Six Sigma Calculations - 1.5 Shift vs Non-Shift Calculation

Hello,
New member to this forum. I'm trying to understand the formula to calculate the UNSHIFTED PPM level. I've found various tables that give the UNSHIFTED PPM levels, such as the table below. But I'm unable to find the formula to give these results. When I use the normal functions in Excel (i.e. NORMSDIST, NORMSINV), it's giving me PPM levels that are exactly 1/2 of the values in the table below. For example:

• At Sigma Level = 3, the Excel formula gives me PPM level 1,350, but the table below gives me 2,699.
• At Sigma Level = 4, the Excel formula gives me PPM Level 32, but the table below gives me 63.
• .... using Excel formula always gives PPM Levels which are exactly 1/2 of the values in the table below.

Note that I've found various tables on the web, and it's giving the same UNSHIFTED PPM as the table below. So I'm trying understand the formula/calculation that gives the UNSHIFTED PPM in the tables.

I noticed that your values are half the tables values. Are you taking both sides of the distribution into consideration?

Several cautions about this entire concept:

1. Processes may approximate a normal distribution, are rarely truly normal. Therefore, these PPM numbers are simply crude approximations for illustrative purposes. Do not expect your results to closely match them.
2. The 1.5 sigma shift concept is speculative and highly divisive among quality professionals. If your process is under SPC or under automated controllers, you should never see this much shift. Even if not under SPC, some processes will shift less than 1.5 sigma, and some may shift more. I view this concept as illustrative of the worst case.

Thanks for the reply. Not really trying to question/understand the argument of the 1.5 Shift concept. Just trying to understand the formula/calculation so I can speak to it if questioned.

I believe the calculations/formula is just one-side, since the Sigma Level is always stated as one-side (i.e. 6 Sigma Level in table actually means +/- 6 Sigma). So I believe the way I'm using the Excel formula to calculate PPM is correct.

Using the Excel formulas, I can validate the PPMs between Shifted and Unshifted data. For example, a 6 Sigma shifted level is equivalent to a 4.5 Sigma UN-shifted level; the PPM level is 3.4. However, the table gives says for a 6 Sigma UN-shifted, the PPM level is 0.002. Doesn't make sense.

The tables are correct - if any mythological math can be said to be correct. The myth goes like this: a 6 sigma process has a ppm value of 3.4 instead of .002 because it will miraculously shift 1.5 Sigma in one direction without cause.

Instead of trying to understand the math, if asked why don't you say the shift is unsupported by any data and is a useless theoretical myth that adds absolutely no insight into any real process or problem.

what would you say if someone asked you how flat the earth was or how many yeti can fit into your back yard?

Rather than relying on the Tables from websites, I'm trying to create a simple Excel file to capture the unshifted PPM. But my formula is giving me 1/2 the value compared to the table. I just use the Excel NORMSDIST function to capture data, but can't seem to replicate the values in tables. For example:

Your formula should be as follows:
Upper tail = 1,000,000 * (1-NORM.S.DIST(1,TRUE)) = 158,655
Lower tail = 1,000,000 * (NORM.S.DIST(-1, TRUE) = 158,655
Upper + Lower tails = 158,655 + 158,655 = 317,311

Ok thanks. That's interesting, for the 1.5 Shift PPM calculation, it's 1-tail, but when you calculate for the Unshifted, it's 2-tail. Not sure why the 1.5 Shift calculation is 1-tail but the Unshifted calculation is 2-tail.

They made a bad assumption that all defects would be on the side of the shift. This is true if you have fairly good capability, but not always true when the variation is wide compared to the spec limits.

I still don’t understand why you care? It’s a thoroughly debunked thing. It has no value except as a mathematical puzzle that has no relationship to the physical world.

The actual 1.5 sigma shift came from a gross interpretation of a paper on tolerance stackups of flat discs and trying to generalize the isolated specific case of a ‘shift’ in the disks. (Much like Purdue Pharma perpetuated teh lie that only 1% of opioid users would get addicted. They misinterpreted adn misapplied a 5 sentence letter to the editor of a medical journal based on a very small, specific and controlled group of hospitalized patients. Like the 1.5 sigma shift the lie lived on despite being debunked many, many, many times.

I'm with Bev - why are you worried with this calculation? It's based on