# MBA in 2 minutes | Lesson 27: I didn't know there is a stats to 6 Sigma

We will be solving practical challenges through MBA concepts. No theory only applications!

Coming from non-core operations background, one of my wow moments in my Ops Class at ISB was when I realized there is so much math and deep statistical meaning to the 6 sigma process. Before that I always six sigma is all about theoretical lean operations building.

With this exciting context, let's directly jump to the lesson of today.

__Step 1: Context__

In both service and product manufacturing industries, the customer is the king.

The customer preferences center around the quality of the product and timely delivery.

Higher accuracy in both of these advances customer satisfaction and eventually revenue. Interventions such as ensuring fewer defects, robustness to external variability, and quicker detection of causes can go a long way in building a 6 sigma process.

__Step 2: What is Six Sigma__

To understand the essence of six sigma, we need a hypothesis test each time we observe a sample:

Do we have sufficient evidence to conclude that the sample belongs to the “in‐control” population or not?

If you are new to my blog, I'd advise you to run through previous lessons on __hypothesis testing etc__.

Often (balancing Type I and Type II errors)

– Upper Control Limit : UCL = Mean + 3 x σXbar

– Lower Control Limit : LCL = Mean – 3 x σXbar

where σ means "how many sigmas is the difference between the mean and the closest specification limit.

The picture below will aid in building intuition to the entire equation. Because of variance in processes, our mean may shift.

But if the mean doesn't move beyond your UCL and LCL, then it is a six sigma (almost error less) process (3σ left+ 3σ right)

__Step 3: Quick Case__

Now, let's quickly solve a short problem to ensure we understand the applicability of the entire concept.

At Flyrock tires, the customer specification for the thickness of rubber sheets being produced is __400 +- 10 thousandth of an inch__. These rubber sheets are extruded through an extruder. After analyzing the output from the extruder, they determined the output thickness to be normally distributed with a mean of __400 and standard deviation of 4__. The output is produced at the rate of __10,000 sheets per hour__. Flyrock has implemented SPC and tests a __sample of 10 sheets __every hour to check if the extrusion process is in control. They use 3‐sigma control limits.

**What are the appropriate control limits that Flyrock should use?**

A. Sample size (n) = 10

B. Mean of sample average = 400, Std. deviation of sample average = 4/sqrt(10) = 1.265

C. UCL = 400 + 3 x 1.265 = 403.795

D. LCL = 400 – 3 x 1.265 = 396.205

To move on advanced question, we can also compute the probability that there will be rubber sheets with a thickness beyond the UCL and LCL. The formulae for the same is

__(1-NORMDIST(UCL, mean, std. dev)+ NORMDIST(LCL, mean,std. dev)__

where NORMDIST is the excel/jmp function.

I can understand if this lesson was technical and dry.

But trust me, businesses today are fighting to save 1 second, improve quality by an inch because of the intense competition. As we are now discussing Term 3 of the MBA curriculum, we are building upon the foundational initial lessons I had shared. These advanced lessons will come really handy during your interview discussions and even during your job as you climb up the ladder.

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If you are new here and wish to now learn these concepts in a better manner via the video format on youtube, you can click __here____.__