In this section, we are going to start with the Problem-Solving Formula in Six Sigma 
Six Sigma uses statistical analysis and measurement in different ways. 
The Six Sigma approach to problem-solving helps to determine the crucial inputs (x) and then to formulate an improvement plan (y). Putting it simply we can say that controlling or modifying the inputs will enable us to change or improve the outputs. 

The concept can be explained using the formula y=f(x) + εwhere 

•    Y refers to the output or the results of the process you are trying to improve, 

•    f is the function or the process that will convert the inputs to the desired result. 

•    x are the inputs or the factors (there can be more than one inputs (x)) required to get the result.

•    ε accounts for the level of error or uncertainty 

It is very important to quantify the process inputs and outputs to effectively determine what is influencing any process. Output depends on the application of a specific function on the inputs. Focusing on a few critical inputs can significantly improve the output.
This equation tells us that all outputs are determined by the way inputs are transformed according to some said process.

Cause and Effect Philosophy: 
The same concept is carried forward in Cause and Effect philosophy, which tells us that all the inputs and functions, and even errors will affect the outcome in some way. Any change in the inputs or some part of the process will have a corresponding effect on the outcome of the process. When we apply this philosophy to Six Sigma, it helps us to determine how the process will respond to variation. It helps us to determine the possible causes of a problem and how they are affecting the result. 

This video will then explain how y = f(x) and DMAIC work together and how to solve a problem using scientific methods for process improvement. The problem-solving formula is a very powerful concept of Six Sigma and is very useful when applying the acronym DMAIC.

Define: In the first step, we define the desired outcome to be achieved. 
Measure: We measure the inputs and causes of variations along with the current status of inputs and outputs. In this phase, the focus is on critical inputs that are producing maximum results or outputs. 
Analyze: The cause and effect of inputs on outputs are analyzed. We quantify the inputs that have maximum impact on the output. 
Improve: We implement the fixes of the variations or inputs that maximize the output. 
Control: Monitor the changes in the process over some time to see that the process does not deviate from the current pattern or revert to its previous pattern.

DMAIC roadmap is extensively used in Six Sigma for process improvement and to get desired results.