6259909357386759+0j)	(1.9020582660690415+0j)	(0.03554893951976799+0j)	(4.170242803379671+0j)
944	(0.02996040780242931+0j)	(0.2230796560000931+0j)	(1.0575797984776576+0j)	(0.5061252890901922+0j)	(0.18447512494113083+0j)	(0.03206033139678966+0j)	(0.07804129248403902+0j)	(0.14513314844255293+0j)	(0.3132407108524525+0j)	(1.4844775152337129+0j)	(0.03721704043693705+0j)	(0.005524774145709235+0j)
945	(0.0012739076259132185+0j)	(0.019582916721641176+0j)	(0.0035843093574926834+0j)	(0.016352646462531487+0j)	(1.4735057910169+0j)	(0.5193070781279815+0j)	(1.3694930249949646+0j)	(0.010096925456422046+0j)	(0.029281245108287075+0j)	(0.13397466926474424+0j)	(2.3849390395546317+0j)	(0.01961292386519952+0j)
946	(0.2895416700129236+0j)	(0.001803817850588841+0j)	(0.6108392266966366+0j)	(0.0661827591796948+0j)	(0.018928431643253092+0j)	(1.6911279037938192+0j)	(0.11233363352685082+0j)	(1.6510283842992475+0j)	(1.0515806038405457+0j)	(1.22241333867659+0j)	(1.8795928206720711+0j)	(0.8627968372351286+0j)
947	(0.2976728868568348+0j)	(0.0638604207990009+0j)	(0.16509832808182417+0j)	(0.993972527477607+0j)	(0.28445977124408556+0j)	(0.16457878799403736+0j)	(0.38408650675401584+0j)	(1.5048203638176478+0j)	(8.24689908132326e-06+0j)	(1.8616773465105543+0j)	(0.24103211532826693+0j)	(0.20564625318511362+0j)
948	(0.4111253925188433+0j)	(0.06453792919461118+0j)	(2.231190708393531+0j)	(1.6048900679279703+0j)	(0.1998269387922019+0j)	(0.5563210142737253+0j)	(2.0769189544229363+0j)	(0.028146968761247983+0j)	(0.4921011110922811+0j)	(0.5878955599600119+0j)	(0.030771133256916102+0j)	(0.13640538359834362+0j)
949	(0.009815711992614308+0j)	(0.07797955030628292+0j)	(0.27090339046767037+0j)	(0.6549454900960082+0j)	(0.3701536303412755+0j)	(0.021785791685920517+0j)	(0.210472826615626+0j)	(0.4375136910441059+0j)	(0.939199519114879+0j)	(0.19821623580903436+0j)	(0.570188074503687+0j)	(1.0911611390894074+0j)
950	(0.0012045252981770667+0j)	(0.09861620413937569+0j)	(0.9192077429556451+0j)	(0.13930943570725765+0j)	(0.1768587208620855+0j)	(0.040947011815117736+0j)	(2.208706648088151+0j)	(0.24131033165804408+0j)	(4.915702420941308+0j)	(0.3247439913188211+0j)	(2.6081510148678064+0j)	(3.0860608409756902+0j)
951	(0.013568886415317697+0j)	(0.006398476588795624+0j)	(0.2687334686794681+0j)	(0.16479095210591824+0j)	(0.0768039991952496+0j)	(0.700428645139962+0j)	(1.183976114866962+0j)	(2.016312144608199+0j)	(3.889817787647945+0j)	(0.1842684025781161+0j)	(0.1161582422326212+0j)	(3.733669079727834+0j)
952	(0.13739703858460975+0j)	(0.03494314999009271+0j)	(0.1763489181560132+0j)	(4.915652408851371+0j)	(0.39509067682542526+0j)	(0.7369737443767518+0j)	(1.5735389082917197+0j)	(0.00012743892569854102+0j)	(0.06445199637896248+0j)	(2.1566028691005132+0j)	(0.05054937275645161+0j)	(0.9906851815696116+0j)
953	(0.09302245941251941+0j)	(0.17411422590521236+0j)	(0.361147237587345+0j)	(2.195164290711987+0j)	(0.04611090183230152+0j)	(0.22072208286558812+0j)	(0.21563669893512183+0j)	(0.002888871749987576+0j)	(1.625824938998357+0j)	(0.5257472066187177+0j)	(6.458771200445408+0j)	(4.110635379418541+0j)
954	(0.08272402595233441+0j)	(0.004916249616858865+0j)	(0.006791682878995382+0j)	(0.8373569924161058+0j)	(0.037813398134112136+0j)	(0.6602699914027209+0j)	(0.07726392717428368+0j)	(5.177358806714732e-05+0j)	(0.03945793518936993+0j)	(0.2703155409224414+0j)	(7.0822716173249525+0j)	(0.08504848929367735+0j)
955	(0.10401231354268732+0j)	(0.019409766971503702+0j)	(0.0056792962353610435+0j)	(0.506794569087241+0j)	(1.4120677256410676+0j)	(0.006711510701388891+0j)	(0.04568871314645485+0j)	(0.9476299550917062+0j)	(0.5828443053926856+0j)	(0.04006745979634974+0j)	(0.09076694755773161+0j)	(0.3963145350286827+0j)
956	(0.02072022942320195+0j)	(0.0055464155541845635+0j)	(0.10791301986112298+0j)	(0.10675374175145451+0j)	(1.6849825723226206+0j)	(1.4462050071280643+0j)	(0.2374475373037865+0j)	(0.027355492119487654+0j)	(2.1403488611383628+0j)	(5.613637155976287+0j)	(0.3105849597991589+0j)	(0.059498509359478625+0j)
957	(0.011312088406649818+0j)	(0.019623629447819844+0j)	(0.18631637887725214+0j)	(1.4792859363015558+0j)	(4.161988194806918+0j)	(1.0140809113656497+0j)	(0.5104499405099208+0j)	(0.8124926199039993+0j)	(0.179890343323379+0j)	(3.0567263135066183+0j)	(0.2407652593728596+0j)	(2.339022218669519+0j)
958	(0.17442846316440894+0j)	(0.06804173859345662+0j)	(0.03784534171358728+0j)	(0.1069569490172357+0j)	(2.042403288018232+0j)	(0.007352881006362536+0j)	(6.886861335490553+0j)	(1.506305438392009+0j)	(1.7047703494120017+0j)	(0.3156625867596572+0j)	(0.7411578468123222+0j)	(0.19112550646227752+0j)
959	(0.2869303252533612+0j)	(0.08387590781324275+0j)	(0.0015016695451436574+0j)	(0.04510855720471311+0j)	(0.0064457326649372485+0j)	(2.981426719715065+0j)	(3.869652071332872+0j)	(0.02741655667550059+0j)	(2.8722207777966484+0j)	(1.4309610532122945+0j)	(0.11712927688895805+0j)	(3.724377281246395+0j)

960 rows × 12 columns

In [14]:

#Calculations of T2
T2 = np.array(T2_matx.sum(axis=1))

#Control limit calculations of T2-UCL
percentil_T2 = 0.99*np.shape(T2)[0]
T2_UCL = np.sort(T2)[int(percentil_T2)]
Hotlling = pd.DataFrame(T2, columns=['T2'])
Hotlling['T2 - UCL'] = T2_UCL

Hotlling.head()

#Calculations of T2 T2 = np.array(T2_matx.sum(axis=1)) #Control limit calculations of T2-UCL percentil_T2 = 0.99*np.shape(T2)[0] T2_UCL = np.sort(T2)[int(percentil_T2)] Hotlling = pd.DataFrame(T2, columns=['T2']) Hotlling['T2 - UCL'] = T2_UCL Hotlling.head()

Out[14]:

	T2	T2 - UCL
0	(0.9811029147695842+0j)	(31.14246696443854+0j)
1	(4.29756297629967+0j)	(31.14246696443854+0j)
2	(5.077951332757397+0j)	(31.14246696443854+0j)
3	(6.539588583875818+0j)	(31.14246696443854+0j)
4	(5.265027675157708+0j)	(31.14246696443854+0j)

In [15]:

# Calculations of the estimated X* Matrix
X_est = np.dot(pca_matx2, np.transpose(auto_vet_matx))

pd.DataFrame(X_est).head()

# Calculations of the estimated X* Matrix X_est = np.dot(pca_matx2, np.transpose(auto_vet_matx)) pd.DataFrame(X_est).head()

Out[15]:

	0	1	2	3	4	5	6	7	8	9	...	42	43	44	45	46	47	48	49	50	51
0	0.022844	0.103805	0.015811	-0.202810	0.237469	-0.213682	-0.091838	0.061435	0.156640	0.127021	...	-0.077091	0.020159	0.355182	-0.089246	0.158603	0.405456	0.307093	-0.013844	0.196572	0.522567
1	0.264641	0.078717	0.073616	-0.493810	0.019124	-0.124415	-0.122445	-0.360045	0.330291	0.064332	...	0.032713	0.257356	0.559885	-0.093367	0.058378	1.793154	-0.243170	0.030323	0.438867	0.364954
2	-0.101658	0.157119	-0.415025	0.226761	-0.196071	0.050953	-0.018397	-0.602955	0.883480	0.063316	...	-0.136782	-0.101117	-0.399496	-0.085027	0.100983	0.468065	-0.924078	-0.006593	0.822179	-1.012814
3	0.175119	-0.323779	-0.322712	0.417411	-0.528822	-0.499850	-0.217340	-0.235032	0.356640	0.211811	...	-0.136624	0.174232	-0.584120	-0.080707	0.213829	-1.389943	-0.127238	0.051698	0.040901	1.011112
4	-0.174076	1.137750	-0.048919	-0.305982	-0.260280	0.396561	0.133831	0.358158	1.150771	-0.621098	...	0.084159	-0.169158	-0.096308	-0.070641	-0.557833	-0.659781	-0.337459	0.116664	1.084648	0.215500

5 rows × 52 columns

In [16]:

# Waste R
R = file2_norm - X_est

R.head()

# Waste R R = file2_norm - X_est R.head()

Out[16]:

	0	1	2	3	4	5	6	7	8	9	...	42	43	44	45	46	47	48	49	50	51
0	-0.101570	1.106319	-0.293740	1.152886	0.185288	-0.490950	0.054334	0.295009	-0.126620	-0.253842	...	0.201725	0.009126	1.287120	-0.641386	-0.084766	-0.019851	-0.100370	0.076418	0.353795	-0.059467
1	-0.338113	0.004395	0.382901	-0.500860	-0.966993	0.094068	0.141938	-0.726129	0.235798	-0.135539	...	-0.557992	-0.233026	0.156070	0.061328	-0.040172	-0.011299	0.079619	-0.008257	0.632852	0.145859
2	0.073718	0.147649	0.092966	0.778207	-0.119202	0.045411	-0.000108	0.868525	-0.317390	-0.080619	...	0.298821	0.082616	0.621062	-0.063041	-0.137018	-0.076216	-0.091698	0.077645	0.369413	-0.098624
3	-0.176791	0.144650	-0.109672	0.038637	-1.291262	-1.114388	0.578819	-1.644392	-1.398759	-0.293284	...	0.396851	-0.218926	0.785438	-0.628170	-0.186583	-0.397527	-0.150961	-0.052713	-0.533235	0.251017
4	-0.018830	-0.061868	0.864779	0.701910	-0.562986	-0.327349	-0.152336	0.206537	-0.048612	-0.438327	...	-0.317211	0.073492	0.151671	0.115956	0.179662	0.132188	0.014674	-0.118150	0.118360	-0.138811

5 rows × 52 columns

In [17]:

# Caltulations of Q
Q = np.diag(np.dot(R,np.transpose(R)))
percentil_Q = 0.99*np.shape(Q)[0]
Q_UCL = np.sort(Q)[int(percentil_Q)]
Q_Chart = pd.DataFrame(Q, columns=['Q'])
Q_Chart['Q - UCL'] = Q_UCL

Q_Chart.head()

# Caltulations of Q Q = np.diag(np.dot(R,np.transpose(R))) percentil_Q = 0.99*np.shape(Q)[0] Q_UCL = np.sort(Q)[int(percentil_Q)] Q_Chart = pd.DataFrame(Q, columns=['Q']) Q_Chart['Q - UCL'] = Q_UCL Q_Chart.head()

Out[17]:

	Q	Q - UCL
0	7.445068	49.067886
1	6.237008	49.067886
2	6.780736	49.067886
3	24.492865	49.067886
4	14.641089	49.067886

In [18]:

#Building the card of T2
chart_T2 = Hotlling.plot.line(style=['-','--'], color=['b','r'], legend = False)
plt.setp(chart_T2, xlabel = 'Observation', ylabel = 'T^2', title = 'Control card - T2   Normal operation')

#Saving the chart T2
plt.savefig('Chart_T2')

#Building the card of Q
chart_Q = Q_Chart.plot.line(style=['-','--'], color=['g','r'], legend = False)
plt.setp(chart_Q, xlabel = 'Observation', ylabel = 'Q', title = 'Control card - Q   Normal operation')

#Saving the chart Q
plt.savefig('Chart_Q')

#Building the card of T2 chart_T2 = Hotlling.plot.line(style=['-','--'], color=['b','r'], legend = False) plt.setp(chart_T2, xlabel = 'Observation', ylabel = 'T^2', title = 'Control card - T2 Normal operation') #Saving the chart T2 plt.savefig('Chart_T2') #Building the card of Q chart_Q = Q_Chart.plot.line(style=['-','--'], color=['g','r'], legend = False) plt.setp(chart_Q, xlabel = 'Observation', ylabel = 'Q', title = 'Control card - Q Normal operation') #Saving the chart Q plt.savefig('Chart_Q')

/home/nbuser/anaconda3_501/lib/python3.6/site-packages/numpy/core/numeric.py:538: ComplexWarning: Casting complex values to real discards the imaginary part
  return array(a, dtype, copy=False, order=order)

Failure Testing¶

In [19]:

files = ['d01_te.dat','d02_te.dat','d03_te.dat','d04_te.dat','d05_te.dat','d06_te.dat','d07_te.dat',
            'd08_te.dat','d09_te.dat','d10_te.dat','d11_te.dat','d12_te.dat','d13_te.dat','d14_te.dat',
            'd15_te.dat','d16_te.dat','d17_te.dat','d18_te.dat','d19_te.dat','d20_te.dat','d21_te.dat']

failures = ['Failure_01','Failure_02','Failure_03','Failure_04','Failure_05','Failure_06','Failure_07',
          'Failure_08','Failure_09','Failure_10','Failure_11','Failure_12','Failure_13','Failure_14',
          'Failure_15','Failure_16','Failure_17','Failure_18','Failure_19','Failure_20','Failure_21']

data_base_T2 = []
data_base_Q = []

detect_T2 = []
detect_Q = []

files = ['d01_te.dat','d02_te.dat','d03_te.dat','d04_te.dat','d05_te.dat','d06_te.dat','d07_te.dat', 'd08_te.dat','d09_te.dat','d10_te.dat','d11_te.dat','d12_te.dat','d13_te.dat','d14_te.dat', 'd15_te.dat','d16_te.dat','d17_te.dat','d18_te.dat','d19_te.dat','d20_te.dat','d21_te.dat'] failures = ['Failure_01','Failure_02','Failure_03','Failure_04','Failure_05','Failure_06','Failure_07', 'Failure_08','Failure_09','Failure_10','Failure_11','Failure_12','Failure_13','Failure_14', 'Failure_15','Failure_16','Failure_17','Failure_18','Failure_19','Failure_20','Failure_21'] data_base_T2 = [] data_base_Q = [] detect_T2 = [] detect_Q = []

In [20]:

for f in range(0,21):
    
    path2 = files[f] 
    fault_file = np.loadtxt(path2)

    if np.shape(fault_file)[0] < np.shape(fault_file)[1]:
        fault_file = np.transpose(fault_file)
    
    #Normalizing Data
    fault_file_norm = fault_file.copy()

    for i in pd.DataFrame(fault_file_norm):
        pd.DataFrame(fault_file_norm)[i] = (pd.DataFrame(fault_file_norm)[i] - averages[i])/desv_pad[i]
    
    
    #Building the Main Components
    fault_pca = np.dot(fault_file_norm , auto_vet_matx)
    
    #Calculating T2
    fault_T2_matx = pd.DataFrame(fault_pca).apply(el2)

    for i in fault_T2_matx :
        fault_T2_matx[i] = fault_T2_matx[i]/auto_val[i]
       
    #Calculations of T2
    fault_T2 = np.array(fault_T2_matx.sum(axis=1))
    fault_Hotlling = pd.DataFrame(fault_T2, columns=['Fault_T2'])
    fault_Hotlling['T2 - UCL'] = T2_UCL
    data_base_T2 += [fault_T2]
    
    
    ##Detection Speed Analysis 
    #Detection Criteria => 6 consecutive points above the control limit
    
    for i in range(0,np.shape(fault_T2)[0]):
        if i > (np.shape(fault_T2)[0] - 6):
            break
    
        if ((fault_T2[i] >  T2_UCL) and (fault_T2[i+1] >  T2_UCL) and (fault_T2[i+2] >  T2_UCL) and (fault_T2[i+3] >  T2_UCL) and (fault_T2[i+4] >  T2_UCL) and (fault_T2[i+5] >  T2_UCL)):
            detect_T2 += [[i+1 , failures[f]]]
            break 
    
    
    ##Calculations of Q
    #Calculation of the estimated X* Matrix of the failure
    fault_X_est = np.dot(fault_pca, np.transpose(auto_vet_matx))
    
    
    #Failure R Residues
    fault_R = fault_file_norm - fault_X_est
    
    
    #Calculations of Q on a Failure
    Q = np.diag(np.dot(fault_R,np.transpose(fault_R)))
    fault_Q_Chart = pd.DataFrame(Q, columns=['Q'])
    fault_Q_Chart['Q - UCL'] = Q_UCL
    data_base_Q += [Q]
    

    ##Detection Speed Analysis 
    #Detection Criteria => 6 consecutive points above the control limit
    
    for i in range(0,np.shape(Q)[0]):
        if i > (np.shape(Q)[0] - 6):
            break
    
        if ((Q[i] > Q_UCL) and (Q[i+1] > Q_UCL) and (Q[i+2] > Q_UCL) and (Q[i+3] > Q_UCL) and (Q[i+4] > Q_UCL) and (Q[i+5] > Q_UCL)):
            detect_Q += [[i+1 , failures[f]]]
            break 

    
    ##Building the chart T2
    fault_chart_T2 = fault_Hotlling.plot.line(style=['-','--'], color=['b','r'], legend = False)
    plt.setp(fault_chart_T2, xlabel = 'Observation', ylabel = 'T^2', title = ('Control Chart - T2   ' + failures[f]))

    #Saving the chart T2
    chart_T2 = failures[f] + ' - T2'
    plt.savefig(chart_T2)


    ##Building the chart Q
    fault_chart_Q = fault_Q_Chart.plot.line(style=['-','--'], color=['g','r'], legend = False)
    plt.setp(fault_chart_Q, xlabel = 'Observation', ylabel = 'Q', title = ('Control Chart - Q   ' + failures[f]))

    #Saving the chart Q
    chart_Q = failures[f] + ' - Q'
    plt.savefig(chart_Q)

for f in range(0,21): path2 = files[f] fault_file = np.loadtxt(path2) if np.shape(fault_file)[0] < np.shape(fault_file)[1]: fault_file = np.transpose(fault_file) #Normalizing Data fault_file_norm = fault_file.copy() for i in pd.DataFrame(fault_file_norm): pd.DataFrame(fault_file_norm)[i] = (pd.DataFrame(fault_file_norm)[i] - averages[i])/desv_pad[i] #Building the Main Components fault_pca = np.dot(fault_file_norm , auto_vet_matx) #Calculating T2 fault_T2_matx = pd.DataFrame(fault_pca).apply(el2) for i in fault_T2_matx : fault_T2_matx[i] = fault_T2_matx[i]/auto_val[i] #Calculations of T2 fault_T2 = np.array(fault_T2_matx.sum(axis=1)) fault_Hotlling = pd.DataFrame(fault_T2, columns=['Fault_T2']) fault_Hotlling['T2 - UCL'] = T2_UCL data_base_T2 += [fault_T2] ##Detection Speed Analysis #Detection Criteria => 6 consecutive points above the control limit for i in range(0,np.shape(fault_T2)[0]): if i > (np.shape(fault_T2)[0] - 6): break if ((fault_T2[i] > T2_UCL) and (fault_T2[i+1] > T2_UCL) and (fault_T2[i+2] > T2_UCL) and (fault_T2[i+3] > T2_UCL) and (fault_T2[i+4] > T2_UCL) and (fault_T2[i+5] > T2_UCL)): detect_T2 += [[i+1 , failures[f]]] break ##Calculations of Q #Calculation of the estimated X* Matrix of the failure fault_X_est = np.dot(fault_pca, np.transpose(auto_vet_matx)) #Failure R Residues fault_R = fault_file_norm - fault_X_est #Calculations of Q on a Failure Q = np.diag(np.dot(fault_R,np.transpose(fault_R))) fault_Q_Chart = pd.DataFrame(Q, columns=['Q']) fault_Q_Chart['Q - UCL'] = Q_UCL data_base_Q += [Q] ##Detection Speed Analysis #Detection Criteria => 6 consecutive points above the control limit for i in range(0,np.shape(Q)[0]): if i > (np.shape(Q)[0] - 6): break if ((Q[i] > Q_UCL) and (Q[i+1] > Q_UCL) and (Q[i+2] > Q_UCL) and (Q[i+3] > Q_UCL) and (Q[i+4] > Q_UCL) and (Q[i+5] > Q_UCL)): detect_Q += [[i+1 , failures[f]]] break ##Building the chart T2 fault_chart_T2 = fault_Hotlling.plot.line(style=['-','--'], color=['b','r'], legend = False) plt.setp(fault_chart_T2, xlabel = 'Observation', ylabel = 'T^2', title = ('Control Chart - T2 ' + failures[f])) #Saving the chart T2 chart_T2 = failures[f] + ' - T2' plt.savefig(chart_T2) ##Building the chart Q fault_chart_Q = fault_Q_Chart.plot.line(style=['-','--'], color=['g','r'], legend = False) plt.setp(fault_chart_Q, xlabel = 'Observation', ylabel = 'Q', title = ('Control Chart - Q ' + failures[f])) #Saving the chart Q chart_Q = failures[f] + ' - Q' plt.savefig(chart_Q)

/home/nbuser/anaconda3_501/lib/python3.6/site-packages/matplotlib/pyplot.py:513: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).
  max_open_warning, RuntimeWarning)

Calculation of MDR¶

In [21]:

#Database partition after failure (t = 160)
#Consideration: if the fault occurs at t = 160, it must be detected at t = 161.
#Therefore, the partition of the array occurs in column 160, 
#which corresponds to the 161st observation, and not in column 159

data_base_T2 = np.array(data_base_T2)[ : , 160:]
data_base_Q = np.array(data_base_Q)[ : , 160:]

#Database partition after failure (t = 160) #Consideration: if the fault occurs at t = 160, it must be detected at t = 161. #Therefore, the partition of the array occurs in column 160, #which corresponds to the 161st observation, and not in column 159 data_base_T2 = np.array(data_base_T2)[ : , 160:] data_base_Q = np.array(data_base_Q)[ : , 160:]

In [22]:

pd.DataFrame(data_base_T2)

pd.DataFrame(data_base_T2)

Out[22]:

	0	1	2	3	4	5	6	7	8	9	...	790	791	792	793	794	795	796	797	798	799
0	(14.355470830862036+0j)	(20.009989645112828+0j)	(11.195623528484468+0j)	(14.620599200014263+0j)	(20.51736009586412+0j)	(22.725909000266704+0j)	(51.98503006547338+0j)	(62.76483388246419+0j)	(134.42501455830484+0j)	(138.2642801105251+0j)	...	(287.62792774903767+0j)	(295.69653641224363+0j)	(226.8290116274844+0j)	(223.5933878796624+0j)	(277.60622528794374+0j)	(304.5876143608009+0j)	(284.90040387365787+0j)	(288.3363771694051+0j)	(301.28973099492055+0j)	(310.6855581737678+0j)
1	(8.22558098096903+0j)	(12.241434636675931+0j)	(7.439378777043604+0j)	(8.314546153563908+0j)	(14.935312385196221+0j)	(11.108420471058238+0j)	(11.960298302118504+0j)	(11.69484556509296+0j)	(16.15127068339416+0j)	(11.649230544287285+0j)	...	(1321.3935386021724+0j)	(1346.7508885789998+0j)	(1339.679727426559+0j)	(1326.4579728007388+0j)	(1312.3468749315089+0j)	(1278.2701927123296+0j)	(1281.8915887164985+0j)	(1280.3728049822764+0j)	(1426.8303740926617+0j)	(1426.7696662445576+0j)
2	(12.136158672206895+0j)	(13.65969691909496+0j)	(15.176175783948432+0j)	(19.47914232916111+0j)	(14.141627097614402+0j)	(11.136021252707165+0j)	(19.80172260311476+0j)	(9.2911803296868+0j)	(17.568450888838655+0j)	(19.699306213997893+0j)	...	(12.163356741507439+0j)	(12.392504586713127+0j)	(11.157633175431146+0j)	(8.405625977615532+0j)	(16.266706852364333+0j)	(20.315118434714613+0j)	(21.23435448885448+0j)	(18.404977441921822+0j)	(22.373993098433658+0j)	(16.19109534163643+0j)
3	(40.471173402726095+0j)	(16.554434041146642+0j)	(24.04298634492865+0j)	(34.50280535996089+0j)	(9.87205162006112+0j)	(17.12331570106297+0j)	(12.050266345222012+0j)	(20.019229123636443+0j)	(20.48667377780687+0j)	(18.353370390792307+0j)	...	(10.074657043380807+0j)	(12.137662824585655+0j)	(9.381402730919806+0j)	(13.565939008079418+0j)	(21.172488373300073+0j)	(14.164246808434616+0j)	(12.907758032450062+0j)	(10.048076268222964+0j)	(11.429006266800613+0j)	(14.396920860260769+0j)
4	(42.6205281998036+0j)	(89.96891903985522+0j)	(99.64191462170739+0j)	(91.94874229251428+0j)	(24.84788939370013+0j)	(14.68958803786076+0j)	(18.390814870398792+0j)	(17.963488799454524+0j)	(27.702435975318856+0j)	(17.48073670186151+0j)	...	(7.085184598769698+0j)	(7.083313798753801+0j)	(5.839978559668298+0j)	(6.2103253714737+0j)	(8.98764666820365+0j)	(8.399656312185058+0j)	(10.160608173879439+0j)	(7.649721366658589+0j)	(7.237490525491543+0j)	(11.456331777229227+0j)
5	(10.782444160633425+0j)	(13.180320611293261+0j)	(11.725889743678403+0j)	(16.376568638333154+0j)	(18.225397073838316+0j)	(23.52939887106143+0j)	(27.32119664819078+0j)	(28.314779810999696+0j)	(29.252400973865175+0j)	(39.95302045037302+0j)	...	(5701.826342460856+0j)	(5703.65472789289+0j)	(5743.717385197226+0j)	(5745.551128954786+0j)	(5653.790614185693+0j)	(5669.061861128334+0j)	(5730.750000415909+0j)	(5732.618053050488+0j)	(5681.701082861686+0j)	(5683.555061227518+0j)
6	(122.39786462274682+0j)	(144.97256210171366+0j)	(177.64110423934545+0j)	(163.43358854426376+0j)	(211.4014079182711+0j)	(220.3452467162728+0j)	(264.51372396222564+0j)	(258.11919777063355+0j)	(369.2879335918283+0j)	(405.6821568667699+0j)	...	(24.564207119856324+0j)	(26.00069921670671+0j)	(36.813859306328325+0j)	(44.76001510425799+0j)	(45.03559561138175+0j)	(40.02601254128306+0j)	(20.282567192047715+0j)	(29.979128261786983+0j)	(27.051391356368345+0j)	(32.15161326550113+0j)
7	(15.938743919810825+0j)	(10.021460829177125+0j)	(9.939545677277682+0j)	(12.209681549879814+0j)	(10.44300635877708+0j)	(13.037849053653941+0j)	(16.436934424953396+0j)	(21.0558719886041+0j)	(13.46204008921309+0j)	(25.318678389649826+0j)	...	(308.36155891468763+0j)	(312.2188963767034+0j)	(393.13911111795886+0j)	(396.8578796566044+0j)	(429.2501517880621+0j)	(443.41685457331874+0j)	(463.83287003600776+0j)	(450.78446371337367+0j)	(458.6829538940723+0j)	(452.77183078717405+0j)
8	(21.43153459660366+0j)	(16.85392720505193+0j)	(27.446994388493025+0j)	(20.332055468385338+0j)	(25.44371282307104+0j)	(30.320415176445508+0j)	(29.191783920213773+0j)	(24.339529028261598+0j)	(36.80288653353112+0j)	(30.021248934956816+0j)	...	(30.481596790189307+0j)	(15.542934295102956+0j)	(18.46515047288444+0j)	(23.031582664433948+0j)	(6.377419158642566+0j)	(7.317696976291377+0j)	(14.216563697781705+0j)	(12.241394080572203+0j)	(14.933434528973601+0j)	(16.707806921434873+0j)
9	(4.349288535058415+0j)	(12.577807692171763+0j)	(2.6295959738088164+0j)	(5.804032557656911+0j)	(12.208413057317953+0j)	(15.299070141851061+0j)	(7.640524458068545+0j)	(22.8664517329749+0j)	(19.295660959509007+0j)	(15.706790394913657+0j)	...	(12.46051336935097+0j)	(13.171950380590864+0j)	(9.857333732339296+0j)	(12.169386127512665+0j)	(9.305438999263702+0j)	(11.20598468448371+0j)	(12.999196265426955+0j)	(10.575045130108762+0j)	(8.728768724415154+0j)	(5.145394452476493+0j)
10	(13.331129900626664+0j)	(14.635616424977194+0j)	(10.30919373424811+0j)	(8.393946297456477+0j)	(12.03021742268542+0j)	(23.84884789991657+0j)	(43.96039944778739+0j)	(35.26982565434817+0j)	(10.918765699573555+0j)	(9.341020874109986+0j)	...	(15.674569751753392+0j)	(14.880520119984057+0j)	(14.514963871391368+0j)	(15.769741389908654+0j)	(14.619538515232822+0j)	(19.029277500559726+0j)	(12.149271483658374+0j)	(15.182056147915572+0j)	(32.35353941108798+0j)	(5.184900156031016+0j)
11	(11.106425349028376+0j)	(14.54080536046198+0j)	(77.66136165180805+0j)	(75.70723544744794+0j)	(29.888005141986653+0j)	(14.71035903124914+0j)	(41.933244205201575+0j)	(125.92632731519004+0j)	(123.64801162527755+0j)	(86.50199232984681+0j)	...	(322.3692514393226+0j)	(306.71854096970094+0j)	(308.7719771525183+0j)	(299.8129013541892+0j)	(381.738314363007+0j)	(513.0414588080394+0j)	(527.0106450446276+0j)	(467.33356605696736+0j)	(367.3948699212375+0j)	(311.55947635750624+0j)
12	(18.702316645980815+0j)	(14.354241342234491+0j)	(10.740146045688082+0j)	(14.015227639683332+0j)	(9.76640649156726+0j)	(7.5071808287111494+0j)	(19.072093299035352+0j)	(21.572495100380067+0j)	(11.039719267169364+0j)	(9.545830326843308+0j)	...	(655.9384962773745+0j)	(643.2006819144942+0j)	(659.851888200805+0j)	(635.5703661206785+0j)	(682.8136465983997+0j)	(672.661434216599+0j)	(645.4878935544018+0j)	(661.5589639522204+0j)	(734.3511172304612+0j)	(737.8393984932117+0j)
13	(11.638455841722525+0j)	(58.72346005919327+0j)	(18.590449235111166+0j)	(44.10880687383725+0j)	(48.24002052478962+0j)	(72.31461180140107+0j)	(158.28111232881446+0j)	(131.9121528907096+0j)	(153.76649314256912+0j)	(94.02655215974721+0j)	...	(197.6546996274416+0j)	(150.33451568860707+0j)	(173.0942255573649+0j)	(149.15068394440524+0j)	(132.31839093685406+0j)	(40.53456468300844+0j)	(57.01801469689106+0j)	(46.3141411534965+0j)	(43.13656244796658+0j)	(134.83814149774645+0j)
14	(16.61294124936336+0j)	(15.868023771212092+0j)	(10.999098579949697+0j)	(10.96917219404629+0j)	(12.867239866079485+0j)	(12.675899995409702+0j)	(10.01161583386703+0j)	(13.260830433850355+0j)	(3.39448453974405+0j)	(5.0758786080664775+0j)	...	(20.271360860883647+0j)	(21.376402681709173+0j)	(19.255993274444677+0j)	(21.428403988544254+0j)	(16.16896055163267+0j)	(20.26410209550517+0j)	(17.613030710900354+0j)	(19.29220064967367+0j)	(15.927551434692557+0j)	(17.838729288151573+0j)
15	(25.98911141564792+0j)	(26.211874437251684+0j)	(14.169263218915805+0j)	(18.192733110302726+0j)	(15.139910214963573+0j)	(8.702431171206056+0j)	(13.307103148219737+0j)	(15.588776251867145+0j)	(10.131845943964736+0j)	(10.330873639311626+0j)	...	(24.141685678706597+0j)	(24.503679439976736+0j)	(25.450273276619125+0j)	(22.668541713036454+0j)	(29.025135708624717+0j)	(31.2731211931364+0j)	(31.03618916416457+0j)	(28.82078616170531+0j)	(31.706950292127814+0j)	(41.890097717706354+0j)
16	(26.170478323418415+0j)	(23.212724567796222+0j)	(5.428852124442132+0j)	(14.24942465360133+0j)	(5.868667053146442+0j)	(8.710746853338877+0j)	(15.383469555131287+0j)	(13.29391055091088+0j)	(5.06990818531135+0j)	(10.912987044210222+0j)	...	(22.669773613693884+0j)	(18.991486634017967+0j)	(27.64002692185419+0j)	(18.696080665069452+0j)	(19.058980621632486+0j)	(11.266531806253012+0j)	(10.987043885643951+0j)	(13.689820042435812+0j)	(14.715279183826667+0j)	(17.939869156155915+0j)
17	(10.827557728266799+0j)	(10.24072500448797+0j)	(10.221625348510855+0j)	(9.639022681003297+0j)	(16.373342953588757+0j)	(19.637214496268847+0j)	(7.185734252358782+0j)	(12.540692308316146+0j)	(9.973284797467375+0j)	(12.721598784980866+0j)	...	(4836.581608824916+0j)	(4836.586317926838+0j)	(4806.238450571209+0j)	(4806.24315613446+0j)	(4856.6045128513615+0j)	(4870.980174963066+0j)	(4871.757594702427+0j)	(4871.762293264794+0j)	(4786.092157726778+0j)	(4786.096861325373+0j)
18	(13.843840146603984+0j)	(13.189546813424982+0j)	(11.212616412853096+0j)	(12.238353973939738+0j)	(14.244257215164549+0j)	(19.51645695865722+0j)	(15.529756172695437+0j)	(20.99607231126494+0j)	(18.143735915784205+0j)	(13.91546224273522+0j)	...	(16.074225603432364+0j)	(9.773725391112455+0j)	(7.495694975937965+0j)	(17.12960631777228+0j)	(16.432880274737677+0j)	(8.834450470104855+0j)	(4.334301768612379+0j)	(16.35932267060293+0j)	(6.117023187841274+0j)	(3.569021696938738+0j)
19	(12.26106632820131+0j)	(16.092446455470988+0j)	(10.017901058136795+0j)	(5.129299760706309+0j)	(10.619764877761192+0j)	(22.793016985532866+0j)	(5.0592544676669835+0j)	(20.587896339149978+0j)	(7.371749636007173+0j)	(9.794236359667693+0j)	...	(17.978658806321175+0j)	(14.92043140832309+0j)	(29.39873619603613+0j)	(31.670199214726644+0j)	(23.90642943610159+0j)	(24.603610896720163+0j)	(21.430639413863542+0j)	(32.783590693077095+0j)	(36.85529006690501+0j)	(34.74937910464746+0j)
20	(13.785281639464+0j)	(8.63022150555863+0j)	(18.58837144791122+0j)	(12.929137267888303+0j)	(12.442775214488792+0j)	(11.93776540453766+0j)	(8.000914004222778+0j)	(7.196861728634174+0j)	(6.36188015722088+0j)	(5.4065837692688055+0j)	...	(117.34801797298664+0j)	(110.64125879959204+0j)	(71.64841686505412+0j)	(82.67640550291516+0j)	(93.25312548531338+0j)	(97.22539314085301+0j)	(89.36187173101168+0j)	(106.72111953228921+0j)	(91.09205047318639+0j)	(94.92669347190319+0j)

21 rows × 800 columns

In [23]:

#Calculations for the Statistics of T2
MDR_T2 = []

for row in data_base_T2:
    count_T2 = 0
    
    for column in row:
        if column < T2_UCL:
            count_T2 += 1
            
    MDR_T2 += [count_T2/800]
MDR_T2 = np.array(MDR_T2)
    
#Calculations for the Statistics of Q
MDR_Q = []

for row in data_base_Q:
    count_Q = 0
    
    for j in row: 
        if j < Q_UCL: 
            count_Q += 1
            
    MDR_Q += [count_Q/800]
MDR_Q = np.array(MDR_Q)

#Benchmarking the Data
MDR_T2_Bench = np.array([0.008,0.020,0.998,0.956,0.775,0.011,0.085,
                0.034,0.994,0.666,0.794,0.029,0.060,0.158,
                0.988,0.834,0.259,0.113,0.996,0.701,0.736])
MDR_Q_Bench = np.array([0.003,0.014,0.991,0.038,0.746,0,0,
              0.024,0.981,0.659,0.356,0.025,0.045,0,
              0.973,0.755,0.108,0.101,0.873,0.550,0.570])

#Calculations for the Statistics of T2 MDR_T2 = [] for row in data_base_T2: count_T2 = 0 for column in row: if column < T2_UCL: count_T2 += 1 MDR_T2 += [count_T2/800] MDR_T2 = np.array(MDR_T2) #Calculations for the Statistics of Q MDR_Q = [] for row in data_base_Q: count_Q = 0 for j in row: if j < Q_UCL: count_Q += 1 MDR_Q += [count_Q/800] MDR_Q = np.array(MDR_Q) #Benchmarking the Data MDR_T2_Bench = np.array([0.008,0.020,0.998,0.956,0.775,0.011,0.085, 0.034,0.994,0.666,0.794,0.029,0.060,0.158, 0.988,0.834,0.259,0.113,0.996,0.701,0.736]) MDR_Q_Bench = np.array([0.003,0.014,0.991,0.038,0.746,0,0, 0.024,0.981,0.659,0.356,0.025,0.045,0, 0.973,0.755,0.108,0.101,0.873,0.550,0.570])

In [24]:

#Difference in Delta Statistics = LOP - Bench
Delta_MDR_T2 = MDR_T2 - MDR_T2_Bench
Delta_MDR_Q = MDR_Q - MDR_Q_Bench

#Difference in Delta Statistics = LOP - Bench Delta_MDR_T2 = MDR_T2 - MDR_T2_Bench Delta_MDR_Q = MDR_Q - MDR_Q_Bench

In [25]:

#Validation Table
Validation = pd.DataFrame([MDR_T2,MDR_Q,MDR_T2_Bench,MDR_Q_Bench,Delta_MDR_T2,Delta_MDR_Q], index = ['T2','Q', 'T2 - Bench', 'Q - Bench', 'Delta - T2', 'Delta - Q']).T

#Validation Table Validation = pd.DataFrame([MDR_T2,MDR_Q,MDR_T2_Bench,MDR_Q_Bench,Delta_MDR_T2,Delta_MDR_Q], index = ['T2','Q', 'T2 - Bench', 'Q - Bench', 'Delta - T2', 'Delta - Q']).T

In [26]:

Validation

Validation

Out[26]:

	T2	Q	T2 - Bench	Q - Bench	Delta - T2	Delta - Q
0	0.00750	0.00250	0.008	0.003	-0.00050	-0.00050
1	0.02000	0.01375	0.020	0.014	0.00000	-0.00025
2	0.99875	0.99000	0.998	0.991	0.00075	-0.00100
3	0.96125	0.03625	0.956	0.038	0.00525	-0.00175
4	0.77375	0.74500	0.775	0.746	-0.00125	-0.00100
5	0.01125	0.00000	0.011	0.000	0.00025	0.00000
6	0.07750	0.00000	0.085	0.000	-0.00750	0.00000
7	0.03250	0.02500	0.034	0.024	-0.00150	0.00100
8	0.99750	0.98000	0.994	0.981	0.00350	-0.00100
9	0.65000	0.64625	0.666	0.659	-0.01600	-0.01275
10	0.78750	0.34250	0.794	0.356	-0.00650	-0.01350
11	0.02125	0.02500	0.029	0.025	-0.00775	0.00000
12	0.06000	0.04500	0.060	0.045	0.00000	0.00000
13	0.12125	0.00000	0.158	0.000	-0.03675	0.00000
14	0.97875	0.97000	0.988	0.973	-0.00925	-0.00300
15	0.82875	0.74750	0.834	0.755	-0.00525	-0.00750
16	0.25250	0.09875	0.259	0.108	-0.00650	-0.00925
17	0.11250	0.10000	0.113	0.101	-0.00050	-0.00100
18	1.00000	0.86125	0.996	0.873	0.00400	-0.01175
19	0.70125	0.54750	0.701	0.550	0.00025	-0.00250
20	0.69375	0.57750	0.736	0.570	-0.04225	0.00750

Detection Speed Analysis¶

In [27]:

#Organization of the Detection Lists so that the faults 
#that were not detected are included in the data list

for fault in failures:
    
    if fault not in np.transpose(np.array(detect_Q)[:,1:]):  
        detect_Q += [['Not detected' , fault]]
        

for fault in failures:
    
    if fault not in np.transpose(np.array(detect_T2)[:,1:]):
        detect_T2 += [['Not detected' , fault]]

#Organization of the Detection Lists so that the faults #that were not detected are included in the data list for fault in failures: if fault not in np.transpose(np.array(detect_Q)[:,1:]): detect_Q += [['Not detected' , fault]] for fault in failures: if fault not in np.transpose(np.array(detect_T2)[:,1:]): detect_T2 += [['Not detected' , fault]]

In [28]:

#Creating data matrices and sorting values with respect to failure order
detect_Q = pd.DataFrame(detect_Q, columns = ['Detection - Q', 'Failure']).sort_values(by='Failure')
detect_T2 = pd.DataFrame(detect_T2, columns = ['Detection - T2', 'Failure']).sort_values(by='Failure')

#Creating data matrices and sorting values with respect to failure order detect_Q = pd.DataFrame(detect_Q, columns = ['Detection - Q', 'Failure']).sort_values(by='Failure') detect_T2 = pd.DataFrame(detect_T2, columns = ['Detection - T2', 'Failure']).sort_values(by='Failure')

In [29]:

#Determines the "Failure" -column as indexes for Q
detect_Q.set_index('Failure', inplace=True)

#Determines the "Failure" -column as indexes for Q detect_Q.set_index('Failure', inplace=True)

In [30]:

#Determining the "Failure" -column as indexes for T2
detect_T2.set_index('Failure', inplace=True)

#Determining the "Failure" -column as indexes for T2 detect_T2.set_index('Failure', inplace=True)

In [31]:

#Combining the detection data frames based on indexes
detect_T2.join(detect_Q)

#Combining the detection data frames based on indexes detect_T2.join(detect_Q)

Out[31]:

	Detection - T2	Detection - Q
Failure
Failure_01	167	163
Failure_02	177	172
Failure_03	Not detected	Not detected
Failure_04	Not detected	165
Failure_05	173	162
Failure_06	170	161
Failure_07	161	161
Failure_08	183	182
Failure_09	Not detected	Not detected
Failure_10	256	209
Failure_11	464	171
Failure_12	182	168
Failure_13	209	197
Failure_14	164	161
Failure_15	Not detected	Not detected
Failure_16	472	356
Failure_17	189	185
Failure_18	253	244
Failure_19	Not detected	Not detected
Failure_20	247	247
Failure_21	723	445