y=f(x) Explained!

y=f(x); read as Y is a function of X(es). That one single statement is probably the most important when it comes to understanding the concept of problem solving. One must realize that most things we are trying to solve in a business environment are measured as output – and these outputs are the ones we are trying to improve.

Let’s define problem

The dictionary defines the problem as “a matter or situation regarded as unwelcome or harmful and needing to be dealt with and overcome.” Read that statement once again. Problem is defined as a situation which is considered to be unwelcome or harmful. In a business scenario, any result that is not desirable for a customer and/or business is considered to unwelcome. Also, any metric that you need to improve because of any reason (even though from service level standpoint it may not truly be a situation that needs to be resolved) is considered as problem.


In simple words, y=f(x) means that each problem has a cause which is affecting it. In other words, it is called root-cause. In this equation, Y is the problem that you are trying to solve for. F means function. And X means the root cause(s) that affect the Y.

We read above that most problems that we try to solve in a business environment are measured at outputs. So, mostly you will have Y metric as an output metric that you are trying to solve. From our article on what a process is we learnt that for an output to be produced, you need inputs and process to churn those inputs into an output. A quick example of a process is energy that your body produces. In this example, input is the food and water and the process of digestion processes the food and water into energy.

Coming back to y=f(x). Since Y is an output metric where would the root-cause of a problem in Y be? Yes, you guessed it right! It will either be in input or the process itself that churns input into output or both in input as well as the process.

Six Sigma has given us a methodology to solve problems and that methodology is DMAIC – Define, Measure, Analyze, Improve and Control. This methodology works on the basic principle of y=f(x).

In DMAIC, you first define the problem then you measure the problem. Once you define and measure the magnitude and effect of the problem, you analyze. Think about that for a second. What do you analyze? This is where the equation y=f(x) comes in. In the measure phase, you identify possible root-causes and measure the potential root-causes. Remember, these root-causes are the Xes. In the analyze phase, you statistically find out the affect / impact of the root-causes on the problem. Once you have statistically identified the impact of the Xes, you then figure out the solutions and implement those solutions in the improve phase. Once the solutions are implemented you keep check and control the output.

So, the whole DMAIC approach is based on y=f(x). We highly encourage that you go through our articles on Lean Six Sigma to understand the DMAIC approach in detail.

Hope you enjoyed learning!

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