## What do we mean by garage’s width = 12σ and car’s width = 6σ?

Amrendra Roy

Right now we are not in a position of going into the details of the standard normal distribution hence, for the time being let’s assume that my manufacturing process is stabilized, which is represented by a symmetrical curve shown below

The main characteristic of this curve is that the 99.7% of the product would be between LCL & UCL or within ±3σ distance from the mean (μ). Only 0.3% or 3000ppm products would be beyond ±3σ or defective products. So width of the car is equivalent to the width of the process = UCL-LCL = voice of the process = VOP = 6σ = ±3σ.

Second point is that the curves never touches the x-axis à means that there will always be some probability of failure even if you move to infinity from the mean (probability can be negligible but will be there).

Now let’s overlap the above process curve with the customer’s specifications (=12σ = ±6σ) or the garage’s specifications.

We can see that there is a safety margin of 3σ on both side of the process control limits (LCL & UCL). In layman words, in order to produce a defective product, my process has to deviate by another 3σ, which has very remote possibility. Statistically ± (position of LSL & USL) from the mean would account for only ~3.4 ppm failure (don’t bother about the calculation right now, just understand the concept). For this has to happen, someone has to disturb the process deliberately. Compare this failure of 3.4 ppm at ±6σ level with 3000ppm at ±3σ level!

Even if the mean of the process deviate by ±1.5σ, there is enough margin of safety and it will not impact the quality and in regular production, this deviation of ±1.5σ is quite common.

Car Parking & Six-Sigma

What’s the big deal, let’s rebuild the garage to fit the bigger car!

How the garage/car example and the six-sigma (6σ) process are related?

Now Let’s start talking about 6sigma

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