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Excellence in Results

Go to solution Solved by Prashanth Datta,

Y = f(X)


Y = f(X) is a common mathematical expression which defines the relationship between the dependent variable 'Y' and the independent variable(s) 'X'. It is read as "Y as a function of X". f denotes the function and it explains the impact of X on Y. In lean six sigma terms, Y is the output metric while X(s) is/are the input metric(s). 


An application-oriented question on the topic along with responses can be seen below. The best answer was provided by Prashanth Datta on 29th January 2019. 


Applause for all the respondents- Prashanth Datta, Vastupal Vashisth, Mathi



Q. 130  Y = F(X) indicates that we need to improve inputs and improve the process to get better outputs than what we got earlier. Is it possible to let one of the two remain at a below industry average level (inputs or process) and focus heavily on the other one to generate excellent results? Give examples to explain your answer. 


Note for website visitors - Two questions are asked every week on this platform. One on Tuesday and the other on Friday.

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Y=F(X) represents a Data Driven Approach to summarize our business problem statement.  It shows Causes (X) which has an impact on Effect (Y). Further, the SIPOC diagram helps us with a more detailed process map which helps us, to start at least with establishing a relationship between X and Y. Schematically representing the same as

Inputs (X) ---> Process --> Output (Y)


By following a DMAIC methodology, we look at improving our Output (Y) by generally addressing those X’s which can be influenced along with working on any process correction opportunities. In summary, an effective output is driven through driving changes both in inputs as well as the process followed. 


We have an interesting question which leads us to explore the fact if only one lever i.e. either Input or Process can be focused to drive an improvement in output Y.  To summarize the two conditions from our question is as below.

A. Focus heavily on X (inputs) while keeping your Process at a below average level.
B. Focus heavily on your Process while keeping your X (inputs) at below average level.

In both the cases, we need to understand that the either Input (X) or Process still plays a role but not leading to any significant changes to Y.


A. For Scenario A, focus on X while Process has minimal impact to the Output

The example I can think through here is that of the McDonalds French Fries.  

  • The desired Output (Y) here is, at their store, deliver tasty French Fries to customer within a committed time. 
  • In order to match to the conditions, key controllable X is Potatoes here. Enough investment is made by the team to ensure that the Input X is controlled from the farming stage itself i.e. grow potatoes under set condition of size, quality, quantity etc., cut to proportion, which then gets processed using the defined ingredients, partially fried, frozen, packed and sent to their Stores.
  • At store, the only process is just to fry and serve to their customer. 

The Input is controlled so well right from the source that it helps deliver the required delight factor to the customer at the store. 

Off late, most of the Ready to Eat food products available in the market are focusing on a better customer experience to provide a tasty product which can be prepared in less time and effort from a customer stand point. They are able to achieve this by controlling their inputs at source so as for the customer the process of preparing is as simple as putting it in a micro oven and heat or dip in boiling water for couple of minutes before it is ready to be served.

B. For Scenario B, Focus on the Process while the input has minimal impact on the Output
The example that I can pick for this scenario is from my kitchen – The water purifier.

  • The desired Output (Y) here is to drink a safe, healthy, tasty and potable water immediately when required. 
  • The input (X), Water once again can be from any source i.e. Bore Well, Storage Tank, Direct Municipal Water Supply and others.
  • My desired output is driven through my Water Purifier which has a set of processes designed within it and helps me achieve my objective. The stages of filtration and purification is methodically designed, so as the input water goes through the systematic process of each stage of purification and helps me with my desired output.

In this case, the water cleaning process plays a significant role to help achieve my output Y.

In the context of this discussion, here is a call-out. In my first example of Scenario A, the Y is decided basis my customer requirement and hence we say only Xs are controlled. But if you look at the process of preparing the French Fries alone, it has his own checks and balances and need to have a balanced approach between both X and Process. 

As last words, basis my observation and understanding, controlling of only X or only the Process is a relative discussion as it depends purely on the Y which we identify to drive. 

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As the question says Y = F(x), that we need to improve inputs and improve the process to get better outputs than what got earlier. 

It is not possible to to let one of the two remain at a below industry average level( input or process) and focus heavily on the other one to generate excellent results.


in previous question we have already seen that there can more than one x which is impacting outcome. Lets see some examples to understand that why is it not possible to let one of the two remain at below industry or standard level and focus heavily on other to get better output.


  1. Body Building in Gym: Some one has started to go Gym, no win this case outcome is a good physique and maintaining of his/her body. So this is Y in this case and to get this Y there are so many inputs and processes like diet plan, protein intake daily, exercise schedule, punctuality, not to eat fast food,  Exercise start finish time, weight training. SO if he or she is having focus on only exercise schedule and timing of exercise and giving full time as per exercise plan and weight training but not having focus on inputs like not following diet plan, not proper protein as per daily requirement and having fast food, so after some time there will no proper result as desired because inputs are not taken properly although exercise schedule followed.
  2. Construction of a building: in this case our Y is the final building as per design given to the contractor. so here inputs are raw material like steel, cement, concrete, plywood, plaster, clay, paint, plastic, adobe, glass, fibre and much more, on the other hand there is a process to finish the building construction from starting of basement to final paint. in this example suppose we have focused heavily on inputs or raw materials but we are not focusing on the process how to construct the building, not seeing how the concrete is being made, how the raw material is used, how to proceed to finish the building. if we do not focus on process first impact that we will not get our desired building as per design within time except the wastage of time and raw material.
  3. Production of a Car: in this example our Y is final product of a designed car as per design  and standard. Inputs are raw material like tyre, Engine, body frame, plastic parts, head light, handle, dashboard, floor mat, doors, glass, power-train etc. to produce a car with all input raw material there is process defined at every section and department. each department has its own process to process production of car from welding of body frame to paint to final assembly of child parts. for example we do focus on input and its quality material used to produce a car but following poor performance processes and not following exact process so at the end after using good quality parts we will not be able to produce a good quality car as per designed standard.
  4. Farming:  it is growing of crops by people for food and raw material. in this case our Y is thew final crop which is used as either food or other raw materials like flowers, nursery plants manure etc. It is part of agriculture. in this case our inputs are seeds, pesticides, fertilizers, water. to get a better output for example 50 metric tons of wheat there is a process that should be followed. on what  time water to be given, what time plantation of seeds to be done, at what time pesticides and fertilizers to be used, crop rotation or we are cultivating same crop of wheat again and again . so even if we use good quality of all inputs like, seeds, fertilizers, water etc but do not follow exact process of giving water, plantation of seeds and time to give fertilizers we will not get desired output of 50 metric tons of wheat.


So from above examples, we can say that we have to focus on improvement of  both input and process. we cant not ignore anyone of them to get better output


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Y= f(x), from this mathematical expressions, we could understand the output of Y depends on functions and the input factors.

In six sigma context, Y is the desired outcome or results that you need from a process ,X- represents the inputs, I.e factors that need to create a desired outcome (Y) f is the function , the way of process carried out to transform all Xs into the outcome.

Say example;

Y = Instant Coffee

X = (Hot water, instant coffee powder, sugar, Milk, utensils, Man)

f = Process of coffee making


Instant coffee Y = f (Hot water, Instant coffee powder, Sugar, Milk, Man, Utensils)

To have a good coffee, we must ensure that the all Xs are in prescribed condition

If the input Xs are not meeting the requirements, obviously we shouldn’t get a good coffee. However, I don’t think all Xs inputs are equal importance, the vital few may have a stronger influence should have understood and manage them correctly to have a consistent and predictable results from the process

Simply, control the inputs to control the output.

Though the process carried out in controlled condition, there will be an uncertainty in the process. So we must consider the error factors in the process, and we have to make sure how well our controlled actions produce the desired or expected results.  

The other way round, though we provide all Xs as per the requirements, the person who makes the coffee is not knowing how to prepare the instant coffee, we won’t get a coffee as we desired.

Hence, hand-to-hand, the process and input variables have to be controlled to have a desired output, otherwise it will be a conventional output, but not as expected or as desired

The underlying message is, don't correct your process until you correct your input materials and don’t correct your input materials until you correct your process

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A thought provoking question which challenges conventinal wisdom. Best answer is provided by Prashanth Datta as he clearly highlights two situations where either the process or the inputs are below industry standard while the other helps achieve excellent results. 

Answers from Vastupal and Mathi are also good reads.

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