Formulations of a Commercial Lubricant

You work at a chemical processing firm. The engineers are testing new formulations of a commercial grade lubricant. This lubricant will be used in high use heavy machinery. They want to know how long each formulation lasts in general, but also how the formulations last under different temperatures and following different storage temperatures. Since these are initial tests they have simplified the predictor variables by forming categories (low, medium, high heat). These tests were performed across three different machines which might vary in some ways. Below is the data from this study. Your task is to provide answers to their questions. Make sure to check the assumptions of your model and to provide a well written summary of the findings.

1. How long each formulation lasts in general? 2. How long formulations last under different temperatures (storage, and running)?

First, lets take a look at the distribution of the life in hours.

Lets convert the variables to factors and subset the data to have two separate frames, one for F1 and another one for F2.

## Classes 'tbl_df', 'tbl' and 'data.frame':    27 obs. of  3 variables:
##  $ Running Temperature: Factor w/ 3 levels "high","low","med": 1 1 1 2 2 2 3 3 3 1 ...
##  $ Storage Temperature: Factor w/ 3 levels "high","low","med": 1 1 1 1 1 1 1 1 1 2 ...
##  $ Life in Hours      : num  25 16 20 27 24 26 26 26 20 24 ...
## Classes 'tbl_df', 'tbl' and 'data.frame':    27 obs. of  3 variables:
##  $ Running Temperature: Factor w/ 3 levels "high","low","med": 1 1 1 2 2 2 3 3 3 1 ...
##  $ Storage Temperature: Factor w/ 3 levels "high","low","med": 1 1 1 1 1 1 1 1 1 2 ...
##  $ Life in Hours      : num  26 24 24 34 28 31 26 31 30 27 ...

Now that we have the variables and data frames in place, we are ready to answer the questions.

1. How long does each formulation lasts in general?

F1 has a lower average duration than F2 (without considering temperature change).

##       F1       F2 
## 27.48148 32.66667

The box plot confirms F2 lasts longer across all temperatures. Let’s run an anova to test difference in means between F1 and F2.

## Analysis of Variance Table
## 
## Response: Lubricant_Formulations$`Life in Hours`
##                                    Df  Sum Sq Mean Sq F value   Pr(>F)   
## Lubricant_Formulations$Formulation  1  362.96  362.96  8.9504 0.004234 **
## Residuals                          52 2108.74   40.55                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

F-value is high and P-value under .05 suggest strong evidence against HO. We accept HA of unequal means across F1 and F2.

Let’s check if duration is different for each machine.

Average duration differs slightly across machines.

##       M1       M3       M2 
## 30.61111 28.55556 31.05556

## Analysis of Variance Table
## 
## Response: Lubricant_Formulations$`Life in Hours`
##                                    Df  Sum Sq Mean Sq F value   Pr(>F)   
## Lubricant_Formulations$Formulation  1  362.96  362.96  8.8757 0.004451 **
## Lubricant_Formulations$Machine      2   64.04   32.02  0.7830 0.462573   
## Residuals                          50 2044.70   40.89                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Low F vlaue and P-value >.05 suggest difference across means is miniscule, perhaps due to chance. We accept HO of unequal means across machines.

2. How long formulations last under different temperatures?

In all instances (F1 and F2) hours of duration decrease as temperature increases, this applies for storage and running temperatures. Take a look at the results:

##     high      low      med 
## 22.88889 31.11111 28.44444

##     high      low      med 
## 23.33333 31.44444 27.66667

##     high      low      med 
## 27.22222 37.22222 33.55556

##     high      low      med 
## 28.22222 36.11111 33.66667

Conclusions:

*F1 duration decreases at the same rate under both storage and running temperatures.

*F2 has a higher duration decrease rate under running temperature than storage.

*Overall, F2 has a higher duration when compared with F1 across all temperatures.