Six Sigma Breakthrough Equation

What is the Six Sigma Breakthrough Equation Y=f (X) + e

To live a good life, it is important to understand the Six Sigma breakthrough equation Y=f(x) + e(epsilon). This simple equation can be called with many names. The ‘breakthrough equation’, the ‘Six Sigma breakthrough equation’, the ‘inputs-outputs equation’, the ‘inputs transformation equation’ and ‘superstitions buster equation’ and perhaps few more.

Let’s first understand what this equation is all about.

Y = The outcome/output

X= The inputs/ ingredients/ contributing factors

F = The role of transformation function or mixing function or processing function

E = It is usually denoted by Greek symbol epsilon. It denotes the presence of error, or the presence of uncertainly or the presence of known or unknown variation.

After having understood the basic symbols, now let’s proceed further. Based on this equation, everything in life whether it is your personal life, job life or business life, every result or outcome is determined by some inputs (Xs) whether there is one input or there are hundred inputs.

Secondly, how you mix those inputs, the conditions and the processes involved which may help to determine the desired output.

Thirdly, after having done the processing part, still there may be some variation in the results, even if you do the same the things same way. Why? It may be based on some known reasons as well as some unknown reasons. 

Now let’s see one easy example first for Six Sigma Breakthrough Equation Y=f(x) + e

When you barbecue the chicken pieces in your home grill, you put all the required ingredients which may include chicken cut to the right sizes, salt, spices, lemon, a bit of oil, and then you start the fire and put the marinated chicken pieces on the grill, and start monitoring, moving and turning around the chicken pieces. After having done that when you taste, do you think every piece is barbered exactly like other?  Most probably not. Why is this variation from piece to piece? This will be explained with the symbol of ‘e’ which denotes the epsilon (the room of error or uncertainty). This is life and we can’t avoid the presence of error in anything what we do, including our own personalities. But as you may know, that is just one last part of the equation in order to take into the role of life and laws of nature. 

However, the main Six Sigma breakthrough equation Y=f(x) … first requires to be developed and implemented to the best of it. It should be properly elaborated. For that, first develop a clarity of what you actually desire or want, the output or the outcome. Do you need more revenue, do you need less expenses, do you need more customer satisfaction, do you need fast delivery times, do you need a beautiful office, do you need high staff morale, do you need cooperative bosses, do you need fast cars, do you need better home, do you need a better wife or husband, do you need a better relationship, do you need better clothes, do you need more children, do you need well behaved children, do you need more friends, do you need more relaxing time… What is that you really need (Y). First get clear on it, one step at a time. 

Suppose, you picked up having a beautiful office as your Y (outcome), Ok now let’s move to the selecting the Xs (inputs / contributing factors), which may include the selection of place, the selection of furniture, stationary, interior décor, (colors. music, scents), the space, the layout. Now when you mix all the ingredients then you have to transform them into a pleasing office ambiance with the help of the ‘f’ (function), which may be about how to do the layout, how to apply the creative skills to help you feel better in the workplace.

After you have done your ‘Y’, your Xs and your ‘f’, now what can the ‘e’ epsilon do, the room for error. Suppose, the interior decorator, who you thought should develop the creative workplace making it comfortable and efficient, actually turned out to be slightly different, which you only realized after a week sitting in the office, because you noticed the rays of sun are getting into your eyes during the noon time.

Despite determining the Y and Xs, still there was variation in the final result. And now you later wanted to change the position of your desk. This error may not be due to the inputs but due to some change of tastes, habits or assumptions. Such errors or uncertainties can be seen anywhere in every situation or process, and may be difficult to control (it is called common-cause variation).

Six Sigma Breakthrough Equation Y=f(x) + e in Business Life

When you are doing something for your company, the six sigma philology says, you cannot leave it to guess work, intuition or gut feeling, that is why you have to use this equation to your advantage.

Let’s suppose, you want to improve the customer satisfaction (Y), now you will have to identify all your Xs which are contributing to your ‘Y’ outcome; the product price, product packing, the place of purchase, the customer’s services, the time it takes to shop and the ambiance of the store. 

To arrive at the final outcome, in this case, it may be a long journey, but definitely this is something of great value to the company and what it desires to achieve at the end. So therefore, now the company should start measuring and analyzing all the Xs in this case and should be able to determine the root causes which are not retarding to achieve the ‘Y’, and finding the ones that will help you achieve the ‘Y’. 

How you will do that is by using the Six Sigma Methodology of DMAIC (Define the problem, Measure the problem, Analyze the root causes of the problem, Improve or remove the problem, and then Control the new status quo so that it should not revert back after some time)

Six Sigma Breakthrough Equation Y=f(x) + e in Personal Life

In my opinion, many a time, personal life apparently appears simple than the business, but in reality, it is far more complex than the business problems.

Let’s assume, in your personal life your ‘Y’ is to earn USD 100 K in one year. What will be your ‘Xs’ for this desired outcome (Y). It may be finding the job of USD 100k, identifying the business with ROI which can provide you USD 100k, investment in stock market, Job + freelance or more. As long as you are concerned about the outcome (Y), you will keep on identifying the ‘Xs’ (inputs) which should help you arrive at that outcome. But as it is said, even you come up with all the right plan. Is there any guarantee that you will start getting USD 100 K every year? Here again comes the role of ‘e’ the epsilon, the room for error. It may also happen that you can earn USD 50k, 70K or even 110K. or probably not at all. (role of variation in the results)

What factors can be contributing to this ‘e’. Let’s see…

The first simple reason being, you may be lazy to exert 12 hours a day, since you have internal habitual variation, you may work for some days, but after a few days there may be a burnout. Secondly, you may die (special cause) and may not earn at all. Thirdly, profit rates by the banks can get reduced making you earn far less.

Now you get that idea about the Six Sigma breakthrough equation Y=f(x) +e

They say, ‘knowledge is power’, and the discipline with persistence is the route to success. In case, if the discipline with persistence is not in your habit or DNA, then you will have to develop it to achieve the desired outcome ‘Y’.

As per the definition of persistence, when it all seems futile, and no results seem to be coming up, but you still maintain your belief and keep moving on. That is the discipline and the will power and the blind belief in the things that you are doing.

The Six Sigma breakthrough equation Y=f(x) +e may prove to be a game changer for you in your personal and business life. It can also help you to completely overhaul your business as well as your whole life in order to get the desired outcomes (Y). 

You can adopt this Six Sigma mindset that provides you with a simple Six Sigma breakthrough equation to start your improvement projects with the desired results.

If you are interested, you can also read another relevant article What Does Y=f(x) Mean? How to Use This Powerful Six Sigma Formula