Comparison of Capability Analysis of Cumulative Cardiac Thoracic Ratio (CTR) Outputs

Table of contents

1. Introduction

dvance knowledge has made the study of process capability analysis not limited to the industry or manufacturing process only but is gaining overwhelming application in other fields of human endeavour especially in medicine for the evaluation of health care performance such as surgical site control, infection rate, response of patient to change in treatment in the hospital, outbreak of epidemic and performance of a forecasting system related to medical studies such as heart false positive radiological examination. This study looks at the process monitoring of CTR output measurements and check its state of stability for abnormality detection.

In medicine, chest radiography is commonly called chest X-ray (CXR). It is a projection of radiography of the chest use to diagnose conditions affecting the chest, its contents and nearly structure. Ribeiro, Jose, Renato, Roberto, Francisco, Domingo, and Beatriz (2012) observed that chest radiography is among the most common films taken to diagnose many conditions. Like all methods of radiography, chest radiography employs ionizing radiation in the form of xrays to generate images of the chest (Ribeiro, et al. (2012).

This research is motivated by the real life application of process capability analysis in the output of Cardio Thoracic Ratio of chest X-ray measurements in the examination of radiological process to establish capability analysis of the CTR experimental values. The aim of this study is to determine the capability analysis of Radiological CTR experimental values and the simulated values. The Specific objectives of the research are:

? To do capability analysis for experimental (Raw) and Simulated Cardiac Thoracic Ratio (CTR) values.

? To compare the capability analysis of the experimental Cardiac Thoracic Ratio (CTR) data (Raw values) and the simulated Cardiac Thoracic Ratio (CTR) data.

? To examine the significant difference in the variance of Cardiac Thoracic Ratio (CTR) data of raw and simulated CTR values. II.

2. Literature Review

The most commonly and widely used indices are p C (Juan 1974), pk C (Kane 1986), pm C (Hsiang and Taguchi 1985) and pmk C (Choiward and Owen 1970; Pearn and Kotz and Chen 1994-95) and their generalization for non-normal process suggested (Pearn and Kotz, 1995;Pearn and Chen 1995). Mukherjee (1995) studied conceptual approaches to process capability analysis. A number of new approaches to process capability analysis have been attempted and experimented (Carr 1991;Flaig 1996). Another index is given by Boyles (1994), when researcher or quality control officer is confronted with processes described by a characteristic whose values are discrete. Therefore, in such cases none of these indices can be used. The indices suggested so far whose assessment is meaningful regardless of whether the studied process in discrete or continuous are those suggested by Yeh and Bhaltachiya (1998). Borges and Ho (2001), Perakis and Xekalaki (2002;2005) In this study, evaluation of cumulative capability characteristics of the experimental CTR values (Raw) and Simulated CTR values using uniform distribution are investigated.

In real life application, calculation of proposed capability index boils down to computation of the process yield. To evaluate the process yield, it is necessary to apply a curve fitting method to approximate the quality characteristic distribution ( ) x f . Polansky (1999) used non-parametric approach particularly Kernel density estimation to estimate process yield for both univariate as well as multivariate quality characteristics. Ciarlini, Gigli and Regoliosi (1999) used bootstrap methodology to estimate failed probabilities even in regions not supported by data with accuracy. Independent of the sample variances is useful when data are not nearly normal. The Pearson distribution was implemented (Clement 1989), the Johnson distribution was suggested (Chou and Polansky 1996;Chou, Polansky and Mason 1998;. Burr distribution was used to describe non-normal process data (Castaghola 1996).

In practice, one may often be faced with processes whose distributions are far from being normal. In this capability study the index and the assumption that the underlying distribution of the examined process is a non-normal form and in particular, exponential. Gunter (1989) observed the experimental distribution arises frequently in industrial processes and were explained in the article (Yeh and Bhattachayya 1998). The normal and exponential process index is achievable for continuous process however; they are useless when the process is discrete. Poison process index pk C is used in the assessment of discrete process. The properties of are examined in the case where the studied process is described by a poison distribution characteristic with parameter m>0. The uniform process index is achievable for continuous process however; it is useful when the process was discrete. Uniform process index pk C is used in the assessment of discrete process. The properties of pk C are examined in the case where the studied process is described by a uniform distribution characteristic with some parameter a and b (Maiti etal., 2009).

In this study chart such as histogram with normal distribution is used to detect the trend behaviour of the CTR distribution outlier for abnormal CTR values. Uniformly simulated data will be compared with the raw CTR values based on capability analysis and variance. Uniform distribution process is simulated to compare with the raw CTR value of chest radiological examination in this study.

3. IV.

4. Simulation Technique

Simulation provides a method for checking your understanding of the world around you and helps us to produce better results faster.

5. a) A Study Simulation

In the study of Cardiac Thoracic Ration of Chest X-ray films examination, the raw values of cardiac and thoracic measure shall be computed to obtain the CTR value of patients that undergo the Chest X-ray examination as:

V V T C CTR = (1)

where V C is the cardiac value and the V T is the thoracic value of the measurements. If the CTR=0.5, the reading is said to be normal with boundary allowances of 0.45 and 0.55 for error of readings accommodation. Hence, the tolerance values are USL=0.55 and LSL=0.45 with the target value

? ? ? ? ? ? + = 2 LSL USL T =0.5.

(

)2

The study employs simulation technique using

6. Design and Implementation of Simulation

The simulation use in this study follows a uniform distribution process which ranges from 0.43 to 0.71 with 5 number of variable as subgroup measurements for 150 sample random number all together making 750 observations. Excel application package is the implementation medium used for the random number generation.

7. VI.

8. Variance ctr Raw and Simulated Processes Comparison

Bartlet 'b'-statistic is assumed as test-statistic that is distributed approximately as ? 2 ? distribution when samples are independently drawn from normal population (Singha, 2002). We test that

2 2 0 : s r H ? ? = and 2 2 0 : s r H ? ? ?

to determine equality of variances (Gomez and Kwanchai, 1984) of both raw and simulated CTR values of Chest X-ray measurement. Comparison of the variances of the raw CTR and Simulated CTR value is carried out in this study to investigate the process equality of variances. In this study, the variance of the CTR raw and simulated values are computed and tested for homogeneity based on the Bartlet Test 'b' statistic. The algorithm for the procedure is described by the following algorithm steps (A4).

9. VII.

10. Research Method

The source of data for the analysis is primary through raw computation and computer simulation using uniform distribution. The raw data are generated through the measurement values of the cardiac and thoracic of films output of Chest X-ray of patients from the radiological machine process. The ratios of the measurements are computed to obtain various CTR values over time. Inspection Coding Sheet (ICS) is used to randomly generate the samples for the study. Limits are set equal to 3sigma as

11. 5

. 0 = T is based on the specification criteria for non-sensitivity analysis (specificity) while statistical process control is investigated to address process stability. Capability analysis is performed for the two processes. The pattern of the means of the raw and simulated values are detected using exploratory data Analysis (EDA) approach like normal probability plots, empirical CDF functions and Box-plot. In addition, homogeneity of variance of the two processes is investigated based on Bartlet's 'b' statistic. The analysis of data is performed electronically with the aid of statistical software MINITAB version 16.0.

12. VIII.

13. Data Analysis and Result

This aspect focuses on exploring data analysis behaviour pattern of Raw and Simulated Cardiac Thoracic Ratio (CTR) values. It also discusses control chart graphs, process capability analysis and the process variance comparison using Bartlet 'b' statistic. The Boxplot of RCTRv and SCTRv illustrate non deviation in the RCTRv but deviation exists in the SCTRv because of the existence of the spike (whiskers of dispersion). This confirms that there is likelihood of more deviation from the 0.5 CTR standard in the SCTRv compare to the RCTRv.

14. Xbar Chart of Mean

15. Figure 1a

From the fig1a, the aggregate observation of 150 samples indicates that all points of the raw CTR values are falling within control limit confirming the process statistical stability and under control with predicted trend of sensitivity.

16. Process Capability of Mean

(using 95.0% confidence)

17. Figure 1b

For sample 150, the mean estimated is 0.5654 where the within and overall standard deviation are 0.0222 and 0.0227,

18. Xbar Chart of Mean

19. Figure 2a

From the fig2a, cumulative 150 samples all points of the simulated CTR values are falling within control limits implying process stable and follow a predictable trend. .This implies that the process is using about 39.1% of the specification band.

Hence, the values of The average estimated value of CTR is 0.57 which is 0.02 higher than the upper specification limit. True sensitivity analysis value of about 59.9% is confirmed fail points among the examined patients while the deviation among the sample measures is 0.023. Both p C and p P are near approximate hence there is little between subgroup variability.

20. g) Bartlet Test 'b' Statistic Computation and Result

The computational result of the Bartlet Test 'b' Statistic value do not exceed the Chi-square value, the variance of the raw and the simulated CTR values have unequal variance.

21. IX.

22. Conclusion

After aggregating all the raw computed CTR values and simulated CTR values obtained, it is empirically confirmed that the system is operating under 1.0 -1.3 sigma level for the raw CTR values. Around 28-39% of the raw CTR values obtained are falling outside the specification limits and 30-45% of the specification band is being used. In addition, the p pk C C < for all the cumulative raw CTR values suggesting that the process is off centred and is towards the lower specification limit. Therefore, the points are falling outside the upper specification limit which clearly indicates that the variability in the raw CTR process is very high.

23. X.

24. Recommendation

Based on the empirical outputs of capability analysis of radiological result of CTR values (raw and simulated), this study therefore recommends that health awareness campaign on slow death resulting from heart failure as a result of absence of early detection of abnormal CTR value among patients should be created by the government and health agencies. Patients should be medically advised on the measure to control and maintain stable CTR. Also on how to adopt better management methods which can subsequently prevent possibility of high CTR and further study should be conducted on large repeated experimental scale to ascertain the reliability of this study. Fellow up study of patients should be undertaken by the cardiologist to reduce the possible health risk that could result from the CTR.

for each sample subgroups respectively.

Step 2 : Calculated the row total values ? = n i i x 1 and the row average value of the sample subgroups and the mean of the mean of sample subgroup as:

? = ? = n i i x n X 1 1

and

? = = = M j j X M X 1 _ 1

Step 3 : Calculate the sample range and the sample subgroup range;

i i i x of MinValue x of MaxValue R ? = and ? = ? = M j j j R M R 1 1

Step 4 : Compute the sample variance and standard

deviation 2 1 1 ? = ? ? ? ? ? ? ? ? ? = n i i X X n ?

Step 5 : Evaluate the limits USL, CL and LSL for the sample mean

? = + = R A X USL 2 ? = ? = R A X LSL 2 = = X CL

Step 6 : Evaluate the limits USL, LSL and CT for the sample range for = 0.577, , when n=5 from the SQC table readings.

? = R D USL 4 ? = R D LSL 3 ? = R CL for 2 A = 0.? = ? ? ? ? ? ? ? ? = n i i X X n s and 2 1 2 2 1 ? = ? ? ? ? ? ? ? ? = n i i X X n s

Step 3 : Calculate the ( )

... 2 , 1 1 2 2 = ? ? = ? i K N S n S i i Step 4 : Compute ( ) ( ) ? ? ? ? = 2 2 log 1 log i i S n S k n Q Step 5 : Calculate ( ) ( ) ( ) ? ? ? ? ? ? ? ? ? ? + = ? K N n k H i 1 1 1 1 3( ) K N S n S i i ? ? = ? 2 2 1 = ( ) ( ) K N S n S n ? ? + ? 2 2 2 2 2 1 1 1 = ( )( ) ( )( ) = ? ? + ? 5 1500 193 . 1 1 5 674 . 0 1 5 0.0515 ( ) ( ) ? ? ? ? = 2 2 log 1 log i i S n S k n Q = ( ) ( ) ( )( ) ( )( ) [ ] 193 . 1 4 674 . 0 4 0515 . 0 log 2 5 + ? ? Q = ( )( ) [ ] 4675 . 7 2882 . 1 3 ? ? = -11.3321 ( ) ( ) ( ) ? ? ? ? ? ? ? ? ? ? + = ? K N n k H i 1 1 1 1 3 1 1 = ( ) ( )( ) ( ) ? ? ? ? ? ? ? ? ? + 5 150 1 4 4 1 1 2 3 1 1 H = ( ) ( ) 006896 . 0 0625 . 0 33 . 1 145 1 16 1 3 1 1 ? = ? ? ? ? ? ? ? + =0.07395 H Q b 3026 . 2 = = ? ? ? ? ? ? ?07395
Figure 1. (
and James (1998) devised control Year 2014 I charts for clinical process improvement and sample size determination for discrete and continuous processes.When the process parameters µ and ? are known, a kind of contour plots of the index PK C , called process performance chart, was introduced to understand capability of a process. To also compare the indices Boyles 1991) used contour plots called ( µ ,? )plots of these indices as functions of the process parameter ( µ , ? ).Deleryd and Vannman (1999) and Vannman (2001) used contour plots, called ( ) ,? ? -plots, as functions of the process parameters to illustrate the restrictions that the different indices in the family impose on the process parameter ( µ , ? ). When the process parameters µ and ? are unknown and need to be estimated,Deleryd and Vannman (1990) and Vannman (2001) developed what they called the ( ) ,? ?rectangle plots. rence about the process capability based on a random studied quality characteristic.
Figure 2. Plot of RCTRv, SCTRv
Empirical CDF of RCTRv, SCTRv
0.50 0.55 0.60 0.65 0.70
RCT Rv SCT Rv RC TRv
100 100 Mean StDev 0.5673 0.03372
N 150
80 80 Mean SC TRv 0.5790
StDev 0.03902
Percent 60 60 N 150
40 40
20 20
0 0
0.55 d) Boxplot of RCTRv and SCTRv 0.50 S CTRv RCTRv 0.60 Probability 0.65 Boxplot of RCTRv, SCTRv
RCT Rv 0.50 0.55 Data SCT Rv 0.60 0.65 Mean StDev RC TRv 0.5673 0.70 0.03372
N 150
A D 0.368
P-Value 0.426
SC TRv
Percent Mean StDev N A D 0.5790 0.03902 150 0.222
P-Value 0.826
Note: Normal -95% CIFigure 1 : Normality Plot of RCTRv and SCTRv The probability plots of raw and simulated CTR Normal Figure 2 :
Figure 3. Table 1 :
1
Process Capability of Mean
(using 95.0% confidence)
LSL Target USL
P rocess D ata W ithin
LS L 0.45 O v erall
T arget U S L S ample M ean S ample N S tD ev (Within) S tD ev (O v erall) 0.0390218 0.5 0.038998 150 0.57904 0.55 C P U C P L U pper C L Low er C L C p P otential (Within) C apability -1.49 6.62 2.85 2.27 2.56
C pk -1.49
Low er C L -1.85
U pper C L -1.13
O v erall C apability
Year 2014 48 P P M < LS L O bserv ed P erformance 0.00 P P M > U S L 786666.67 P P M T otal 786666.67 0.630 E xp. O v erall P erformance 0.585 0.540 468.34 0.495 E xp. Within P erformance 0.450 P P M < LS L P P M < LS L 471.72 P P M > U S L 771760.32 P P M > U S L 771623.09 P P M T otal 772228.65 P P M T otal 772094.80 0.675 Low er C L U pper C L P P L P P U P pk Low er C L U pper C L C pm P p Low er C L 2.27 2.85 6.61 -1.49 -1.49 -1.85 -1.13 2.56 1.13 1.07
XIV Issue I Version I Figure 2b For cumulative sample 150, the mean estimated is 0.5790 where the within and overall standard deviation are 0.0289 and 0.0290, 56 . 2 = p C , 49 . 1 ? = pk C , 12 . 1 = pm C since the p pk C C < , the process is off centred and is toward the lower specification limits. The percentage of the specification band that the process uses up is % 1 . 39 100 * ) / 1 ( = = p C P . This implies that the process is using about 39.1% of the specification band. Therefore, the values of 56 . 2 = p C and 56 . 2 = p P are equal therefore the process has little between subgroup variability. The empirical analysis results and findings of process capability analysis of raw and simulated CTR values are summarized in the table below:
Global Journal of Researches in Engineering ( ) Volume I n µ ? C C C p p pk pm P ? ? ? ? p C 1 ? ? ? ? = P p C ? ? ? ? ? 1 p C P ? ? ? ? p * 100 Raw Cardiac Thoracic Ratio Value (RCTRv) 50 75 100 0.5654 25 0.5658 0.5745 0.5681 0.0323 0.0276 0.0275 0.0226 4.42 2.99 4.40 4.27 -2.14 -1.27 -2.16 -1.58 1.07 1.21 1.19 1.12 2.09 2.66 2.66 2.97 0.226 0.334 0.227 0.234 22.6% 33.4% 22.7% 23.4% p p P C < p p P C < p p P C < p p P C < 125 0.5648 0.0229 4.55 -2.15 1.26 2.94 0.2180 22% p C < p P 150 0.0227 4.42 -1.52 1.22 2.97 0.2260 22.6% p P p C < 0.5654
Source: Results extracted from Minitab 16.0
For cumulative sample 150, the mean estimated uses up is P = 1 ( / C p ) * 100 = 39 % 1 . . This implies
is 0.5790 where the within and overall standard deviation that the process is using about 39.1% of the
are 0.0289 and 0.0290, C p = 2 . 56 , C pk = 1 ? 49 . , specification band. Values of p C and p P are barely
C pm = . 1 12 since the p C < , the process is off pk C equal hence there is substantial between subgroup
centred and is toward the lower specification limits. The variability.
percentage of the specification band that the process
© 2014 Global Journals Inc. (US)
Figure 4. Table 2 :
2
Simulated Cardiac Thoracic Ratio Value (SCTRv)
n 25 50 75 100 125 150
µ 0.5651 0.5724 0.5768 0.5771 0.5771 0.5790
? 0.0422 0.0413 0.0400 0.0280 0.0280 0.0227
C p 2.21 2.38 2.56 2.62 2.61 2.56
C pk -2.14 -1.08 -1.28 -1.42 -1.42 -1.49
C pm 1.07 1.19 1.15 1.16 1.16 1.22
p P 2.09 2.66 2.66 2.97 2.94 2.97
? ? ? ? p 1 C ? ? ? ? 0.4516 0.4201 0.3908 0.3821 0.3827 0.3907
P = ? ? ? ? 1 p C ? ? ? ? * 100 45.2% 42% 39.1% 38.2% 38.2% 39.1%
p C ? p P p C < p P p C < p P p C < p P p C < p P p C < p P p C < p P
Source: Results extracted from Minitab 16.0
For cumulative sample 150, the mean estimate
is 0.5790 where the within and overall standard deviation
are 0.0289 and 0.0290, C p = 2 . 56 , C pk = 49 . 1 ? ,
C pm = . 1 12 since the pk C < C p , the process is off
centred and is toward the lower specification limits. The
percentage of the specification band that the process
uses up is P = 1 ( / C p ) * 100 = . 39 % 1 . This implies
that the process is using about 39.1% of the
specification band. Values of p C and p P are barely
equal hence there is substantial between subgroup
variability.
For the total sample 150, the mean value
estimated is 0.5790 where the within and overall
standard deviation are 0.0289 and 0.0290, C p = . 2 56 ,
C pk = 49 . 1 ? , C pm = 1 12 . since the pk C < C p ,the
process is off centred and is toward the lower
specification limits. The percentage of the specification
band that the process uses up is
P = 1 ( / C p ) * 100 = % 1 . 39
Figure 5.
Compute b
A4 : Bartlet 'b' Statistic computational results for Raw and Simulated CTR values
Raw CTR Variance Simulated CTR Variance
1 s 2 0.674 s 2 2 1.193
1 log s 2 -0.172 log s 2 2 0.0765
Figure 6. Sub 2 Sub 3 Sub 4 Sub 5 Total Mean Range Sample Sub 1 Sub 2 Sub 3 Sub 4 Sub 5 Total Mean Range Variance
Appendix B
B3
0.003 0.010 0.005 0.005 0.009 0.010 0.009 0.010 0.011 0.010 0.007 . . 0.006 0.011 0.010 0.001 0.007 0.006 0.006 0.003 0.005 0.012 0.012 0.002 0.008 0.005
0.14 0.21 0.19 0.17 0.22 0.22 0.23 0.24 0.26 0.22 0.18 . . 0.21 0.25 0.24 0.06 0.18 0.2 0.21 0.15 0.15 0.24 0.26 0.12 0.23 0.16
Year 2014 3.07 0.61 2.76 0.55 2.73 0.55 2.55 0.51 2.5 0.5 2.84 0.57 2.79 0.56 3.05 0.61 2.65 0.53 3.06 0.61 2.69 0.54 . . . . 2.86 0.57 2.95 0.59 2.78 0.56 2.86 0.57 2.87 0.57 2.77 0.55 2.82 0.56 3.27 0.65 3.16 0.63 2.97 0.59 3.07 0.61 2.55 0.51 3.04 0.61 3.17 0.63
XIV Issue I Version I 54 0.64 0.65 0.59 0.66 0.52 0.65 0.57 0.64 0.47 0.43 0.55 0.64 0.56 0.54 0.44 0.6 0.56 0.43 0.48 0.48 0.64 0.42 0.47 0.42 0.54 0.45 0.47 0.63 0.68 0.61 0.49 0.68 0.45 0.55 0.62 0.48 0.67 0.72 0.64 0.54 0.45 0.51 0.54 0.44 0.7 0.62 0.7 0.52 0.51 0.72 0.64 0.62 0.51 0.46 0.47 . . . . . . . . 0.55 0.54 0.68 0.47 0.62 0.53 0.67 0.73 0.48 0.54 0.68 0.62 0.51 0.43 0.53 0.56 0.58 0.59 0.54 0.6 0.47 0.65 0.61 0.63 0.5 0.51 0.54 0.61 0.66 0.46 0.67 0.55 0.55 0.46 0.59 0.65 0.69 0.67 0.56 0.7 0.56 0.7 0.71 0.6 0.59 0.73 0.52 0.53 0.49 0.69 0.46 0.63 0.71 0.55 0.72 0.54 0.56 0.52 0.44 0.49 0.61 0.47 0.66 0.59 0.7 0.71 0.56 0.63 0.57 0.69
I ( ) Volume Global Journal of Researches in Engineering 0.013 1 0.71 0.7 0.76 3.25 0.65 0.29 Sample Sub 1 1 0.62 0.47 0.005 2 0.73 0.59 0.56 3.23 0.65 0.17 2 0.65 0.7 0.008 3 0.74 0.57 0.63 3.13 0.63 0.23 3 0.67 0.51 0.013 4 0.78 0.68 0.52 3.11 0.62 0.27 4 0.51 0.63 0.009 5 0.6 0.69 0.51 3.05 0.61 0.2 5 0.72 0.53 0.007 6 0.73 0.55 0.57 2.99 0.6 0.21 6 0.63 0.52 0.008 7 0.71 0.61 0.46 2.94 0.59 0.25 7 0.6 0.56 0.001 8 0.51 0.59 0.57 2.71 0.54 0.09 8 0.53 0.52 0.006 9 0.68 0.54 0.48 2.87 0.57 0.2 9 0.54 0.63 0.007 10 0.64 0.61 0.56 3.02 0.6 0.21 10 0.71 0.49 0.006 11 0.5 0.52 0.66 2.76 0.55 0.18 11 0.61 0.48 . . . . . . . . . . . 0.005 137 0.64 0.72 0.53 3.1 0.62 0.19 137 0.59 0.62 0.001 138 0.61 0.58 0.57 3.03 0.61 0.08 138 0.66 0.62 0.002 139 0.46 0.52 0.53 2.59 0.52 0.11 139 0.57 0.5 0.002 140 0.55 0.5 0.5 2.71 0.54 0.1 140 0.6 0.57 0.008 141 0.74 0.64 0.5 3.03 0.61 0.24 141 0.58 0.57 0.007 142 0.71 0.66 0.51 3.08 0.62 0.2 142 0.66 0.54 0.003 143 0.61 0.68 0.52 3 0.6 0.16 143 0.6 0.58 0.005 144 0.55 0.67 0.58 2.91 0.58 0.19 144 0.63 0.48 0.009 145 0.56 0.67 0.52 3.01 0.6 0.21 145 0.73 0.53 0.008 146 0.56 0.55 0.52 2.86 0.57 0.23 146 0.73 0.5 0.003 147 0.57 0.62 0.62 2.98 0.6 0.15 147 0.66 0.52 0.001 148 0.59 0.56 0.63 2.87 0.57 0.1 148 0.57 0.53 0.000 149 0.6 0.59 0.61 3 0.6 0.05 149 0.62 0.57 0.007 150 0.59 0.75 0.62 3.06 0.61 0.22 150 0.58 0.53 Source: Chest X-
Figure 7. ray Radiological Readings 2011 Source: Chest X-ray Radiological Simulation Readings 2011 Raw Computed Data Simulated Cardio-Thoracic Ratio Using Uniform Distribution Radiographic Films Readings of Chest X-ray Radiographic Films Readings of Chest X-ray For congestive Heart Failure Cardiomegaly Conditions For congestive Heart Failure Cardiomegaly Conditions Cadio-Thoracic Ratio Variance Cadio-Thoracic Ratio
1
2

Appendix A

Appendix A.1

Appendix B

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Notes
1
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2.
? value, both processes do not have equal variance.© 2014 Global Journals Inc. (US)
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Date: 2014-01-15