This module is an extension of “Engine Carbon Brushes Replacement-EDA”. Here are analyzed the correlations between brushSTD variable and vibration of engine rear bearing and between dust emission via the stack and engine power.

Correlation between brushSTD variable and vibration of engine rear bearing.

brushSTD - is the average deviation from average lifespan of carbon brushes at the moment of each engine running. In the beginning, we have a negative correlation (-0.49) between the variables. The situation could be interpreted in the following way: in almost in half cases rise of brushSTD cause to the reduction of vibration on rear bearing.

Actually, the correlation could point to the kind of connection between variables, without establishing cause and effect. But here, each change of brushSTD variable points to the carbon brush replacement. Because, the changes initiated by the staff, we can say that there are cause and effect.
In case the information is correct, we can find a way to reduce the vibration of the engine. Let’s learn the issue deeper.
Firstly, let’s understand what does it mean increasing and/or decreasing of average variance of carbon brushes lifespan (brushSTD variable).

How it was shown in the previous research- Cement Mill 1, the average lifespan of the engine carbon brush on CM1 is 364 days, but there are cases of lifespan for about five years.
Actually, the replacement of carbon brushes with the lifespan close to the average lifespan cause to increase the variance of brushes lifespans at the moment of replacement. For example, replacement at 02-May-2010 of C1R08 carbon brush, which was replaced 311 days ago, and C3R04 carbon brush, which was replaced 467days ago, increased brushSTD variable from 179 to 193.
Replacement of “frozen” carbon brushes with long lifespans cause to decrease of variance. For example, replacement at 15-Jul-2013 of C3R03 carbon brush, which was replaced 1231 days ago, decreased brushSTD variable from 242 to 216.

How it was shown in the previous research- Cement Mill 1, there are periods, of probably lost information of replacement of the engine carbon brushes - calculation of brushSTD variable during those periods actually provides fake information. Here are periods, found in the previous research: 

##   intervalDays  fromtDate     toDate
## 1           40 2006-10-04 2006-11-13
## 2          514 2013-12-23 2015-05-21
## 3          156 2016-05-31 2016-11-03
## 4           56 2017-01-31 2017-03-28
## 5           45 2017-04-30 2017-06-14
Let’s remove those periods from dataset.

Now let’s explore the second variable “Vibration of rear bearing”.

Here is a behaviour of the variable during the researched period:

In the beginning, we removed all observations with NA, but this variable has “0” value until 2015. Obviously, it is a fake information, but those observations were taken to the calculation of correlation. Let’s remove those observations from the dataset and calculate correlation.

After data clearance, we have dataset of 1223 observations. Newly calculated correlation shows that there is no any connection between the behaviours of these two researched variables “variance of carbon brushes lifespans” and “vibration of engine rear bearing”.



Correlation between dust emission via the stack and engine power

Next correlation for research is the dust emission via the stack and engine power. General cross-correlation table gives the negative value -0.31. It can be interpreted as- on 31% of observations, there is an opposede connection between increasing engine power and decreasing of dust emission. Let’s research this relationship.
Here I intend to answer three questions:
a) Whether correlation becomes stronger in different ranges of engine power;
b) Whether correlation becomes stronger in different ranges of dust emission;
c) What the reason for this correlation.

In the beginning, let’s remove from the raw dataset:
a) all redundant variables (leave only Date, Dust emission, and power);
b) “NA”s;
c) “-1” (“-1” was intentionally set during the data retrieval in cases where data was not availible)

When we use the same clearance measurements in two variables dataset, we can keep more observations than in a big raw dataset. As a result, we have a different correlation (bigger) than correlation from the whole raw dataset.
Next, start the routine to find a range of power, where the correlation between power and dust emission is stronger: 

## [1] "The strongest correlation is -0.49, in the range of power: 9 and 3354.5"

Next, start the routine to find a range of dust emission, where the correlation between power and dust emission is stronger: 

## [1] "The strongest correlation is -0.56, in the range of dust: 32.6 and 100"

How we can see, the correlation is relevant for above-allowed limit emissions (above 30 mg/m3). Understanding the reason for the phenomena will help to care environmental issue.
Attracts attention, that the range of power begins from numbers close to the zero. Actually, the average power is about 3000 kV/h, and power rises from the zero to the regular value very quickly after the engine start. The only reason that we have the average power of the engine run period very close to the zero - the engine run period is too short. On the other hand, a negative correlation means that lower power expects hight dust emission at least in 50% of cases.
Let’s show the data on a chart, combining power, time of engine work period, and dust emission.

How it was expected, the average value of dust emission significantly high for short work periods, as well as a lower average power value. Actually, every cement mill start accompanied by relatively high dust emission, during the work time current dust emission value has been stabilized and the average value decreases. Short periods (according to the chart) less than 50 min or so, not enough to reduce the average dust emission value and increase the average power value- that the reason for the correlation between mill engine power and dust emission.

Based on this research, we can conclude - in order to reduce dust emission, better to reduce the number of mill starts and increase the duration of each work period.