Calculation of Sigma Level of Defects for a Manufacturing Process

Hello everyone the forum is great! Anyway I am new here and excuse me for my bad English in advance. I am trying to calculate the sigma level of defects for a manufacturing process for an essay.
The numbers are based on a real factory that produces let's say something like 100 different product lines. I don't have any ASL/LSL. I checked the overall defect rate distribution is normal, I didn't check per line because they are so many of them ;p)

First, I weighted the lines according to what proportion contribute for the general production (like Pareto). The final, overall weighted value of defects was something like 20%.

Then, I tried to convert it to DPMO. It's a compound product and since 2 main controls are made in order to considered good (optical/dimensional), I used 2 at the fraction. However, my DPMO number is something like 15.000, and thus shows my process much better than it really is.

So is it better to rely on the dpu=20% instead? Is there a way to convert it into a sigma level?

Any advice or any comment on the procedure I followed is more than welcome and needed.

Re: Calculation of Sigma Level

tsider said:

Hello everyone the forum is great! Anyway i am new here and excuse me for my bad english in advance. I am trying to calculate the sigma level of defects for a manufacturing process for an essay.
The numbers are based on a real factory that produces lets say something like 100 different product lines.i dont have any ASL/LSL.I checked the overall defect rate distribution is normal,i didnt check per line cause they are so much of them;p)

First i weighted the lines according to what proportion contribute for the general production (like pareto).The final,overall weighted value of defects was something like 20%

Then, i tried to convert it to DPMO.Its a compound product and since 2 main controls are made in order to considered good (optical/dimensional),i used 2 at the fraction.However,my DPMO number is something like 15.000,and thus,shows my process much better than it really is.

So its better to rely on the dpu=20% instead?Is there a way to convert it into a sigma level?

Any advice or any comment on the procedure i followed is more than welcome and needed.

Click to expand...

Welcome to the Cove

Weekends are bit slow and hence the response may be delayed.

Welcome to the Cove!

Ajit is right - it is slow right now. But until we can provide a specific response (I'm sorry to say it's out of my area of expertise) you can still review related threads that are listed at the bottom of this screen.

Also, can you perhaps attach a spreadsheet with some data you are trying to analyze?

Pending further response, here are some related threads which you may want to go through.

Thank you all!

Sadly i cannot provide real numbers.It is based on my thesis with a real factory so..
I saw the threads,very helpful indeed but sorry to say i am not quite sure yet.

Some extra info:1 production line, 100 product lines of the same product (ceramic tile), 2 quality controls

According to month,the overall distribution of th defect rate (and not categorised to product lines) is a normal distr,N=11 months, Mean=0,1209, (12,09% defect rate) StDev=0,03296.So i was thinking the reason the DPMO is so inacurate is maybe cause it fails the assumption of 1,5 sigma sift and it means like the number of the average defects due to dimensional control and optical control respectively when 1000000 of products are being produced?

I could also acquire the data of how much of them (not according to product lines,overall) are defects because of optical and how much because of dimensional. Maybe i ll calculate a DPMO=E.G 30%DPMO(optical) + 70%DPMO (dimensional) ?Divided by one respectively.Or in the optical by more?(Cause they are more opportunities of failing optically like little holes,black spots etc?).But the number wouldnt be the same as the overall DPMO?

I think that the Dpu already shows me an real estimation of an existing problem (a process tha produces a lot of defectives),so i could just use that for reference after any improvement has been made. But how could i explain to my professors that the Dpmo is so different?Is there a chance to use it accurately and calculate a sigma level?

Sorry i have to present my thesis next week and i am so devastated.Any help is welcome.Thank u all.

Because the OP is preparing a thesis, I moved this thread to the "Student Research Questions" Forum.

Fellow Moderators, feel free to move again if needed.

Stijloor, Forum Moderator.

Hey its funny talking alone but since i got some progress its better for the potential answerer to review this new post.

My RTY=(sadly my final yield from the process after the quality controls),i mean tis not an 100% Rolled Through out Yield (more like a final yield) is lets say 0,87.

From Schmid and Launsby 1997 :
Sigma level = 0.8406 +sqrt(29.37-2.221 * ln (ppm)) (1.1)
I ve noticed that Breyfogle and others consider DPMO=ppm in this function.

Since it is an one line process, and a compound product (ceramic tile) and it has two controls one after the other but u cannot determine if it could be defective by both of them i just know that from the, e.g 100000 square meters, (thats the unit), 8000 where considered defective from optical defect and 5000 from dimensional defect.Therefore, since i cannot discriminate the interaction between optical and dimensional in defects, i consider, since it is a compound product also,oportunity=1 and,thus, DPU=DPO.

With RTY=0,87 and the formula RTY=e^(DPU) (Breyfogle et al 2003)(1.2) i found DPU,i consider it as i told before equal to DPO and putting it in (1.1) i have sigma level= 2.6 something.

1.Is it right?I realize that is just messing with numbers with no contribution to the project whatsover, since the whole of the factory does not use sigma metric in its other procedures etc. But since my thesis is in Six Sigma i want to present it,but still i am not sure.

2.I saw the distribution of defects by month (N=11) has StDev of 0,03296 and mean=12 (which is also really in accordance with the RTY).If my above calculations are right, 2,6 sigma level- 1,5 drift= my StDev should be 1,1??Something is going wrong here?

3.Thirdly, (so as not to write in this post again).As Crucial X the specific weight (im not sure of the terminology) of the pulp in the mills has been determined.I wannat calculate the Cp/Pp.When a mill (4 of them) is changing (is not a fixed time) the company measures the specific weight.So i have the last 100 measurements, of course by several mills.However, i dont think it can be considered a speciment cause these are the whole numbers of the process .The mills are random and not specific by product.However, my subgroup is one or 4?(equal to the mills).If it is considered 4 i dont have equal ''speciments'' by subgroup.Some mills are used more,so i have more specific weights from them.

My data werent normal (a sign of smthng goin wrong?).With Box-Cot transformation it wasnt still.With distribution Minitab analysis i used Johnson transformation and they became.With subgroup 1,Cp and Pp werent good at all.So i think something has to be done in the Improve phase.But, i noticed that Pp # Cp (which in normal distr i think thay have to be equal) and even Cp>Pp (which cannot be possible).So may i have to use subgroups?Something else??

HUGE post i am tottaly 6s sorry,but plz help me graduate!

I'm having trouble following some of what you are doing.

Some commentary you might find helpful (or not at this point)

The formula you cite in 1. is correct IF you are dealing with defects not defectives AND the defects are all independent of each other within a unit. Remember that defects are individual things that can be out of spec and you can have multiple defects on a single unit of product.

The 1.5 sigma shift you reference is a myth and NOT helpful to your analysis - this is why you got an odd result that didn't match your data.

Data in the real world are rarely Normal. There is nothing inherently wrong with a process that is non-Normal.

Thank u very much, your comment is more than appreciated and really sorry for tha puzzle i wrote above.
1.So i cannot convert RTY to ppm and then use the formula?I also found a table that calculates sigma straight from yield in Breyfogle. However, i wanted to use sigma level just to compare the factory with the infamous Motorola's 6s.

2.N=11 is not a fairly poor sample for the estimation of Normal?(It is the average defect rate per month)When i put the data of daily defectives (not categorised by product also)
they are far from normal.

3.Is that safe to use Capability indices when my process in not inherently normal?And after i transform it to normal shouldnt Pp almost equal to Cp and even Cp<Pp?(based on the way that stdv is calculated in the respective types).Maybe i should consider subgroup=4 and not 1,but the data from the real procedure (its not a speciment is all that we can know) and the mills are randomly used and have supposedly equal performance (equal potential of producing defects)

Excuse me for so many questions but i am going to present my thesis without sufficient statistical help from my supervisor and a statistician in the examination board.Thus i really need to know ,so not to make a fool out of myself and i dont have anyone who can answer me.Thank u a lot.