What is the formula in term of the cumulative standard norma

What is the formula in term of the cumulative standard normal function if the quality characteristic x has a 2.5 sigma shift for 6 sigma processes?To clarify the question: What is the defect ppm if there is a 2.5 sigma shift for a 6 sigma process? Please answer it in term of the cumulative normal function Pi.

What is the defect number in ppm for a 2.5 sigma shift of a 6 sigma process? round up number to the nearest integer.

Solution

we could use -2.5 as our Z value and use it to find the probability

If you’re wondering about that negative sign, let me explain. Excel and most other calculators use the cumulative normal distribution to calculate values. That means they start from the left and work their way forward. If we entered =NORMSDIST(2.5), we would get 1-0.006210 as our answer. We could certainly work with that; it’s just not as convenient.

So, 0.006210 is a probability. To get this into PPM, we would multiply by a million.

That gives us 6209.665326 PPM