Which field of math will help me find a correlation between component data and overheating? I have the rpm (revolution per minute) data of multiple similar machines and the temperatures of their oil ( I have real time data of rpm and temperature sensors). The oil when goes above a certain temperature then machine is called being "overheated".
In some conditions it happens quite immediately (10 minutes of starting machine) when machine is switched on & in such case we (the maintenance team for these machines)  know that a certain component has caused that. There may be other patterns too, for other components which cause overheat in different pattern. Like in one case of overheat when machine has been immediately stopped while being in high rpm which causes the circulation of oil to stop leading to overheat.
Now, I want guidance about which field of maths/stats will help me find a correlation to predict which component has caused that type of overheat.
Additional info, if it matters: The rpms of machine keeps on fluctuating all the time, they can come to zero and raise again. Temperature does not fluctuate that much, it rises gradually and falls when rpm drops or the machine stops.
For my mathematics background, I have taken multivariate calculus, vector calculus, vectors, multivariate complex analysis, complex calculus, ODEs, PDEs etc.  in my college time. I have no knowledge of any statistics.  Where should I start and which technique & tools (software) will help me? Do share prerequisites for that.
 A: I would say the part of math you need most is data analysis, which some may think is more statistics than math.  You are really being asked for something closer to scientific research.  The rest may belong more on workplace than math, but it is how I would address the problem.  I will be guessing a lot because I don't know your machine at all.
I envision the thought behind the request being that you have found a symptom the tells you exactly what to fix, which is quite convenient.  Maybe if you look harder you will find more symptoms that can pinpoint other problems.  
I suspect this will be hard.  Overtemperature monitors are typically there to protect the machine, not to help you identify the cause of failure.  They often assume all the oil is at the same temperature, so it doesn't matter where it is located.  I would think it likely that the component that causes the 10 minute failure somehow causes heat to be dumped into the system near the sensor.  
I would start by identifying all the data that is available to you and listing all the failures you have information on.  I would look for periods when the machine was operating normally and at the same speed for a long time to see if I could identify the relationship between rpm and steady state temperature.  I would then look for times when the speed was changed and the new speed maintained for a long time.  You can see what the time constant is for achieving the new steady state temperature.  You can also see how repeatable the steady state temperature is.  Does it depend on outside temperature?  Does it depend on what is being processed?  Do you have other data like the difference between the commanded speed and the actual speed?  What you would like to do is find a way to predict the temperature of the machine for arbitrary speed changes.  If you are quite lucky the answer may be some convolution of the steady state temperatures associated with the commanded speeds with time decay.  Finally look at the times before known failures to see if there is a divergence between the predicted and actual temperatures.
Where I worked, the minute you ask anybody to help you with collecting more data, say by making a log of the material processed at each time or the temperature in the room you will be accused of making this into a science fair.  The accusation is true, but that is what you have been asked for.  Bulk temperature is often a very poor sensor for problems.  
Keep a careful record of all you do.  If you are successful in finding some symptoms that identify failures people will be very happy.  If you are not successful you want to be able to show how hard you tried.  
You might want to think about this for a week and make a presentation that describes the approach you think is best.  As it is research, the data may lead you in other directions, but you can make some best case estimates for how much time and money it will take.  You can compare that with some wild guesses on how much you will save by isolating failures more quickly and speeding the repair.  Show the people requesting this what you have and ask if they still want you to do it.  
If you do attack this, I hope you enjoy it.  Some people will, some will not.
