Calc defects from Sigma and Opportunity values
Six Sigma – iSixSigma › Forums › Old Forums › General › Calc defects from Sigma and Opportunity values
 This topic has 14 replies, 4 voices, and was last updated 17 years, 1 month ago by Anton Javier.

AuthorPosts

August 25, 2005 at 9:06 pm #40497
Bob PtacekParticipant@BobPtacek Include @BobPtacek in your post and this person will
be notified via email.Is there a method to calculate the defects when one has only the Sigma Value and the Opportinities. I know I can back into the defects knowing opportunities and the DPMO results, but can’t seem to locate how to do it with sigma. Would appreciate and be thankful for any help or guidance.
0August 25, 2005 at 9:10 pm #125843You can look up the sigma value in a Ztable, found in any stats book. This will give you the proportion defective. You may need to adjust for shift, as a regular Ztable will show 4.5ppm @ 4.5 sigma.
0August 25, 2005 at 9:11 pm #125844Correction… 3.4ppm @ 4.5 sigma (Zvalue). Typing too fast….
0August 25, 2005 at 9:14 pm #125845
Bob PtacekParticipant@BobPtacek Include @BobPtacek in your post and this person will
be notified via email.I’m trying to do this in Excel so that I can enter any given Sigma value with the known Opportunities to calculate the defects that madeup the sigma.
0August 26, 2005 at 5:04 am #125859Hey Bob,
If I understand you correctly you have the Sigma value, and the number of opportunities as the inputs–and, you would like to get to an estimate of perhaps average defect level or possibly yield as the output. Hopefully I got your question right…
I believe MrIAM got you moving in the right direction. But, there is a small adjustment to realize in these estimate of expected defect level. First, let’s start from the beginning with an example. Suppose you have a process with a Sigma Quality Level of 3.0, and it has say 10 process steps–where we will establish each process step as an opportunity. In a Normal ztable for the zvalue of 3.0 you receive a probability of 0.0013. Now we know the accepted defect rate for an SQL of 3.0 is about 67,000 dpmo. So, we need to make an adjustment.
First, given an SQL of 3.0 subtract 1.5 from this value, as suggested by MrIAM. Next, go to the ztable for z=1.5 to obtain a probability of 0.0668 or 0.0668 defects per opportunity. Next, your process has 10 opportunities–one for each process step. Given 0.0668 defects per opportunity * 10 opportunities provides 0.668 defects per unit on average. Finally, you can estimate the average process throughput yield by:Ytp(avg) = exp(DPUavg)
for our example, we would calculate:Ytp(avg) = exp(0.668) = 0.513 or 51.3%
Another way to do this is to recognize that that you have 0.0668 defects per opportunity, or:Ytpo(avg) = exp(0.0668) = 0.935 or 93.5%
The Rolled Throughput Yield across 10 process steps with each step providing a normalized yield of 93.5% is:Yrt = Ytpo*exp(# opportunities) = 0.935*exp(10) = 0.513 or 51.3%
Average defect rate = 1 – Yrt = (1 – 0.513)*100 = 48.7%
Just a minor point. All of these estimates rely heavily on a Normal approximation to the Poisson distribution. There is a lot riding on the distributional requirements for these estimates. You usually require fairly large sample sizes to achieve any reasonable confidence in these estimates. The upshot is–use these estimates as rough approximations, and not firm knowns. Doing so will place you on much better ground when the actual process numbers don’t match the estimates.
Hope this helps.
Ken0August 26, 2005 at 2:39 pm #125884
Bob PtacekParticipant@BobPtacek Include @BobPtacek in your post and this person will
be notified via email.Ken,
thank you so very much for the great detailed explanation. As you and Mr IAM suggested, the ztable look up is the starting point and that has been my obstacle. I know if I could get the probability, I will be able to back into the defect. It’s the ztable look up that had me stymied. Without it, I had hoped there was a formula. Is there such an animal as an electronic version of a ztable?
Again, thank you so much for your explanation, it helped.
Bob
0August 26, 2005 at 2:46 pm #125887I believe you can use the NormInv formula in excel. I have not used it in quite some time but I’m sure this is a way to go from Z to % in excel and I think NormInv is it. Check it out…..
0August 26, 2005 at 2:47 pm #125888Bob,
Glad to help. I believe that I have an Excel conversion table that goes one better. It lists the associated DPMOs per each Sigma Quality Level to the nearest tenth of an SQL. I will try to find it on my PC, and if you’re interested in it please provide an email address for me to send it to.
Cheers,
Ken0August 26, 2005 at 2:50 pm #125889
Bob PtacekParticipant@BobPtacek Include @BobPtacek in your post and this person will
be notified via email.Thank you for that suggestion. Since Excel’s NORMSINV is used to calculate the Sigma from defects and opportunities, I had hoped that the NORMINV might be able to the backward trip. But I tried some examples and just never could make it happen. Maybe I was interpreting the values to use incorrectly. I’ll go back and give that another shot.
Thank you for your help
Bob0August 26, 2005 at 2:54 pm #125890Sorry, it’s NORMSDIST that you want :)
0August 26, 2005 at 2:56 pm #125891
Bob PtacekParticipant@BobPtacek Include @BobPtacek in your post and this person will
be notified via email.Ken,
that would be absolutly fantastic.If you find it you can send it to either of these addresses.
[email protected] or [email protected]
Thanks again,
Bob0August 26, 2005 at 2:59 pm #125892
Bob PtacekParticipant@BobPtacek Include @BobPtacek in your post and this person will
be notified via email.Had not tried that one. I’ll check it out. Between you and Ken, I am confident that I will be able to do what I want..
Thank you so much for your help.
Bob0August 26, 2005 at 3:06 pm #125895NORMSDIST works.
I entered 0, (zero) and then did the Normsdist excel function and got .5, as the result. So, that makes sense. A Zvalue of Zero = .5 or 50%, half of the distribution. That is what your trying to do I believe.0August 26, 2005 at 7:03 pm #125925
Bob PtacekParticipant@BobPtacek Include @BobPtacek in your post and this person will
be notified via email.Had not tried that one. I’ll check it out. Between you and Ken, I am confident that I will be able to do what I want..
Thank you so much for your help.
Bob0September 8, 2005 at 5:21 am #126490
Anton JavierParticipant@AntonJavier Include @AntonJavier in your post and this person will
be notified via email.Bob, I will share my sigma calculator with you. Please send your email at [email protected]
This calculator should fix your problem.
Anton Javier
0 
AuthorPosts
The forum ‘General’ is closed to new topics and replies.